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is a sequence of length one and its only coordinate, its first coordinate, is p. Only sequences of the same length can be equal, and they are equal precisely when both of their respective coordinates are equal, as defined next: Equality of ordered sets. <x1, . . . , xi, . . . , xn> = iff xj = yj, for each j, 1 ≤ j ≤ n.
DEFINITION 7.
Thus, for example, is not equal to , for even though they have the same members, some of the coordinates of one have members different from the corresponding coordinates of the other. Specifically, while the first coordinates of each of the triples are equal, the second coordinates are not, and neither are the third coordinates. The operation that yields from the sets A1 through An the set of all sequences of length n where the ith coordinate is a member of Ai is called the generalized Cartesian product. It is defined as follows: DEFINITION 8. Generalized Cartesian product. Let X1 through Xn be sets. Then, <x1, . . . , xn> ∈ X1 × . . . × Xn iff, for each i (where 1 ≤ i ≤ n), xi ∈ Xi.
Logically equivalent to this definition is this equality: X1 × . . . × Xn = {<x1, . . . , xn > : xi ∈ Xi where 1 ≤ i ≤ n}
8.4 Families of sets A set can have sets as members. A set all of whose members are sets is often said to be a family of sets. Thus, for example, {{1,2}, {2,3}, {1,3}} is a set all of whose members are sets. It is, then, a family of sets. In this section, we discuss an operation that creates a family of sets from a set and two operations that create a set from a family of sets.
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8.4.1 The power set operation There is an operation that operates on a set to yield a family of sets. It is known as the power set operation, and it is denoted by the expression Pow. In particular, the power set operation collects into one set all the subsets of a given set. Consider, for example, the set {1,2}. Its power set is the set of all its subsets, namely, {∅, {1},{2},{1,2}} DEFINITION 9.
The power set operation. X ∈ Pow(Y) iff X ⊆ Y.
This definition of the power set operation is in the form of a biconditional. Logically equivalent to this definition is the following equality: Pow(Y) = {X : X ⊆ Y}.
Here are two more examples of applications of the power set operation. Pow({1}) = {∅, {1}} Pow({1,2,3}) = {∅, {1}, {2}, {3}, {1,2}, {2,3}, {1,3}, {1,2,3}}
The first two facts identify permanent members of any power set: the set from which the power set is formed and the empty set: FACTS ABOUT THE POWER SET
(1) Every set is a member of its power set. (2) ∅ ∈ Pow(X). (3) |Pow(X)| = 2|X|
8.4.2 Generalized union and generalized intersection In this section, we define two operations that are generalizations of the binary operations of union and intersection, introduced earlier. Those binary operations take pairs of sets and yield a set. Their generalizations take not just a pair of sets but a family of sets and yield a set. We begin with generalized union: DEFINITION 10.
Generalized union. x ∈ ∪Z iff, for some Y ∈ Z, x ∈> Y.
This definition leads to the following equality: ∪Z = {x: x ∈ Y, for some Y ∈ Z} DEFINITION 11.
Generalized intersection. x ∈ ∩Z iff, for each Y ∈ Z, x ∈ Y.
This definition leads to the following equality: ∩Z = {x: x ∈ Y, for each Y ∈ Z }
To see how these operations apply, consider this family of sets: A = {{1,2,3}, {2,3,4}, {3,4,5}} ∪A = {1,2,3,4,5} ∩A = {3}
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Now, in all cases where the cardinality of the family of sets is finite, generalized union and generalized intersection reduce to a finite iteration of the binary operations of union and intersection, respectively. In other words, if A = {A1, . . . ,An}, then ∪A = A1 ∪ . . . ∪ An. ∩A = A1 ∩ . . . ∩ An.
8.5 Relations and functions A relation is something that connects a number of entities. It is important to distinguish a relation from the instances that instantiate it. While this distinction may sound a bit arcane, it is not. After all, one easily distinguishes the color red from the instances that instantiate it. That is, one easily distinguishes the color red, on the one hand, from red fire trucks, red pencils, red hats, and so forth, on the other. The distinction between a relation and the instances that instantiate it is parallel. That is, the relation of being a father is distinct from any given pair comprising a father and the person of whom he is the father. A relation that has pairs as instances is a binary relation. One that has triples as instances is a ternary relation. And one that has quadruples as instances is a quaternary relation. In general, a relation that has n-tuples as instances is an n-ary relation. An example of a binary relation is the relation of being a brother. This relation pairs a human male with any one of his siblings. Commonsense relations involving more than just pairs are unusual. From a mathematical point of view, a relation comprises a set of sequences, and an instance of the relation is any one of these sequences. A binary relation comprises a set of ordered pairs, and each of its instances is an ordered pair in this set. A ternary relation comprises a set of triples, and each of its instances is a triplet in this set. We confine our attention to binary relations and their instances: that is, sets of ordered pairs and their members. We just said that, from a mathematical point of view, a binary relation is a set of ordered pairs. Sometimes it is convenient to view a binary relation as comprising three sets: the set of candidates for the first coordinates of a set of ordered pairs, the set of candidates for the second coordinates of the same set of ordered pairs, and the set of ordered pairs itself. Consider, for example, the relation of being a city in a country. On the one hand, one can view it as comprising nothing more than a list of ordered pairs of city and the country in which the city is located. On the other hand, one might think of it as comprising three lists: the list of all cities, the list of all countries, and the list that pairs each city with the country in which it is located. We use the term graph for the view that treats relations merely as a set of n-tuples (i.e., ordered sets of length n) and reserve the term relation for the view that treats relations as n-tuples together with the potential candidates for each coordinate of any n-tuple of the relation. In particular, we shall call a binary relation any specification comprising the set of things that may be related, the set of things that may be related to, and the actual pairing. In addition, we shall call a binary relation’s set of ordered pairs its graph, the set of things that may serve as first coordinates in the graph its domain, and the set of things that may serve as second coordinates in the graph its codomain. Finally, we shall see that functions are just special binary relations. 8.5.1 Binary graphs Let us first consider binary graphs. As stated, a binary graph is simply a set of ordered pairs. There are two reasons a set of ordered pairs is called a graph. First, in elementary algebra, a graph, or figure, depicted on a plane with Cartesian coordinates, itself corresponds to a set of ordered pairs—namely, the pairs of coordinates corresponding to each point in the graph or
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figure. Second, it is natural, then, to call a set of ordered pairs a graph. In graph theory, a graph comprises a set of nodes, depicted as points, and a set of edges, depicted as lines, where every edge connects a pair of nodes, depicted by every line, corresponding to an edge, linking the points corresponding to the nodes connected by the edge. A special kind of graph is called a directed graph. It is just like a graph, except that its edges are directed. Such edges are known as directed edges or arcs and are depicted by arrows. As we shall see, the graphs of graph theory are especially useful in displaying important properties of binary graphs. Now suppose we have a set of ordered pairs. Each member of any ordered pair can be viewed as a node, and hence depicted by a point, and each ordered pair can be viewed as an arc, and hence depicted by an arrow. The point corresponding to the ordered pair’s first coordinate is at the butt of the arrow, while the point corresponding to the very same ordered pair’s second coordinate is at the tip of the arrow. An example will help make this clearer. Consider the following set of ordered pairs: {, , , , , }
This set of ordered pairs can be depicted as the directed graph in Figure 8.6. Binary graphs can also be viewed as what, in graph theory, is known as a bipartite directed graph. A bipartite directed graph is a kind of directed graph in which the points can be partitioned into two groups such that one group has nothing but points that coincide with the nocks of the graph’s arrows, while the other group has nothing but points that coincide with the tips of the graph’s arrows. Usually, such a graph is depicted as two vertical columns of points, with arrows (directed edges or arcs) connecting some or all of the points in the left column with all or some of the points in the right column. One uses a bipartite directed graph to view a binary graph as follows: One makes two columns of nodes. The nodes in the first column correspond with the elements occurring in the first coordinates of the members of the binary graph, while the nodes in the second column correspond with the elements occurring in the second coordinates of the members of the binary graph. The arrows of the bipartite graph correspond with members of the binary graph. When a binary graph is viewed as a bipartite directed graph, one observes that from every point in the left-hand column emanates some arrow and into every point in the right-hand column terminates some arrow. The binary graph stated above is depicted in Figure 8.7 with a bipartite directed graph. 8.5.2 Binary relations Recall that a binary graph is a set of ordered pairs and that a binary relation is any specification comprising the set of things that may be related, the set of things that may be related to, and the actual pairing. Here is the formal definition of a binary relation:
FIGURE
8.6 Directed graph of ordered pairs
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FIGURE
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8.7 Bipartite directed graph
Binary relation. Let R be <X, Y, G>. R is a binary relation iff X and Y are sets and G ⊆ X × Y.
DEFINITION 12.
Suppose that one has two sets A and B. How many binary relations are there from A to B? The answer is: there are as many binary relations from A to B as there are distinct sets of ordered pairs whose first coordinate is a member of A and whose second coordinate is a member of B. Thus, the number of binary relations from A to B is 2|A × B|, or 2|A| × |B|. Two special relations among the set of all possible relations from A to B are the one whose graph is A × B and the one whose graph is the empty set. The former relation is known as the universal relation from A to B, and the latter is known as the empty relation or the null relation from A to B. Binary relations can be depicted by either of these two kinds of diagrams used to depict binary graphs: namely, by diagrams for directed graphs and by diagrams for bipartite directed graphs. Next we discuss how each kind of diagram is used to depict a binary relation. Recall that a directed graph comprises a set of nodes, depicted as points, and a set of directed edges, depicted as arrows, where every directed edge connects a pair of nodes. Notice that while it is required that every directed edge connect a pair of nodes, it is not required that every node be connected to some node. In contrast, a node of a binary graph may not be connected with any node. As an example, consider the binary relation where A = {1,2,3,4,6}, B = {2,3,5}, G = {, , , , , }
Its directed graph diagram is as in Figure 8.8
FIGURE
8.8 Directed graph of
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What distinguishes a binary graph from a binary relation is the fact that a relation’s domain and codomain may be proper supersets of its graph’s domain and range, respectively. For this reason, the diagrams of bipartite directed graphs are suited for depicting binary relations better than the diagrams of mere directed graphs. In such diagrams, the points in the left-hand column stand for the elements in the relation’s domain, the points in the right-hand column stand for the elements in the relation’s codomain, and the elements linked by arrows stand for the pairs of elements in the relation’s graph. Under these conventions, the binary relation given above yields the bipartite directed graph diagram in Figure 8.9. The last thing we wish to draw the reader’s attention to in this initial discussion of binary relations is the following notational convention. We shall sometimes write “aRb” instead of the more cumbersome ∈ GR. Left totality, right totality, left monogamy, and right monogamy are four important properties that binary relations may have. Each property has a role in determining functions and various kinds of functions, which is the subject of the next section. A binary relation is left total precisely when each member of its domain bears the relation to some member of its codomain: DEFINITION 13. Left totality. Let R = <X,Y,G> be a binary relation. R is left total iff, for each x ∈ X, there is a y ∈ Y, such that xRy.
The relation R1 is left total, R1 = where A = {a,b,c}, B = {2,4,6,8}, G = {, , , , }
while the relation R2 is not: R2 = where C = {d,e,f}, D = {1,3,5,7}, H = {, , , }
Seen in terms of a diagram for a bipartite directed graph, a left total relation has at least one arrow emanating from each point in its left-hand column. R1 satisfies this characterization, as one can see from an inspection of its bipartite directed graph diagram below; R2 does not, since no arrow emanates from e.
FIGURE
8.9 Bipartite directed graph of
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8.10 R1 is left total; R2 is not left total relation.
A binary relation is right total precisely when each member of its codomain has the relation borne to it by some member of its domain: DEFINITION 14. Right totality. Let R = <X,Y,G> be a binary relation. R is right total iff, for each y ∈ Y, there is a x ∈ X, such that xRy.
The relation R1, given above, is right total, but the relation R2 is not. Characterizations fully parallel to those given for left totality apply here. Looking at the bipartite directed graph diagram for R2, one sees that there is one element in its codomain into which no arrow terminates. Hence, R2 is not right total. Looking at the diagram for R1, however, one sees that each element in its codomain has at least one arrow terminating into it. For that reason, R1 is right total. In general, a binary relation is right total just in case its bipartite directed graph diagram has the following property: each node in the codomain has at least one arrow terminating into it. In the examples given, the very same relation is both left total and right total. This is a coincidence. Consider S1, which is just like R1, except that c is not related to 8. S1 is right total but not left total. Moreover, consider S2, which is just like R2, except that e is related to 5. S2 is left total but not right total (Figure 8.11). A binary relation is left monogamous precisely when no member of its domain bears the relation to more than one member of its codomain. Neither R1 nor R2 above is left monogamous, since, on the one hand, aR12 and aR16, and, on the other hand, fR25 and fR27. The relation T1 is left monogamous, however: T1 = where A = {a,b,c}, D = {1,3,5,7}, H = {, , }
Notice that, in the bipartite directed graph diagram of T1, Figure 8.12, at most one arrow emanates from any point in its left-hand column. This is a defining characteristic of left monogamous relations.
FIGURE
8.11 S1 is right total, but not left total; S2 is left total, but not right total.
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FIGURE
8.12 T1 is left monogamous.
Left monogamy2. Let R = <X,Y,G> be a binary relation. R is left monogamous iff, for each x ∈ X and each y, z ∈ Y, if xRy and xRz, then y = z.
DEFINITION 15.
Paired with the notion of left monogamy is the notion of right monogamy. A binary relation is right monogamous precisely when no member of its codomain has the relation borne to it by more than one member of its domain: DEFINITION 16. Right monogamy. Let R = <X,Y,G> be a binary relation. R is right monogamous iff, for each x, z ∈ X and for each y ∈ Y, if xRy and zRy, then x = z.
None of the relations R1, R2, and T1, is right monogamous. T1, for example, is not right monogamous, since both bT17 and cT17. However, T2 is right monogamous: T2 = where C = {d,e,f}, B = {2,4,6,8}, J = {, , }
In the bipartite directed graph of a right monogamous binary relation, at most one arrow terminates into any point in its right-hand column. This is illustrated in Figure 8.13. 8.5.3
Function
In high school algebra, everyone studies functions. Such functions are typically rather complex, hiding their rather simple nature. Functions involve three things: a domain, codomain, and a graph. The domain is a set of entities—entities of any sort, though in high school algebra, it is usually the set of real numbers. The codomain is also a set of entities—again, entities of any sort, though in high school algebra, it is usually the set of real numbers. To understand the graph of a function, imagine the domain and the codomain to have all of their elements exhaustively listed in their own respective lists, each list comprising a column of names. The graph of the function, then, is a pairing of members on the first list with members of the second list represented by an arrow going from each member on the first list to exactly one member on the second list. In other words, a function is a binary relation that is left total and left monogamous.
FIGURE
8.13 T2 is right monogamous.
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To see better what is involved, consider R and S: R is a function, while S is not. Observe that R comprises two lists, the list on the left being the domain and the list on the right being the codomain. Further, exactly one arrow connects each member of the domain with some member of the codomain. S fails to be a function for two reasons: first, there is no arrow connecting e to any member of the codomain; second, both d and f have more than one arrow connecting them to members of the codomain (Figure 8.14). Since a function is a special kind of binary relation, the terminology and notation that apply to binary relations also apply to functions. However, since the mathematics of functions preceded the mathematics of binary relations, much of the mathematics of functions has notation and terminology peculiar to it. Thus, it is customary to denote a function, not as f = <X,Y,G>,
but as f : X → Y,
specifying its graph separately. The graph’s specification is not in the usual notation for a set of ordered pairsbut in the form of a vertical, irredundant list of pairs, where a butted arrow () between the elements of each pair replaces the angle brackets that would otherwise enclose them. For example, the following functional relation, ,
whose graph can be expressed by the bipartite graph diagram in Figure 8.15, is displayed as follows: f : {1,2,3,4} → {a,b,c} where 1 a 2a 3c 4b
This way of displaying a function’s graph is in a form similar to that of a bipartite graph, except here, all arrows are parallel, and some members of the codomain may not appear, whereas in a proper bipartite graph, all arrows need not be parallel, and not only must each member from the domain appear exactly once, but also each member from the codomain must appear exactly once. Thus, functions with finite graphs may be displayed in at least two forms: in the form of a bipartite graph and in the form of a vertical list. It might be helpful at this point to rehearse how the defining properties of a function, namely left totality and left monogamy, are reflected in these displays. In the bipartite graph display, each element in the left-hand column is connected
FIGURE
8.14 Bipartite directed graph of R and bipartite directed graph of S.
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FIGURE
8.15 Directed graph of functional relation Gf
by an arrow to exactly one element in the right-hand column: it is connected by at least one arrow, to satisfy the condition of left totality, and it is connected by at most one arrow, to satisfy the condition of left monogamy. In the vertical list display, each member of the domain appears exactly once: it appears at least once, to satisfy the condition of left totality, and it appears at most once, to satisfy the condition of left monogamy. For most mathematical applications, the domain and codomain of a function are infinite, and so the function’s graph cannot be enumerated. In such cases, it is customary to write down a rule from which any ordered pair in the function’s graph can be calculated. I shall call such a rule a rule of association. For example, the function, part of whose graph is set out below, f : Z+ → Z– where 1 –2 2 –4 3 –6
can be precisely specified in any of several ways: f : Z+ → Z– where x –2x; f : Z+ → Z– where x y such that –2x = y; f : Z+ → Z– where f(x) = –2x.
Sometimes, the rule of association must be more complex: the domain of the function is partitioned and a distinct rule is given for the elements of each set in the partition. For example,
x x + 1 for x ∈ Conm2 and each member of Conm2 is a descendant of a subexpression of represents iff for some x ∈ V (i) x ∈ Um1; (ii) , ∈ Conm'1 and every member of Conm1 other than is a descendant of an occurrence of a subexpression of ; and (iii) . Here i and f' are as above, r is the index of the occurrence of g in the relevant occurrence of every bg, and d is determined as follows: let z be the sentence from which the relative clause has been formed through “wh-movement”; d is obtained by substituting x in z for the pronoun occurrence which was eliminated in the transition from z to g. Next we must give the definition of partial Discourse Representation Structures. DEFINITION 2. A partial DRS (Discourse Representation Structure) for D is a set k of possible DR’s for D such that whenever m is a member of K and Conm contains a conditional or universal sentence , then there is at most one pair of members m1 and m2 of K which represents .
We say that a member m' of K is immediately subordinate to m iff either (i) there is a conditional or universal sentence occurrence ∈ Conm such that m' is the first member of a pair which represents ; or (ii) m is itself the first member of such a pair and m' is the second member of that pair. And m' is subordinate to m iff there exists a finite chain of immediate subordinates connecting m and m'. The rules for constructing DRS’s will guarantee that they will always have a principal member. If the partial DRS K contains such a member, it will be denoted as m0 (K). Where K and K' are partial DRS’s, we say that K' extends K iff there is a one-to-one map f from K into K' such that for each m ∈ K f(m) extends m. For m ∈ K we denote as K≥ (m) the set consisting of m and all the U ” and “U≥K (m)” for members of K that are superordinate to m. We shall also write “UK” for “∪ meK m “UM c ∪{Um' : m' ∈ K and m' is superordinate to m}”.We say that a partial DRS K is complete iff (i) every member of K is maximal and (ii) whenever m is a member of K and Conm contains an occurrence of of a conditional or universal sentence K contains a pair which represents . We can now proceed to give a precise statement of the rules for DRS-construction. It is they, I must repeat here, that carry virtually all the empirical import of the theory. Their exact formulation is therefore of the greatest importance. Instead of trying to do justice to all relevant linguistic facts at once, I shall begin by stating the rules in a fairly simple manner. This will then serve as a basis for further exploration. For the fragment L0 there are five rules: one for proper names, one for indefinite descriptions, one for pronouns, one for conditionals, and one for universal terms. The effect of applying a rule to a particular condition in some member of a DRS is always an extension of that DRS. Only the rules for conditionals and universals lead to the introduction of new DR’s. But this does not mean that the effect of each of the other rules is confined to the particular DR m which contains the condition to which the rule is applied. Thus, for instance—and this is a point we have so far neglected in our examples—the application of the rule for proper names will always result in the introduction of a new discourse referent into the principal DR of the DRS, even if the condition to which the rule is being applied belongs itself to some other member of the structure. (I shall argue below that the rule for proper names must operate in this fashion.) Directly connected with this is the need to refer, in the statement of the rule for pronouns, not just to the universe of the DR
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m that contains the relevant condition, but also to the universes of certain other members of the DRS—in fact, as it turns out, of all those members which are superordinate to m. To state the first three rules, let us assume that K is a partial DRS, that m e K, that ∈ Conm is an unreduced member of m, and that is an occurrence of a term in which has maximal scope in : CR1. Suppose a is a proper name. We add to Um0(K) an element u from V\UK. Furthermore, we add to Conm0(K) the occurrence and to Conm the occurrence , where f' is the result of replacing the occurrence of a in with index i by u. CR2. Assume a is an indefinite singular term. (a) a is of the form a(n)b, where b is a common noun. We add to Um an element u from V\UK and to Conm the occurrences (where r is the index of the occurrence of b in ) and to Conm.
NB: I have given a deliberately “fudgey” formulation of this rule by inserting the word “suitable.” To state what, in any particular application of the rule, the set of suitable referents is, we would have to make explicit what the strategies are that speakers follow when they select the antecedents of anaphoric pronouns. In the applications we shall consider below, the restriction to “suitable” referents that I have built into CR3 will never play an overt role (although I will occasionally ignore, without comment, readings of the sampled sentences which would impose anaphoric links that are ruled out by various factors that enter into these strategies, such as, for example, the principle of gender agreement). Nonetheless, I have included “suitable” in the formulation of CR3, as a reminder that the rule is incomplete as it stands. To state the last two rules, let us assume that K and m are as above, that is an unreduced member of Conm and that f is either a universal sentence or a conditional: CR4. Assume is a conditional with antecedent and consequent . We add to K the member and . CR5. Assume is a universal sentence and the term with maximal scope is <every b,i>, with b a basic CN. We add, for some u ∈ V\UK , and where b e CN and g e RC, the DRs that must be added are and >>) 1 2 3
Example (8) decomposes each conceptual constituent into three basic feature complexes, one of which, the argument structure feature, allows for recursion of conceptual structure and hence an infinite class of possible concepts. In addition, observation (a) above—the fact that major syntactic phrases correspond to major conceptual constituents—can be formalized as a general correspondence rule of the form (9); and observation (f)—the basic correspondence of syntactic and conceptual argument structure— can be formalized as a general correspondence rule of the form (10). (XP stands for any major syntactic constituent; Xo stands for any lexical item that occurs with (optional) complements YP and ZP.) (9) (10)
XP corresponds to Entity Xo — < YP < ZP >> corresponds to
Entity F (< E ,< E ,< E >>) 1 2 3
where YP corresponds to E2, ZP corresponds to E3, and the subject (if there is one) corresponds to E1. The examples in (a)–(f) above show that the syntactic category and the value of the conceptual n–ary feature Thing/Event/Place . . . are irrelevant to the general form of these rules. The algebra of conceptual structure and its relation to syntax are best stated cross-categorially. 6.2 Organization of Semantic Fields A second cross-categorial property of conceptual structure forms a central concern of the “localistic” theory of Gruber 1965 and others. The basic insight of this theory is that the formalism for encoding concepts of spatial location and motion, suitably abstracted, can be generalized to many other semantic fields. The standard evidence for this claim is the fact that many verbs and prepositions appear in two or more semantic fields, forming intuitively related paradigms. Example (11) illustrates some basic cases: (11) a. Spatial location and motion i. The bird went from the ground to the tree. ii. The bird is in the tree. iii. Harry kept the bird in the cage. b. Possession i. The inheritance went to Philip. ii. The money is Philip’s. iii. Susan kept the money. c. Ascription of properties i. The light went/changed from green to red. Harry went from elated to depressed. ii. The light is red. Harry is depressed. iii. Sam kept the crowd happy.
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d. Scheduling of activities i. The meeting was changed from Tuesday to Monday. ii. The meeting is on Monday. iii. Let’s keep the trip on Saturday.
Each of these sets contains a verb go or change (connected with the prepositions from and/or to), the verb be, and the verb keep. The go sentences each express a change of some sort, and their respective terminal states are described by the corresponding be sentences. The keep sentences all denote the causation of a state that endures over a period of time. One has the sense, then, that this variety of uses is not accidental. On the other hand, the generalization of lexical items across semantic fields is by no means totally free. Each word is quite particular about what fields it appears in. For instance, go cannot be substituted for change in (11d), and change cannot be substituted for go in (11a). Travel occurs as a verb of change only in the spatial field; donate only in possessional; become only in ascriptional; and schedule only in scheduling. Gruber’s Thematic Relations Hypothesis, as adapted in Jackendoff (1972; 1976; 1983, ch. 10), accounts for the paradigms in (11) by claiming that they are each realizations of the basic conceptual paradigm given in (12). (The ontological category variable is notated as a subscript on the brackets; nothing except convenience hangs on this notational choice as opposed to that in (8).) (12) i. [Event GO ([
],
Path
FROM ([ TO ([
ii. [State BE ([ ], [ Place ])] iii. [Event STAY ([ ], [ Place ])]
])
)] ])
The paradigms are distinguished from one another by a semantic field feature that designates the field in which the Event or State is defined. In the works cited above, the field feature is notated as a subscript on the function: GOSpatial (or, more often, plain GO) vs. GOPass vs. GOIdent (using Gruber’s term Identificational) vs. GOTemp. Again, not much hangs on this particular notation. The point is that at this grain of analysis the four semantic fields have parallel conceptual structure. They differ only in what counts as an entity being in a Place. In the spatial field, a Thing is located spatially; in possessional, a Thing belongs to someone; in ascriptional, a Thing has a property; in scheduling, an Event is located in a time period. This notation captures the lexical parallelisms in (11) neatly: the different uses of the words go, change, be, keep, from, and to in (11) are distinguished only by the semantic field feature, despite the radically different sorts of real-world events and states they pick out. On the other hand, the exact values of the field feature that a particular verb or preposition may carry is a lexical fact that must be learned. Thus be and keep are unrestricted; go is marked for spatial, possessional, or ascriptional, and change is marked for ascriptional or scheduling. By contrast, travel, donate, become, and schedule are listed with only a single value of the field feature. Similarly, from and to are unrestricted, but across is only spatial and during is only temporal. Recall that in each paradigm in (11), the be sentence expresses the endstate of the go sentence. This can be captured in the informally stated inference rule (13), which is independent of semantic field. (13) At the termination of [EventGO ([X], [PathTO ([Y])])], it is the case that [StateBE ([X], [PlaceAT ([Y])])].
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A variety of such inference rules appear, in slightly different formalism, in Jackendoff 1976. In particular, it is shown that many so-called implicative properties of verbs follow from generalized forms of inference rules developed to account for verbs of spatial motion and location. Thus inferential properties such as “factive,” “implicative,” and “semi-factive” need not be stated as arbitrary meaning postulates. This is exactly the sort of explanatory power one wants from a theory of lexical decomposition into conceptual features. Each semantic field has its own particular inference patterns as well. For instance, in the spatial field, one fundamental principle stipulates that an object cannot be in two disjoint places at once. From this principle plus rule (13), it follows that an object that travels from one place to another is not still in its original position. But in the field of information transfer, this inference does not hold. If Bill transfers information to Harry, by (13) we can infer that Harry ends up having the information. But since information, unlike objects, can be in more than one place at a time, Bill still may have the information, too. Hence rule (13) generalizes from the spatial field to information transfer, but the principle of exclusive location does not. Thus inference rules as well as lexical entries benefit from a featural decomposition of concepts: the Thematic Relations Hypothesis and the use of the semantic field feature permit us to generalize just those aspects that are general, while retaining necessary distinctions.4 Notice how this treatment of the paradigms in (11) addresses the issues of learnability discussed in section 3. The claim is that the different concepts expressed by keep, for example, are not unrelated: they share the same functional structure and differ only in the semantic field variable. This being the case, it is easier for a child learning English to extend keep to a new field than to learn an entirely new word. In addition, the words that cross fields can serve as scaffolding upon which a child can organize new semantic fields of abstract character (for instance scheduling), in turn providing a framework for learning the words in that field that are peculiar to it. Thus the Thematic Relations Hypothesis, motivated by numerous paradigms like (11) in English and many other languages, forms an important component of a mentalistic theory of concepts and how humans can grasp them. 6.3
Aggregation and boundedness
The phenomena discussed so far in this section involve areas where the syntactic category system and the conceptual category system match up fairly well. In a way, the relation between the two systems serves as a partial explication of the categorial and functional properties of syntax: syntax presumably evolved as a means to express conceptual structure, so it is natural to expect that some of the structural properties of concepts would be mirrored in the organization of syntax. On the other hand, there are other aspects of conceptual structure that display a strong featural character but which are not expressed in so regular a fashion in syntax (at least in English). One such aspect (discussed in Vendler 1967a; Verkuyl 1972; Mourelatos 1981; Talmy 1978; Platzack 1979; Declerck 1979; Dowty 1979; Hinrichs 1985; and Bach 1986b, among others) can be illustrated by the examples in (14): (14)
For hours, {Until noon,} a. b. c. d. e. f. g.
Bill slept. the light flashed. [repetition only] lights flashed. *Bill ate the hot dog. Bill ate hot dogs. *Bill ate some hot dogs. Bill was eating the hot dog.
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h. i. j. k. l. m. n. o.
?Bill ran into the house. [repetition only] people ran into the house. ?some people ran into the house. [repetition only] Bill ran toward the house. Bill ran into houses. Bill ran into some houses. [repetition only] Bill ran down the road. *Bill ran 5 miles down the road. [ok only on reading where 5 miles down the road is where Bill was, not where 5 miles down the road is how far he got.]
The question raised by these examples is why prefixing for hours or until noon should have such effects: sometimes it leaves a sentence acceptable, sometimes it renders it ungrammatical, and sometimes it adds a sense of repetition. The essential insight is that for hours places a measure on an otherwise temporally unbounded process, and that until noon places a temporal boundary on an otherwise temporally unbounded process. Bill slept, for instance, inherently expresses an unbounded process, so it can be felicitously prefixed with these expressions. On the other hand, Bill ate the hot dog expresses a temporally bounded event, so it cannot be further measured or bounded. In turn, there are two ways in which a sentence can be interpreted as a temporally unbounded process. One is for the sentence to inherently express a temporally unbounded process, as is the case in (14a, c, e, g, i, k, l, n). We will return to these cases shortly. The other is for the sentence to be interpreted as an indefinite repetition of an inherently bounded process, as in (14b, h, j, m). (Bill ate the hot dog, like Bill died, is bounded but unrepeatable, so it cannot be interpreted in this fashion.) This sense of repetition has no syntactic reflex in English, though some languages such as Hungarian and Finnish have an iterative aspect that does express it. How should this sense of iteration be encoded in conceptual structure? It would appear most natural to conceive of it as an operator that maps a single Event into a repeated sequence of individual Events of the same type. Brief consideration suggests that in fact this operator has exactly the same semantic value as the plural marker, which maps individual Things into collections of Things of the same type. That is, this operator is not formulated specifically in terms of Events, but should be applicable in cross-categorial fashion to any conceptual entity that admits of individuation. The fact that this operator does not receive consistent expression across syntactic categories should not obscure the essential semantic generalization. Returning to the inherently unbounded cases, it has often been observed that the bounded/ unbounded (event/process, telic/atelic) distinction is strongly parallel to the count/mass distinction in NPs. An important criterion for the count/mass distinction has to do with the description of parts of an entity. For instance, a part of an apple (count) cannot itself be described as an apple; but any part of a body of water (mass) can itself be described as water (unless the part gets too small with respect to its molecular structure). This same criterion applies to the event/ process distinction: a part of John ate the sandwich (event) cannot itself be described as John ate the sandwich. By contrast, any part of John ran toward the house (process) can itself be described as John ran toward the house (unless the part gets smaller than a single stride). These similarities suggest that conceptual structure should encode this distinction cross-categorially too, so that the relevant inference rules do not care whether they are dealing with Things vs. Substances or Events vs. Processes. It has also been often observed that plurals behave in many respects like mass nouns, and that repeated events behave like processes. (Talmy 1978 suggests the term “medium” to encompass them both.) The difference is only that plural nouns and repeated events fix the “grain size” in terms of the singular individuals making up the unbounded medium, so that decomposition of
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the medium into parts is not as arbitrary as it is with substances and processes. Thus the structure of the desired feature system is organized as in (15): (15)
Entity Medium
singular Thing singular Event Substance
plural Things
Process
plural Events
That is, the features that distinguish Things from Events are orthogonal to the features differentiating individuals from media, and within media, homogeneous media from aggregates of individuals. The examples in (14) provide evidence that Paths also participate in the system shown in (15). For instance, to the house is a bounded Path; no parts of it except those including the terminus can be described as to the house. By contrast, toward the house and down the road are unbounded Paths, any part of which can also be described as toward the house or down the road. Into houses describes multiple bounded Paths, one per house. Thus the cross-categorial feature system in (15) extends to yet another major ontological category. Here is an example that illustrates some of the explanatory power achieved through the system of features in (15): the meaning of the word end. For a first approximation, an end is a zerodimensional boundary of an entity conceived of as one-dimensional. So, for the simplest case, the end of a line is a point. A beam is conceived of (as in Marr 1982) as a long axis elaborated by a cross-section. The end of a beam is a point bounding the long axis, elaborated by the same cross-section; this makes it two-dimensional. A table can be said to have an end just in case it can be seen as having a long axis (e.g., it is rectangular or oval but not square or circular); the end is then just the boundary of the long axis elaborated by the short axis. However, in the expected cross-categorial fashion, we can speak of the end of a week (a point bounding a onedimensional period of time) and the end of a talk (a zero-dimensional State bounding an Event that extends over time). However, there is an apparent difficulty in this account of end. If the end of a talk is a point in time, how can one felicitously say, “I am now giving the end of my talk” or “I am now finishing my talk”? The progressive aspect in these sentences implies the existence of a process taking place over time and therefore seems to attribute a temporal extent to the end. The answer is provided by looking at the treatment of the boundaries of Things. Consider what is meant by Bill cut off the end of the ribbon. Bill cannot have cut off just the geometrical boundary of the ribbon. Rather, the sense of this sentence shows that the notion of end permits an optional elaboration: the end may consist of a part of the object it bounds, extending from the actual boundary into the object some small distance e. There are other boundary words that obligatorily include this sort of elaboration. For instance, a crust is a two-dimensional boundary of a three-dimensional volume, elaborated by extending it some distance e into the volume. Border carries a stronger implication of such elaboration than does edge: consider that the border of the rug is liable to include a pattern in the body of the rug, while the edge of the rug is more liable to include only the binding. The claim, then, is that end includes such an elaboration as an optional part of its meaning. Going back to the case of Events, I can therefore felicitously say “I am giving the end of my talk” or “I am finishing my talk” if I am within the region that extends backward the permissible distance e from the actual cessation of speech. In other words, the featural machinery of
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dimensionality and boundaries, with which we characterize Things and the regions of space they occupy, extends over to Events as well. That’s why the word end is so natural in either context. The main difference in the systems is that Things have a maximum dimensionality of three, while Events have a maximum dimensionality of only one, so that certain distinctions in the Thing system are leveled out or unavailable in the Event system. Only in a theory of conceptual structure that permits this sort of cross-categorial generalization can even the existence of a word like end be explained, much less the peculiarities of its use in so many different contexts—and the fact that these peculiarities are evidently learnable. (This subsystem of conceptual structure will be treated in detail in Jackendoff 1991.) A general conclusion emerges from these three brief case studies. Beneath the surface complexity of natural language concepts lies a highly abstract formal algebraic system that lays out the major parameters of thought. The distinctions in this system are quite sharp and do not appear to be based on experience. Rather, I would claim, they are the machinery available to the human mind to channel the ways in which all experience can be mentally encoded—elements of the Universal Grammar for conceptual structure. Significantly, the primitives of this system cannot appear in isolation. Rather, they are like phonological features or the quarks of particle physics: they can only be observed in combination, built up into conceptual constituents, and their existence must be inferred from their effects on language and cognition as a whole. This result militates against Fodor’s Intentional Realism, in that one should not expect constant counterparts in reality for every aspect of the conceptual system. Roughly speaking, concepthood is a property of conceptual constituents, not conceptual features.
7 Where traditional features fail One of the abiding reasons for skepticism about feature-based semantics, even among those who believe in semantic decomposition, is that simple categorical features are clearly inadequate to the full task of conceptual description. These suspicions have been voiced since the earliest days of semantics in generative grammar (Bolinger 1965; Weinreich 1966) and continue to the present day (e.g., Lakoff 1987). This section will briefly mention three of the problems and the forms of enrichment proposed within Conceptual Semantics to deal with them. 7.1 Spatial structure of objects The first problem has to do with specifying the shapes of objects. For instance, consider the lexical entries for duck and goose. Both of these presumably carry features to the effect that they are animate, nonhuman, categories of Things, that they are types of birds, perhaps types of waterfowl. But what comes next?—how are they distinguished from one another? One possible factor, which clearly enters into learning the words in the first place, is how ducks and geese look, how they differ in appearance. But to encode this difference in binary features, say [± long neck], is patently ridiculous. Similarly, how is a chair to be distinguished from a stool? Do they differ in a feature [± has-a-back]? What sort of feature is this? It is surely not a primitive. But, if composite, how far down does one have to go to reach primitives—if one can at all? To put a ± sign and a pair of brackets around any old expression simply doesn’t make it into a legitimate conceptual feature. This problem is addressed in Jackendoff 1987 chapter 10, in the context of the connection between the linguistic and visual faculties. In order for an organism to accomplish visual identification and categorization, independent of language, there must be a form of visual representation that encodes geometric and topological properties of physical objects. The most plausible
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proposal I have encountered for such a representation is the 3D model structure of Marr 1982. In turn, this structure can be interfaced with conceptual structure via a set of correspondence rules, as suggested in example (1) above. This correspondence effects a translation of visual information into linguistic format, enabling us to talk about what we see. Marr’s approach is interesting because of the way it goes beyond a simple template theory of visual recognition. The 3D model is much more than a “statue in the head.” It is an articulated structure that encodes the decomposition of objects into parts, the geometric systems of spatial axes around which objects are organized, and the relations among the parts. Within this framework, it is possible to represent not just single objects in single positions, but ranges of sizes, ranges of angles of attachment of parts, and ranges of detail from coarse- to fine-grained. Thus it is admirably suited to encoding just those geometric aspects of an object’s appearance that are an embarrassment to any reasonable feature system. Jackendoff 1987 suggests, therefore, that the lexical entry for a physical object word includes a 3D model representation in addition to its phonological, syntactic, and conceptual structures. The 3D model, in fact, plays the role sometimes assigned to an “image of a stereotypical instance,” except that it is much more highly structured, along the lines suggested by Marr, and it includes parameters of variation among instances. The distinctions between duck and goose and between chair and stool, then, can appear in the 3D model instead of conceptual structure. We thereby eliminate the need for a plethora of objectionable conceptual features in favor of a geometric representation with entirely different primitives and principles of combination. It is shown that this natural division of labor is of benefit not only to the theory of the lexicon but also to the theory of visual categorization; I will not repeat the arguments here. I should add, however, that the use of the 3D model need not pertain just to objects and the nouns that denote them. Marr and Vaina 1982 propose a natural extension of the 3D model to encode action patterns such as throwing and saluting. This can be used to address a parallel problem in the verbal system: how is one to distinguish, say, running from jogging from loping, or throwing from tossing from lobbing? If the lexical entries for these verbs contain a 3D model representation of the action in question, no distinction at all need be made in conceptual structure. The first set of verbs will all simply be treated in conceptual structure as verbs of locomotion, the second set as verbs of propulsion. Thus again we are relieved of the need for otiose feature analyses of such fine-scale distinctions. 7.2 Focal values in a continuous domain A second area in which a simple feature analysis fails concerns domains with a continuous rather than a discrete range of values. Consider the domain expressed by temperature words (hot, warm, tepid, cool, cold, etc.) or the domain of color words. One cannot decompose hot or red exhaustively into discrete features that distinguish them from cold and yellow, respectively. The proper analysis seems to be that these words have a semantic field feature (Temperature or Color) that picks out a “cognitive space” consisting of a continuous range of values. In the case of Temperature, the space is essentially linear; in the case of Color, it is the familiar three-dimensional color solid (Miller and Johnson-Laird 1976). For a first approximation, each temperature or color word picks out a point in its space, which serves as a focal value for the word. According to this analysis, a percept is categorized in terms of its relative distance from available focal values. So, for example, a percept whose value in color space is close to focal red is easily categorized as red; a percept whose value lies midway between focal red and focal orange is categorized with less certainty and with more contextual dependence. Thus color categorization is a result of the interaction between the intrinsic structure of the color space—including physiologically determined salient values—and the number and position of color values for which the language has words (Berlin and Kay 1969).
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Refinements can be imagined in the structure of such spaces. For example, the field of temperature has both positive and negative directions, so one can ask either how hot? or how cold? By contrast, the field of size words has only a positive direction from the zero point, so that how big? asks a neutral question about size but how small? is intended in relation to some contextually understood small standard. I will not pursue such refinements here. The point is that the introduction of continuous “cognitive spaces” in which words pick out focal values is an important enrichment of the expressive power of conceptual structure beyond simple categorical feature systems. 7.3 Preference rule systems A different challenge to feature systems arises in the treatment of so-called cluster concepts. Consider the following examples: (16)
a. b. c. d.
Bill climbed (up) the mountain. Bill climbed down the mountain. The snake climbed (up) the tree. ?*The snake climbed down the tree.
Climbing appears to involve two independent conceptual conditions: (1) an individual is traveling upward; and (2) the individual is moving with characteristic effortful grasping motions, for which a convenient term is clambering. On the most likely interpretation of (16a), both these conditions are met. However, (16b) violates the first condition, and, since snakes can’t clamber, (16c) violates the second. If both conditions are violated, as in (16d), the action cannot at all be characterized as climbing. Thus neither of the two conditions is necessary, but either is sufficient. However, the meaning of the word climb is not just the disjunction of these two conditions. That would be in effect equivalent to saying that there are two unrelated senses of the word, one having to do with going up, and one having to do with clambering. If this were the correct analysis, we would have the intuition that (16a) is as ambiguous as Bill went down to the bank, which may refer equally to a river bank or a savings bank. But in fact we do not. Rather, (16a), which satisfies both conditions at once, is more “stereotypical” climbing. Actions that satisfy only one of the conditions, such as (16b, c), are somewhat more marginal but still perfectly legitimate instances of climbing. In other words, the two conditions combine in the meaning of a single lexical item climb, but not according to a standard Boolean conjunction or disjunction. Jackendoff 1983, chapter 8, calls a set of conditions combined in this way a preference rule system, and the conditions in the set preference rules or preference conditions.5 A similar paradigm can be displayed for the verb see: (17)
a. b. c. d.
Bill saw Harry. Bill saw a vision of dancing devils. Bill saw the tree, but he didn’t notice it at the time. *Bill saw a vision of dancing devils, but he didn’t notice it at the time.
The two preference conditions for x sees y are roughly that (1) x’s gaze makes contact with y, and (2) x has a visual experience of y. Stereotypical seeing—that is, veridical seeing—satisfies both these conditions: x makes visual contact with some object and thereby has a visual experience of it. Example (17b) violates condition (1), and (17c) violates condition (2), yet both felicitously use the word see. But if both are violated at once, as in (17d), the sentence is extremely odd. Again, we don’t want to say that there are two homonymous verbs see and hence that (17a) is ambiguous. The solution is to claim that these two conditions form a preference rule system,
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in which stereotypical seeing satisfies both conditions and less central cases satisfy only one— but either one.6 Similar phenomena arise in the lexical entries for nouns that denote functional categories: form and function often are combined in a preference rule system. For instance, a stereotypical chair has a stereotypical form (specified by a 3D model) and a standard function (roughly “portable thing for one person to sit on”). Objects with the proper function but the wrong form—say beanbag chairs—are more marginal instances of the category; and so are objects that have the right form but which cannot fulfill the function—say chairs made of newspaper or giant chairs. An object that violates both conditions, say a pile of crumpled newspaper, is by no stretch of imagination a chair. This is precisely the behavior we saw in climb and see. A further aspect of preference rule systems is that when one lacks information about the satisfaction of the condition, they are invariably assumed to be satisfied as default values. Thus, the reason (16a) and (17a) are interpreted as stereotypical climbing and seeing is that the sentences give no information to the contrary. It is only in the b and c sentences, which do give information to the contrary, that a condition is relinquished. The examples of preference rule systems given here have all involved only a pair of conditions. Systems with a larger number of conditions are likely to exist, but are harder to ferret out and articulate without detailed analysis. A preference rule system with only one condition degenerates to a standard default value. More generally, preference rule systems are capable of accounting for “family resemblance” categories such as Wittgenstein’s 1953 well-known example game, for Rosch’s 1978 “prototypes,” and for other cases in which systems of necessary and sufficient conditions have failed because all putative conditions have counterexamples (but not all at once). Still more broadly, Jackendoff 1983 shows that preference rule systems are an appropriate formalism for a vast range of psychological phenomena, from low-level visual and phonetic perception to high-level operations such as conscious decision-making. The formalism was in fact developed originally to deal with phenomena of musical cognition (Lerdahl and Jackendoff 1983) and was anticipated by the gestalt psychologists in their study of visual perception (Wertheimer 1923). There seems every reason, then, to believe that preference rule systems are a pervasive element of mental computation; we should therefore have no hesitation in adopting them as a legitimate element in a theory of I-concepts. (See Jackendoff 1983 chapters 7 and 8, for extended discussion of preference rule systems, including comparison with systems of necessary and sufficient conditions, prototype theory, and fuzzy set theory.) To sum up, this section has suggested three ways in which the decomposition of lexical concepts goes beyond simple categorical feature oppositions. These mechanisms conspire to make word meanings far richer than classical categories. Each of them creates a continuum between stereotypical and marginal instances, and each can create fuzziness or vagueness at category boundaries. Moreover, each of them can be motivated on more general cognitive grounds, so we are not multiplying artifices just to save the theory of lexical decomposition. And indeed, they appear collectively to go a long way toward making a suitably expressive theory of word meaning attainable.
8 Lexical composition versus meaning postulates Section 3 argued from the creativity of lexical concept formation to the position that lexical conceptual structures must be compositional, and that one has an innate “universal grammar of concepts” that enables one to construct new lexical concepts as needed. An important aspect of Fodor’s work on the Language of Thought Hypothesis has been to deny lexical compositionality. Not that Fodor has offered any alternative analysis of lexical concepts that deals with any of the
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problems discussed in the last two sections; indeed his arguments are almost exclusively negative. Nevertheless, for completeness I had better address his concerns. Fodor’s first set of arguments (Fodor 1970; Fodor, Garrett, Walker, and Parkes 1980) builds on the virtual impossibility of giving precise definitions for most words. If definitions are impossible, Fodor argues, there is no reason to believe that words have internal structure. But, in fact, all this observation shows is that if there are principles of lexical conceptual composition, they are not entirely identical with the principles of phrasal conceptual composition. If the principles are not identical, it will often be impossible to build up an expression of conceptual structure phrasally that completely duplicates a lexical concept. In particular, it appears that the nondiscrete elements discussed in section 7 play a role only in lexical semantics and never appear as a result of phrasal combination. Hence phrasal expansions of these aspects of lexical meaning cannot be constructed. Yet they are indubitably compositional. So this argument of Fodor’s does not go through; it is founded on a false assumption of complete uniformity of lexical and phrasal composition. The second set of arguments concerns processing. Fodor’s supposition is that if lexical concepts are composite, a more complex word ought to induce a greater processing load and/or take more time to access or process than a less complex word. Finding no experimental evidence for such effects (Fodor, Fodor, and Garrett 1975), Fodor concludes again that lexical items cannot have compositional structure.7 I see no reason to accept the premise of this argument. As is well known, the acquisition of motor concepts (such as playing a scale on the piano) speeds up performance over sequential performance of the constituent parts. Nevertheless, such motor concepts must still be compositional, since in the end the same complex motor patterns must be evoked. It stands to reason, then, that acquisition of a lexical concept might also speed up processing over a syntactically complex paraphrase, without in any way reducing conceptual complexity: a lexical item is “chunked,” whereas a phrasal equivalent is not. Because Fodor can find no system of lexical composition that satisfies his criteria of intentionality and of decomposition into necessary and sufficient conditions (both of which are abandoned in Conceptual Semantics), he decides that the enterprise is impossible and that lexical concepts must in fact be indissoluble monads. He recognizes two difficulties in this position having to do with inference and acquisition, and he offers answers. Let me take these up in turn. The first issue is how inference can be driven by lexical concepts with no internal structure. If one is dealing with inferences such as (P & Q) → P, as Fodor does in most of his discussion, there is little problem, assuming principles of standard logic. But for inferences that involve nonlogical lexical items, such as John forced Harry to leave → Harry left or Sue approached the house → Sue got closer to the house, there can be no general principles. Rather, each lexical item must be accompanied by its own specific meaning postulates that determine the entailments of sentences it occurs in. This is the solution Fodor advocates, though he does not propose how it is to be accomplished except perhaps in the most trivial of cases, such as Rover is a dog → Rover is an animal. The trouble with such an approach, even if it can succeed observationally, is that it denies the possibility of generalizing among the inferential properties of different lexical items. Each item is a world unto itself. Thus, for instance, consider the entailment relationship between the members of causative-noncausative pairs such as those in (18): (18)
a. b. c. d.
x killed y → y died x lifted y → y rose x gave z to y → y received z x persuaded y that P → y came to believe that P
In a meaning-postulate theory, these inferences are totally unrelated. Intuitively, though, they are all instances of a schema stated roughly as (19), where E is an Event:
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(19)
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x cause E to occur → E occur
In order to invoke a general schema like (19), the left-hand verbs in (18) must have meaning postulates like (20), in which the bracketed expressions are Events: (20)
a. b. c. d.
x kill y → x cause [y die] x lift y → x cause [y rise] x give z to y → x cause [y receive z] x persuade y that P → x cause [y come to believe that P]
But this is a notational variant of the analysis of causatives in a lexical decomposition theory: it claims that there is an element cause which (1) is mentioned in the analysis (here, the lexical meaning postulates) of many lexical items and (2) gives access to more general-purpose rules of inference. I suggest that, for fans of meaning postulates, lexical decomposition can be regarded systematically in this light: each element in a lexical decomposition can be regarded as that item’s access to more general-purpose rules of inference. The problem of lexical decomposition, then, is to find a vocabulary for decomposition that permits the linguistically significant generalizations of inference patterns to be captured formally in terms of schemas like (19) and rule (13) in section 6.2. (See Jackendoff 1976 for a range of such rules of inference.) I conclude therefore that a meaning postulate approach to inference either misses all generalizations across inferential properties of lexical items or else is essentially equivalent to a decomposition theory. Thus Fodor has correctly identified a problem for his approach but has proposed a nonsolution. The second difficulty Fodor sees for noncompositional lexical concepts is how one could possibly acquire them. In any computational theory, “learning” can consist only of creating novel combinations of primitives already innately available. This is one of the fundamental arguments of Fodor 1975, and one that I accept unconditionally. However, since for Fodor all lexical concepts are primitive, they cannot be learned as combinations of primitive vocabulary. It follows that all lexical concepts must be innate, including such exotica as telephone, spumoni, funicular, and soffit, a conclusion that strains credulity but which Fodor evidently embraces. Notice how Fodor’s position is different from saying that all lexical concepts must be within the innate expressive power of the grammar of conceptual structure, as advocated here. The difference is that in the present approach it is the potential of an infinite number of lexical concepts that is inherent in the grammar of conceptual structure—just as the potential for the syntactic structures of all human languages is inherent in Universal Grammar; lexical acquisition then requires constructing a particular lexical concept and associating it with a syntactic and phonological structure. Fodor notes, of course, that not every speaker has a phonological realization of every lexical concept. Since his notion of “realization” cannot include learning, he advocates that somehow the attachment of an innate lexical concept to a phonological structure is “triggered” by relevant experience, perhaps by analogy with the way parameter settings in syntax are said to be triggered. However, the analogy is less than convincing. The setting of syntactic parameters is determined within a highly articulated theory of syntactic structure, where there is a limited number of choices for the setting. Fodor’s proposed triggering of lexical concepts takes place in a domain where there is by hypothesis no relevant structure, and where the choices are grossly underdetermined. As far as I know, then, Fodor has offered no account of lexical concept realization other than a suggestive name. By contrast, real studies of language acquisition have benefited from decompositional theories of lexical concepts (e.g., Landau and Gleitman 1985; Pinker 1989), so the decomposition theory has empirical results on its side in this area as well.
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An especially unpleasant consequence of Fodor’s position is that, given the finiteness of the brain, there can be only a finite number of possible lexical concepts. This seems highly implausible, since one can coin new names for arbitrary new types of objects and actions (“This is a glarf; now watch me snarf it”), and we have no sense that we will someday run out of names for things. More pointedly, the number of potential category concepts is at least as large as the number of concepts for individuals (tokens), since for every individual X one can form a category of ‘things just like X’ and give it a monomorphemic name. It is hard to believe that nature has equipped us with an ability to recognize individual things in the world that is limited to a finite number. So far as I know, Fodor has not addressed this objection. (See Jackendoff 1983, sec. 5.2, for a stronger version of this argument.) From these considerations I condude that Fodor’s theory of lexical concepts cannot deal at all with the creativity of concept formation and with concept acquisition. Nor can any other theory that relies on monadic predicates linked by meaning postulates. By contrast, a compositional theory in principle offers solutions parallel to those for the creativity and acquisition of syntax.
9 Ending So what is a concept? I have shown here that for the purpose of understanding the mind, the apposite focus of inquiry is the notion of I-concept, a species of mental information structure. The program of Conceptual Semantics provides a theoretical realization of this notion that unifies it in many ways with a mentalistic theory of the language faculty and with the theories of perception, cognition, and learning. In particular, I have identified the notion of I-concept with the formal notion of conceptual constituent as developed in Conceptual Semantics. Furthermore, I have sketched a number of the major elements of the internal structure of concepts, showing how the approach accounts for various basic phenomena in the semantics of natural language, and how the approach meets various well-known objections to theories of lexical decomposition. In evaluating this approach, I think two things must be borne in mind. First, It does not address what are taken to be some of the standard hurdles for a theory of concepts—for example, Putnam’s Twin Earth problem. What must be asked with respect to such problems, though, is whether they are relevant at all to a theory of I-concepts, or whether they are germane only to the theory of E-concepts, as I believe is the case with the Twin Earth problem. If they are problems only for E-conceptual theory, they play no role in evaluating the present approach. Second, what I find appealing about the present approach is that it leads one into problems of richer and richer articulation: What are the ontological categories, and do they themselves have internal structure? What sorts of fundamental functions are there that create Events, States, Places, and Paths? How are various semantic fields alike in structure, and how do they diverge? How do nondiscrete features interact with each other in phrasal combination? What are the conceptual primitives underlying social cognition and “folk psychology”? How are conceptual systems learnable? And so forth. The fact that Conceptual Semantics begins to provide a formal vocabulary in which such questions can be couched suggests to me that, despite its being at odds with most of the recent philosophical tradition, it is a fruitful framework in which to conduct scientific inquiry. Notes Much of this paper is excerpted from my monograph Semantic Structures (1990). The title was selected with apologies to Warren McCulloch. I am grateful to Noam Chomsky, John Macnamara, and Jerry Fodor for comments on an earlier version of the paper. I do not, however, intend to imply by this that they endorse my approach; in particular, Fodor doesn’t believe a word of it. This research was supported in part by National Science Foundation Grant IST 84-20073 to Brandeis University.
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1. My interpretation here is confirmed by Dennett’s (1987, p. 288) revealing remarks on Fodor. 2. Generative Semantics used this observation as motivation for assimilating semantics to syntactic principles. The central program of the theory was to reduce all semantic compositionality to syntax. As more and more was discovered about semantic structure, it became clear that this program was not feasible. For at least some Generative Semanticists, the conclusion was that syntax should be abandoned altogether. As seen in example (1), the approach here is to retain syntax for its proper traditional purposes, but to invest semantic expressivity in a different component with appropriate expressive power: conceptual structure. 3. A point of notation: I will use angle brackets < > to enclose an optional constituent in a formal expression, the traditional parentheses being reserved to notate arguments of a function. 4. See Jackendoff (1983), Semantics and Cognition, sections 10.3–5 for further discussion of the Thematic Relations Hypothesis, in particular how it is different from a theory of “metaphor” à la Lakoff and Johnson 1980, and why it is justification for the approach of Conceptual Semantics as opposed to model-theoretic (E-)semantics. These sections also implicitly answer Dowty’s 1989 charge that the “metaphorical extension” of thematic relations to nonspatial fields is incoherent; basically, Dowty is looking for an explication of thematic relations based on E-semantics, and the generalization of thematic relations probably only makes sense in terms of I-semantics. 5. This analysis of climb was to my knowledge first proposed by Fillmore 1982; a formal treatment in terms of preference rules appears in Jackendoff 1985. 6. This analysis of see is adapted from Miller and Johnson-Laird 1976 and appears in more detail in Jackendoff 1983, chapter 8. 7. Actually, he finds evidence but disregards it: see Jackendoff 1983, pp. 125–127 and p. 256, note 8.
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17 GILLES FAUCONNIER
Mental Spaces, Language Modalities, and Conceptual Integration
Ioutn how working on matters related to language over the years, my greatest surprise has been to find little of the rich meanings we construct is explicitly contained in the forms of language itself. I had taken it for granted, at first, that languages were essentially coding systems for semantic relations, and that sentences, when appropriately associated with “natural” pragmatic specifications, would yield full meanings. Quite interestingly, this is not the way language works, nor is it the way that meaning is constructed. Rather, language, along with other aspects of expression and contextual framing, serves as a powerful means of prompting dynamic on-line constructions of meaning that go far beyond anything explicitly provided by the lexical and grammatical forms. This is not a matter of vagueness or ambiguity; it is in the very nature of our systems of thought. But grammar, in this scheme, is not to be disdained, for although it does not provide the landscape or the means of moving through it, it does show us the way. It guides our elaborate conceptual work with an admirable economy of overt indications, and an impressive reliability in moving us along conceptual paths. Mental spaces are part of this story. They organize the processes that take place behind the scenes as we think and talk. They proliferate in the unfolding of discourse, map onto each other in intricate ways, and provide abstract mental structure for shifting of anchoring, viewpoint, and focus, allowing us to direct our attention at any time onto very partial and simple structures, while maintaining an elaborate web of connections in working memory, and in long-term memory. We are not conscious of these processes. What we are conscious of, to a high degree, is language form on the one hand and experiencing “meaning” on the other. The effect is magical; as soon as we have form, we also have meaning, with no awareness of the intervening cognition. Introspectively, our experience in this regard is analogous to perception—we see an object because it is there, we understand a sentence instantly because it “has” that meaning. This remarkable and invisible efficiency of our meaning-assigning capacities drives our folk theories about language, which conflate form and meaning, just as folk theories about the world conflate existence and perception. Gilles Fauconnier (1998) Mental spaces, language modalities, and conceptual integration. In Michael Tomasello (ed.), The New Psychology of Language, 251–277. Reprinted by permission of Lawrence Erlbaum Publishers.
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The technical description of mental space phenomena is developed in a number of publications.1 I would like to attempt, in this chapter, to give a more informal view of the phenomena, their complexity, and their importance for psychologists interested in language and thought.
An example: Connectors and access paths Consider the simple statement Max thought the winner received $100. Perhaps the most obvious way to understand this is to assume that there was a contest, that prizes were given out, that one person won the contest and received a prize, and that Max, who was aware of all this, believed that prize to have been $100. But the statement by itself contains none of this. It just fits a plausible scenario, which our background knowledge makes available. We shall see that it also fits many other scenarios, some of which might be more appropriate in some contexts, and some of which are extremely implausible. What exactly then is the sentence telling us? An important part of what the language form is doing is prompting us to set up mental spaces, elements, and connections between them. The form provides key indications about the mental process in which we need to engage, but it is also deeply underspecified, which accounts for the multiplicity of scenarios that it may successfully fit. An interesting challenge for cognitive science at large is to understand how this underspecification can be resolved, how and why in certain situations certain mental space configurations are unconsciously chosen over others, and how the understander converges on specific appropriate scenarios and connection patterns. Mental spaces are small conceptual packets constructed as we think and talk, for purposes of local understanding and action. They are very partial assemblies containing elements, and structured by frames and cognitive models. They are interconnected and can be modified as thought and discourse unfold. In our example, two mental spaces are set up.2 One is the base space, B, the initial space with partial structure corresponding to what has already been introduced at that point in the discourse, or what may be introduced freely because it is pragmatically available in the situation. Another mental space, M, subordinate to this one will contain partial structure corresponding to ‘what Max thinks’. It is structured by the form “_____received $100” (the subordinate complement clause of thought). That form evokes a general frame <x receive y>, of which we may know a great number of more specific instances (receive money, a shock, a letter, guests, etc.). The expression Max thought is called a space builder, because it explicitly sets up the second mental space. Max and the winner are noun phrases and will provide access to elements in the spaces. This happens as follows: The noun phrase is a name or description that either fits some already established element in some space, or introduces a new element in some space. That element, in turn, may provide access to another element, through a cognitive connection (called a connector), as we shall illustrate and explain. Elements are conceived of as high-order mental entities (like nodes in Shastri’s models3). They may or may not themselves refer to objects in the world. In our example, the name Max accesses an element a in B, the base space (which intuitively might correspond to a real or fictive person called Max). The description the winner accesses an element w that we call a role, and is assumed to belong to a general frame of winning (w wins), and also to a more specific instance of that frame appropriate for the given context (winning a particular race, lottery, game, etc.). Roles can have values, and a role element can always access another element that is the value of that role. So we can say The winner will get $100, without pointing to any particular individual. This is the role interpretation. Or we can say The winner is bald, where being bald is a property of the individual who happened to win, not a condition for getting the prize. This is the value interpretation. Roles, then, are linked cognitively to their values by a role-value connector. The two mental spaces B and M are connected. There can be counterparts of elements of B in M. For example, if we said Max thinks he will win, intending the pronoun he to refer back to Max,
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then space B would contain a (for Max) and space M (Max thinks_______) would contain a counterpart a' of a. In space M, a relation equivalent to ‘a' wins’ would be satisfied, whereas the same relation would not necessarily be satisfied in the base B for a (the counterpart of a'). It is convenient to use mental space diagrams such as that shown in Fig. 17.1 to represent this evolving structure. An important principle defines a general procedure for accessing elements: ACCESS PRINCIPLE
If two elements a and a' are linked by a connector F [a' = F(a)] then element a' can be identified by naming, describing, or pointing to, its counterpart a.
This very general principle applies to all types of connectors across and within mental spaces (identity, analogy, metaphor, metonymy, role/value). A simple example of its application would be Max thinks Harry’s name is Joe. An element e associated with the name Harry is set up in the base. Its counterpart e' in M satisfies <e' named Joe>. And e' is accessed by means of its counterpart e in the base, using the name Harry associated with e. In other words, even though Harry is the appropriate name in one space, it can be used to access the corresponding element in another space, where another name is appropriate. Returning now to the original example, let’s see what the accessing possibilities might be. Suppose first that the access principle does not apply at all. Then the description the winner must identify a role w directly in space M. The structure added to M by the sentence is <w receive $100>. This is a pure role interpretation within space M. It does not access any corresponding value for that role. Therefore, the interpretation is that Max thought there was a contest, and that he thought it was a feature of that contest to award $100 to whoever wins. This accessing strategy is noncommittal as to whether the speaker also assumes there was such a contest, and as to whether an actual winner was ever selected, or as to whether Max thinks that a winner was selected. The sentence under this strategy would be appropriate in a variety of contexts. For example, minidiscourses like the following could include the above strategy: The Boston marathon will take place next week. Max thought the winner received $100, but it turns out there won’t be any prize money. My friends were under the impression that I was running a lottery in my garage. Max thought the winner received $100. But they were all wrong, there was no lottery.
a: NAME Max
a
Base space B a' WIN
a' Belief space M
FIGURE
17.1 Mental space diagram
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Suppose now that the accessing principle operates, but only within the subordinate space M, linking the role “winner” to a value of that role, b. As before, Max believes that there was a contest, and moreover that somebody won and he has additional beliefs about the person whom he assumes won. The structure in M is now . Although a likely default is that the $100 was prize money, this is no longer imposed. Max may believe that something else happened, causing the person who won to receive $100 independently. In plain English, this is illustrated most distinctly by a situation in which (according to the speaker) Max believes (perhaps incorrectly) that Susan won a race, and that she also independently got $100 for the used car that she was selling. In the two accessing possibilities just considered, a word (winner) simply evokes a script within a single space. But the access principle may also operate across spaces. The speaker may have a particular contest in mind, for which there is a role winner, set up as an element w in the base B. That role can have a value a (for example, Harry) with a counterpart a' in M. The access principle allows the winner to access w, and then its value a, and finally the counterpart of a, element a' in the subordinate space M. The structure set up in M is r +c ⋅ p({M' ∈ Lc: Mc ⊆ M'})} {u ∈ U: [Qi1(v1)]M,c,a g with (a > g) ∧ (b > g) among his theorems but reject the monotonicity principle a > b & g → a ⇒ g > b. To be sure, in the formalism this can be regarded as a property of the > rather than as a property of ∨, which retains it normal truth-condition, but there is nothing in the natural linguistic facts of the case to make us so regard its natural counterpart, and much about the behavior of or in other environments to make us suspect that such if-clause occurrences of or are more naturally regarded as conjunctive than as disjunctive, including uses, also ut nunc conjunctive, in then-clauses: (3)
I will fight you here in London, or, if you are afraid of that, I will go over to France, or to America, if that will suit you better. (Trollope 1972[1864], 748)
A second linguistic fact that ought to cast suspicion upon the doctrine of the centrality of truth-tabular disjunction as the ultimate explanation for this apparent diversity is historical in character. The modern English word or is a contraction of other, and seems to be the result of a coalescence of two distinct Old English words ‘oþer’ meaning ‘other’ or ‘second’ (as in ‘every other day’) and ‘oþþe’, which we usually translate as ‘or’, but which seems to have a range of uses similar to that of or in modern English. More generally, it seems to be a fact of linguistic evolution that all functional vocabulary is descended from vocabulary that was lexical in its earlier deployments. There is simply no reason why we should expect anything but diversity from evolutionary developments, and certainly no reason to suppose, in the case of or, that all the inherent tendencies of such an item as ‘other’ toward adverbialization, then adsentential uses (otherwise, alternatively), and metalinguistic ones such that of (4)
Sometimes, for a minute or two, he was inclined to think—or rather to say to himself, that Lucy was perhaps not worth the trouble which she threw in his way. (Trollope 1984[1861], 401)
would be absent from the development of its contracted form. One has almost to adopt a creationist’s picture of language development to suppose that there would be one use of or in English, or of any such connective vocabulary of any natural language, and that use the one corresponding to a truth-conditionally definable item of twentieth-century invention. That the truth-table specifically has been the instrument of seduction, there can be no doubt. There are no parallel claims in Grice’s writings or in those of his followers that in the case of
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since or so, both logical words to be sure, the illative uses are primary and their non-illative uses derivative or the illusory products of conversational conventions. No one denies that the since of “I’ve a vehicle since I’ve a car” is different from the since of “I’ve been driving since I woke up,” or that, moreover, if either is the more primitive, the nonlogical use is. No one denies that the so of “Fred is happy, so I’m happy” is different from the so of “Fred is happy; so Fred is a conscious being.” Parallel remarks are warranted by the varieties of uses of therefore, because, for, and so on. Their logical uses are derivative, in ways that are not immediately clear, from their nonlogical uses. A semantic theory of the former, like a semantic theory of the latter, will not depend on truth-conditions but will, rather, outline a practice; an explanatory theory will tell us how one practice gave rise to the other, and thereby what the later practice is. 2.2 The case of but It is unclear why Grice should have had such faith in the capacity of truth-tables to provide, with the help of a theory of implicatures, a sufficient semantic account of all uses of or in English, unless he was simply under the spell of a logico-philosophical habit of thinking of or rather than any other connective vocabulary of natural language as the reading of ∨. For if we set that habit aside, consider what parallel universal claims would be grounded by a similar fit. The sole premise vis-à-vis the vocabulary is that there is a use of it that truth-conditionally matches the table. The conclusion is that there are no uses of the vocabulary that do not. By this reasoning we could infer, for example, that the truth-table for ∨, if augmented by a theory of implicatures provides a sufficient semantic account of all of the uses of but in English, since the sentence “He avoids me but he wants to borrow money” on one reading has exactly the truth-conditions of the table. In fact, the case of but shows remarkable parallels with that of or since each has distinct uses that are approximately in the relationship of duality. The disjunctive use of but, like that of or is relatively rare; it more commonly found in conjunctive constructions, but as in the case of or, the whole story of its conjunctive uses cannot be given by a truth-tabular account. Even when we have acquired a conversationally sufficient understanding of it, we have great difficulty in explaining, even to the standards of folk-linguistic explanations what distinguishes the contexts in which it is the right connective to use. Dictionaries resort to providing approximate synonyms that are both varied and equally difficult. The Concise Oxford Dictionary entry adequately illustrates those of the rest: on the contrary, nevertheless, however, on the other hand, moreover, yet. Paedagogical grammars classify it as adversative. Even speakers of the most exquisitely cultivated sensitivity, such as H. W. Fowler have a little difficulty: “the mere presence of the opposed facts is not enough to justify but; the sentences must be so expressed that the total effect of one is opposed to that of the other.” That opposition is not the feature is evident from such examples as “He got here, but he got here late,” and any explanation must be such as to explain the conversational inequivalence of that sentence with “He got here late, but he got here.” In the end, the way to learn how to use but is to become immersed in the practice of its use. Of course, such an immersion does not afford us an articulable account of what we are doing when we use it. That task, I wish to claim, must fall to an explanatory theory of connectives. Indeed, any sufficient explanatory theory must be capable of explaining satisfactorily the distinctive coordinating role of but. It must also yield a unified account of all the uses of but, including all of those exemplified by the following: 1. 2. 3. 4.
But for your help I’d be dead. No one but his mother calls him that. It never rains but it pours. She wanted to come but she couldn’t.
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5. She was but fifteen years of age. 6. My, but that’s a handsome desk! Such a theory will also unify those Modern English uses of but with Old English butan (‘outside’), as it will unify uses of or with Old English oþer.
3 The shape of a biological theory 3.1 The representation of meaning If the physical significance of utterance or inscription lies in its effects, then an explanatory theory will make of a meaning an effect-type. For purposes of outline, it wouldn’t matter where in the physical world those effect-types were located, but as a convenient first approximation, they can be thought of as neurophysiological and, more specifically, as types of neurophysiological effects that are accessible to the processes that give rise to speech production and other overt intervention. That restriction at least accommodates the fact that speech and inscription sometimes give rise to speech- or inscription-production, but they need not do so. It also occasions future inconvenience, since any such theory must eventually settle on a theoretical language capable of typing such neurophysiological effects in such as way as to accommodate the facts of multiple neurophysiological realization. As will become evident, ultimately such a theory must be capable of distinguishing between two kinds of differences: (a) the differences between two realizations by two different recipients of a single syntactic structure, and (b) the differences between realizations by two different such recipients when one such realization agrees with that of the producer of the string and the other does not. That is to say, it must eventually provide the means of distinguishing the class of realizations that are correct from the class of those that are in error. Certainly at this stage, we can say little or nothing about the fine structure of that language or the details of the effects. Nor do I intend any guesses as to their nature in labeling such effects inferential effects, a label intended here simply to locate rather than to characterize the effects in question. The biological theory to be outlined is a theory at the level of population biology, and although even at this level it applies the language of cellular biology, it applies that language to the syntax of sentences, not to the human brain. Now the facts of linguistic transmission and change are such that the types of what I am labeling inferential effects must constitute species, where the notion of a species is that of a union of populations temporally ordered by a relation of engendering. The facts of change lend such species features that are also features of biological species. First, virtually every such species is a nonclassical set: every member of it has ancestors for which there is no principled way of deciding whether or not they are members. Second, every member of it has ancestors that are not members of it. Of course, the earliest linguistic species are temporally compressed, as are the earliest biological species, and artificially engineered species (those engendered by convention) require a different story from that of those naturally occurring, but for an explanatory theory of the connectives of English, the language of evolutionary biology is a good fit: if meanings are identified with inferential effect types, then meanings can be spoken of as evolving and historical changes in the range of uses of words as evolutionary changes. The utility of the identification must be judged when the theory has attempted some explanatory work. 3.2
The picture
Two points serve to give concreteness and a sense of scale to what must here be no more than a schematic account. They are not premises of an argument for the account, but they are part of the picture of things upon which the schema to some extent relies. The first remark is a global one:
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this representation, though it is constructed for detailed and temporally local explanation, is also promising as a theoretical framework for couching an account of how human or pre-human language began. It is a fair assumption that linguistic inferential effects have ancestors that are nonlinguistic inferential effects and even earlier ancestors that are noninferential effects, such as those consisting in a tendency to detect motion and visually track moving objects. It is plausible to suppose that the earliest steps toward language involved the opportunistic exploitation of such effects. At the other extreme of scale, the theory invites us to think of a syntactically structured string as a complex system—in fact, in much the way that a microbiologist might think of a polypeptide chain or a larger component of genetic material. The parallels, as they apply to connectives are striking, but again to be judged by the standards of explanatory usefulness rather than by competing disanalogies with the biological case. The parallels come to light only as they are revealed by the conjectured facts of linguistic evolution; they are conclusions, not premises. I register them beforehand only to give concreteness to the picture the account presents. Biological organisms come in a great variety of shapes and sizes, from viruses to whales. The cells of medium-sized organisms also vary over a wide range of sizes. But by and large, smaller organisms are not smaller because their cells are smaller, but because they have fewer of them, and if we descend to the level of the nuclei of cells, there is remarkably little difference in nuclear size between the smallest and the largest cells of medium-sized organisms and even between the smallest and the largest organisms. It is not a coincidence that nuclei are uniformly so small: it is an essential feature of a method of chemical synthesis that depends on the coincidence of weak molecular forces and therefore on the orientation and proximity of molecules. That is the first point. The second is that the ultimate molecular components of the products of this synthesis have their informational significance not in themselves but in the combinations into which they enter—and, ultimately, in the places of those combinations in the higher-order combinations that constitute the whole. DNA has a syntax. Finally, the uncorrected reading frame errors that give rise to biological mutations are essentially syntactic in character. The emerging linguistic parallels, which are only general in character, seem to be these: the smallest verbal components have their inferential significance only as they occur within sentences and are dependent for their inferential effects on a hierarchy of structural features of the sentence. Thus, for example, the or of “He is asleep or comatose” will be read disjunctively; the or of “He may be asleep or he may be comatose” will be read conjunctively. We do not write longer novels by writing longer sentences, but by writing more sentences within a relatively narrow range of lengths. There is some evidence that in conversation we set durational targets for the sentences we produce. There are limitations on our capacities to be reliably affected by complexities of syntax, and those limitations mainly enforce these durational restrictions. Our apprehension of syntactic structure is prosodically assisted. Thus, for example, we distinguish the two syntactic readings of “But for my son I’d stay and fight” by differences of lengthening, pitch contour, and stress. Prosodic control of syntax apprehension also enforces limitations of sentence length. Finally, mutations occur in the meanings of connective vocabulary through undetected and therefore uncorrected misapprehensions of syntax. 3.3
Compositionality
It will already have become evident from the account I am presenting that only some weakened version of the compositionality thesis will be true of natural languages. But some weak version will survive. On whatever account we give of meaning, the meaning of a sentence has something to do with the meanings of its component vocabulary together with its syntax, even if the connection between the two is a little murky. As I have already remarked, which meanings the elements of component vocabulary have must sometimes be gathered from an apprehension of syntax
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in the prosodic presentation. Consider the difference between “What is this thing called love?” and “What is this thing called, Love?” Sometimes, prosodic clues having been missed, the determining syntactic judgement must depend on the comparative plausibility of the alternative construals, as in “I’ll have breakfast only if we are short of food.” Again, I hope that I have already said enough to counter any such suggestion as that semantic problems can arise only for readings of notional vocabulary, that compositional problems arise for connective vocabulary, only through insufficiently marked syntax, that since the semantics is fixed, ambiguities must be ambiguities of scope. As we have seen, even that modest view cannot survive attention to human speech. We might read (5) as a disjunction: (5)
It will be useful or it will be harmful.
But we would not give a disjunctive reading to (6) except under very unusual contextual pressure, and then we would be at a loss how to take the significance of the disjunction: (6)
It could be useful or it could be harmful. (Gilbert 1976, 187)
In fact, there is something unrealistically hypothetical and itself ut nunc about the usual basis for claims of compositionality. Some such principle is claimed to be required to explain our capacity to produce novel constructions in speech production and understand them in the speech of others. This may be so, but the fact is that in the course of a day’s compositions, we neither produce nor process that many constructions—novel or otherwise. More important, such composition as does go on must, in fact, be a vehicle of meaning change. Else how, for example, did the word internecine come to have anything essentially to do with matters within a family, or specious anything essentially to do with spuriousness? That notional meanings undergo changes is hardly news, though the details of these changes probably deserve more philosophical study and interest than they naturally excite. Of greater significance for this study is the global fact about connective vocabulary: All the connective vocabulary of any natural language has descended from lexical vocabulary, in most cases, from the vocabulary of temporal, spatial, and other physical relationships. Thus, as we have remarked, the English or is a contraction of other, but descends from butan meaning ’outside’, if probably from a coalescence of Old English gif (if) itself a descendent from the language of doubt and the verb giefan (give). Much of the vocabulary retains, in modern English, residual nonlogical physical uses (since, then, therefore, yet, for, as); some such as or have evolved a distinct morphology that masks their provenance. These facts have philosophical significance beyond the trivial remarking of etymologies. If we think that every meaning is the meaning of something, then we will conclude from this that at least all naturally occurring logical meanings descend from nonlogical meanings. And if I may interject a further large-scale remark: we will also conclude that human intellectual capacities that reveal themselves in propositionally expressed reasoning have their roots in the natural nonlinguistic propensities of human and pre-human organisms, and we will have some concrete clues as to how the one might have given rise to the other. As a topic of study, the descent of connective vocabulary from its physical forbears might be called logicalization, in imitation of the related topic that linguists call grammaticalization, the process by which lexical vocabulary acquires functional uses (as the have and will auxiliaries in English tense structure; the -abo and -ibo endings of Latin past and future verbs, and so on.) Logicalization, in being confined to connective vocabulary, is narrower in scope than grammaticalization, but it is also more protracted as a temporal development, since for much of the vocabulary, connective meanings continue to multiply, even after logicalization. Moreover, these diversities are, on the face of things, sufficiently systematic that any theory of logicalization
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with pretensions to completeness had better provide the means of explaining them. Now there is sufficient justification for a study of logicalization in its showing us things about our languages that we did not know. The promise that if it gets matters approximately right, its theoretical framework might shed light on the origins of language ought to earn it passive tolerance. But it will have more immediate philosophical cash value also, for if a plausible theory of logicalization individuates multiple meanings of connectives in virtue of its assigning them distinct causal histories, then the theory is an advance on the Gricean theory that connectives have only one meaning, and that the apparent diversity is attributable to conversational implicatures. It will at any rate have provided an argument where Grice has provided none.
4 Evolutionary tendencies 4.1 Usative relations On a standard semantic account, an n-place predicate û is interpreted as a n-ary relation, ƒû„ understood extensionally as a set of ordered n-tuples. The intuitive understanding of the interpretation is that the meaning of an n place predicate, û, is given extensionally by the set {<x1, . . . , xn> | ûx1 . . . xn}
—that is, the set of ordered n-tuples of which it is correctly predicated. Thus, for example, a meaning of the preposition between is the set of triples <x,y,z> of which it is true that x is between y and z. Since we are interested in the evolution of meanings, that standard semantic account will not quite do for our purpose. The representation we require is not that of a putative established meaning but that of the establishing of it. For this we must broaden our purview to include what I shall call the usative relation, «û» of a predicate, û. This «û» includes the set of n-tuples <x1, . . . , xn> of items of which it has ever been claimed that ûx1 . . . xn. Statistically it would make little difference if it also included the set of n-tuples of items <x1, . . . , xn> of which ûx1 . . . xn has been denied. And it also ought to include the set of n-tuples of items of which ûx1 . . . xn has been enjoined, and so on. Our purposes do not require a precise or even detailed definition of a usative relation, only mention of its intended role—namely, that it should be the relation that records the accumulated historical uses of the item of speech: that is to say, the set of compositions in which the predicate has played a part. In the case of between, it may be said, the record would not be a relation, but a hyperrelation, since it would contain n-tuples and m-tuples for m ≠ n. In particular, it would include a set of quadruples, each of which comprises a speaker, a hearer, a lamp post, and a piece of information. Neither will it be uniformly spatial or temporal but will include a set of triples, each of which contains two alternative conditions and a choice, as in (7)
The choice was between five hundred pounds a year . . . or penal servitude. (Trollope 1993a[1871], 181)
It will include another set of triples each containing two items and a relation, as in (8)
. . . the difference between sinking or floating. (Engel 1990, 252)
It will also record all of the accumulated nonce uses and misuses of the vocabulary, not marking, other than statistically or incidentally, any distinctions among misrepresentations of fact, correct uses, and incomprehensible ones. A usative relation «û»” is the union of a temporally ordered set of relations {«û»t | t ∈ T}. Each «û»t can be defined by «û»t = i∪ ≤ t {«û»i}. Hence, if t ≤ t', then «û»t ⊆ «û»t'. This temporal
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monotonicity is a potent instrument of semantic innovation, since, in general, the more the n-tuples in the relation, the less the n-tuples have in common and, more particularly, the more varied the compositions experienced by any given speaker of the language of which it is an element. Again, the more varied the uses, the fewer the inferential effects that all of the experienced uses have in common and the more frequent the instances of use for which none of the subspecific inferential effects of previous spatial uses is forced or expected. Examples of vocabulary that, without having acquired logicalized meanings, have acquired nonspatial meanings partly through extensional saturation and consequent inferential dilution are just, straight, right, flat, even, and downright. But prepositions such as but, without, and outside that have now acquired logicalized meanings also have antecedently acquired nonlogical but also schematized nonspatial meanings. The point, once appreciated, should make us skeptical of the place of metaphor in these developments. No doubt explicitly metaphorical, nonspatial extensions of physical vocabulary do occur. But we ought to resist the temptation to lay much of the generalizing work of schematization to their influence. The gradual wearing away of the capacity, independently of other cues, sometimes even with them, to occasion particularistic relational inferences can for the most part be regarded as a natural effect of ordinary nonmetaphorical use. The effect has a counterpart in the model-theoretic slogan that the wider the class of models, the fewer the valid formulae, simply because the broader the class of models, the more opportunities there are for any particular formula to be falsified. The larger the usative relation (or hyperrelation), the fewer the particularistic inferential effects supported. What schematization amounts to in particular cases depends on the character of the ancestral vocabulary. Vocabulary that supports inferences as to spatial relationships will acquire despatialized uses in which no such inferences are supported; temporal vocabulary will acquire detemporalized uses, and so on. There is no reason to suppose, nor does my account require, that the traffic of evolution is all one way in this regard. Plenty of examples come to hand of spatial meanings with temporal ancestors or the reverse and of temporal meanings whose ancestors are inferences of relationship of manner or character. The word as alone furnishes sufficient examples. 4.2 Schematization and spatial and temporal examples Much of the logical connective vocabulary of natural language is descended from ancestral vocabulary whose explication would require mention of spatial relationships, and much of that same connective vocabulary has existent homonymic cousins carrying on in much the original family business and others in related branches of trade. But at an early stage of its evolutionary development, schematized, in these cases, despatialized meanings must have emerged. Thus, for example, the subordinator where as (9) He was four years younger than Donovan with the same fair hair. Where Donovan’s was glossy, Bennet’s was coarse. (Grafton 1995, 30)
Here, though there are spatial, locational implications expressible using where, they are incidental to this fully logicalized use. Again, the conjunction but of (10) Mrs. Pipkin’s morals were good wearing morals, but she was not strait-laced. (Trollope 1982[1875], 399),
since it takes a sentential filling, may be regarded as a logicalized use even if it is unclear which. Nevertheless, it has a distant but homographic Scottish cousin laboring as an adjective meaning ‘physically outside’, and often seen in company with ben, meaning ‘inside’:
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(11) It cannot be brought But that is not the Ben. (OED. BUT s.v.) (12) Gae but, and wait while I am ready. (OED. BUT s.v.)
Elsewhere, adverbial/prepositional but is present only in schematized nonspatial uses. Such a remark as (13) There is no one but the house
would seem a curious, perhaps precious, personalization, if not a selection error. The reason is that outside of the much constricted geographical regions in which but retains its spatial uses, the residual prepositional use is that of representing schematized relations: categorial outsideness: (14) I could see nothing but sunshine caught in leaves . . . (Cornwell 1992, 8)
or circumstantial outsideness: (15) But for the storm he would have given way. (Trollope 1982[1875], 354)
Though schematic, these are not yet logicalized uses. They do, however, take us close, since circumstances can be specified sententially or gerundially. Thus, but, though prepositional, could be labeled protological in (16) But for the fact that there was a storm he would have given way
as it could in (17) But that there was a storm he would have given way
a use that takes us to a stage only an ellipsis away from one of the completely logicalized uses such as that of (18) It never rains but it pours.
Were this the only logicalized use of but, the story could perhaps stop with that explanation. But, as we have seen, and as this sentence bears witness, it is not. It is relatively easy to see how but may have become logicalized as a disjunctive connective; the account of its conjunctive logical uses must await a later discussion. More familiar than the surviving Scottish but, which, had its original spelling survived to justify its sense, would be spelled by out (as ben would be spelled by in), is the orthographically more forthright without of: (19) There is a green hill far away, Without a city wall . . .
a use corresponding to within. This spatial without has acquired—and, in turn, nearly lost—certain quasi-spatial prepositional uses (20) A very violent and painful heat cannot exist without [≈ outside] the mind. (Berkeley 1940[1713], 533)
that can, of course, be party to spatial metaphors:
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(21) he would be beyond the reach of law, and regarded even as without the pale of life. (Trollope 1993b[1882], 26)
This metaphorical spatiality is palpably present in (22) I cannot hold myself without abusing him. (Trollope 1992[1882], 134)
but is all but absent in the most usual uses of the word: (23) I shall always do as I like in such matters without reference to you. (Trollope 1991[1859], 499)
These are schematized, but not logicalized uses. Yet even without can do duty as a sentential connective: (24) She could not write the letter without some word of tenderness should go from her to him. (Trollope 1992[1882], 133)
or, more crudely, (25) He’s a local lad and he won’t get far without he’s noticed (Hare 1991a[1938], 123),
in which some trace of the ancestral meaning is still discernible. The curious dualization that, in the case of but is apparent only in its fully logicalized uses, emerges in the schematized but still protological uses of without. Whereas the but dualization has yielded an and/or split, the without-meanings, are roughly distinguishable as and not and if not. The divergence is apparent in the following two examples: (26) He’ll die without help. (if not) (27) He’ll die without fear. (and not)
It is worth mentioning as an aside that both without and with have protological uses, with a meaning approaching that of because of : (28) We haven’t formally started to review it, but with it hitting the news . . . hopefully we’ll be getting together next week and bring our findings to Caucus on Sept. 19 (Coquitlam, Port Coquitlam, Port Moody Now, 1994-09-03)
Like without, with has both conjunctive and conditional uses: (29) With frugality we’ll get by. (if) (30) We’ll get by with plenty to spare. (and)
English likewise puts outside to schematized, nonspatial uses, as Groucho Marx noticed: (31) Outside of a dog, a book is man’s best friend; inside of a dog, it’s too dark to read.
Compare: (32) His driver’s license says he’s Hulon Miller, Jr., but I doubt if there’s anyone outside of his mother calls him Hulon. (Leonard 1992, 153)
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Even under has found schematized uses, as (33) Manners were all that could be safely judged of, under a much longer knowledge than they had yet had of Mr. Churchill. (Austen 1957[1816], 129)
English also affords many examples of schematized meanings that descend from previously temporal ones. I present here only two illustrations: yet and still. Homographic descendents of giet find themselves employed in work, some at greater, some at less remove from the earlier meaning of before. Some have meant something like in all the time before that time: (34) She had no plan of revenge yet formed. (Trollope 1982[1875], i, 255)
Others mean something like despite that circumstance: (35) He need not fear the claws of an offended lioness:—and yet she was angry as a lioness who had lost her cub. (Trollope 1982[1875], 254)
Again, the obsistive still of (36) Mr. O’Callaghan was known to be condescending and mild under the influence of tea and muffins—sweetly so if the cream be plentiful and the muffins soft with butter; but still, as a man and a pastor, he was severe. (Trollope 1991[1859], 277)
is cousin to the adjective meaning unmoving: (37) Mr. Bertram sat still in his chair. (Trollope 1991[1859], 307)
and to the persistive adverb of: (38) He still kept rubbing his hands . . . (Trollope 1991[1859], 307).
Having illustrated developments at the earliest stages of logicalization, we move to a much later stage, without pretending that there is no more to be said of stages in between. In fact, a complete account must mention the process by which certain originally multivalent vocabulary acquires trivialized—that is, two-valued readings—and must explain how words that are originally prepositions or relative adjectives come to punctuate acts of speech. Here I offer only what I hope is sufficient evidence of the explanatory usefulness of the approach. So we move to what is perhaps the most intriguing finding of the research. 4.3
Allotropy
The label, allotropy is intended to suggest the physical use of the term and its cognates—that is, as denoting or pertaining to a variation in physical properties without variation of elementary matter. Diamonds and coal are allotropic forms of carbon; ozone is an allotrope of oxygen. As applied to a natural language, allotropy picks out classes of sentences that are capable of presenting themselves as of one syntactic kind to one user and of a different syntactic kind to another, while being assigned the same satisfaction-conditions by both. As a nearly trivial example, we may consider the following. A speaker says, (39) No trees have fallen over here
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expecting the words of the sentence to be taken as having the roles that they have in “Over here no trees have fallen,” and a hearer understands the sentence as “Here no trees have fallen over.” They agree on the satisfaction-conditions of the sentence, but disagree on its syntax. The neartriviality of the example lies in the semantic idleness of the over. Of course, one might argue that the over of fallen over must therefore have a different meaning from that of the over of over here. But the effect of over in both constructions is at best vestigial, and the difference falls below the threshold of interest for this study. Nontrivial examples present themselves. Consider the two forms (x)(ûx → a) and (∃x)ûx → a, where a contains no free occurrence of x. They are both formalizations of the schema ‘If any x û’s, then a’, and either represents a way of understanding the structure ot that schema. For some instances of the schema for which the different structural understandings corresponding to the two formalizations require no difference in the understandings of the satisfaction-conditions. The alternative formalizations correspond to allotropes of the schema. Notice that in one allotrope the work of any in the original schema is that of a long-scope universal quantifier; in the other it is that of a short-scope existential quantifier. Now for some a’s, in particular, for those in which there is anaphoric reference to the whole if-clause, a satisfaction-conditionally significant syntactic ambiguity persists. The sentence (40) If any student touches my whisky, I’ll know it
remains ambiguous as between (41) and (42): (41) If any student touches my whisky, I’ll know that some student has touched my whisky. (42) If any student touches my whisky, I’ll know that that student has touched my whisky.
Indeed, the availability of the former reading should sufficiently tarnish the sometime-expressed thesis that any is just a natural language long-scope universal quantifier. But, such examples aside, such conditionals are generally capable of distinct but allotropic representations of the sort given. The ambiguous anaphora of (40) confirms that neither allotrope is a uniquely correct representation and that the contrary assumption for particular cases buys no greater simplicity overall. Negative environments also can be allotropic. Consider (43) I will not be brought under the power of any (I Corinthians 6:12),
which could be represented by the form ¬ (∃x)Bx or by the form (x) ¬ Bx. By contrast, interrogatives, which together with hypotheticals and negations make up all of the occurrences of any in the King James Version of the Bible, are nonallotropic, requiring something akin to an existential reading. The allotropy hypothesis, as applied to the evolution of meanings, is the hypothesis that certain meanings of certain connective vocabulary are the product of a development that depends on allotropy in the sense given. In the generation of such meanings, there is a stage in which identical sequences of words, with identical or sufficiently similar satisfaction-conditions, presents one syntactic structure to one subpopulation of their users and a distinct syntactic structure to another. The evolutionary significance of allotropy is that, by using it, the earliest populations of a new meaning can be hidden and therefore protected from correction by mature populations of an older one. For convenience I shall refer to new meanings allotropically nurtured in this way as succubinal meanings and distinguish them by overlining. This suggests that the older, fostering meaning should be called incubinal and marked by underlining. Were the account to be applied directly to any, and were the case as simple as an examination of the King JamesVersion of the Bible might suggest, it would regard the uses that tempt or require representation by existential
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quantifiers as having common ancestors with incubinal, any, those, such as “free choice” any that seem to require representation by universal quantifiers as descendents of succubinal, any. In fact, if some such developments account for the existential/universal dual personality of any, they must have occurred much earlier than in Jacobean times. The duality of use is likely inherited from aenig, which, in written remains, occurs predominantly in allotropic and interrogative environments earlier than the eighth century, but in its normal universal role in comparisons as well. Beowulf boasts to Unferth that he has more strength in swimming “þonne aenig oþer man” (l. 534). It will be evident that the adjective succubinal refers to a stage in the generation of a new meaning. At that stage the population of users can be classified accordingly as their parsings require the incubinal or succubinal representation. So while that stage persists, there may be no generally accessible evidence that a new meaning is emerging. It is only when the new meaning is out from under the old that there can be said to be two meanings in the ordinary way of speaking—which is to say, two meanings equally available to both populations of users. The new meaning must migrate to nonallotropic environments in which commonly recognized satisfaction-conditions demand the formerly succubinal meaning. In the case of any, such an environment might be permissive or probabilistic, or the use may be triggered by adjacent vocabulary, such as (44) Those people probably saw things much stranger any given day of the week. (Grafton 1995, 171)
Here, perhaps, the comparative “stranger” triggers the use of any because comparatives normally take any (as stranger than any fiction). We will return to the matter later, but the point deserves a little flag here. The evidence suggests that adjacent vocabulary triggers use, rather than that conscious consideration of the meanings of adjacent vocabulary gives rise to deliberate deployments. As we shall see, this involuntary feature of speech-production quickly gives rise to hybridizations as vocabulary with formerly succubinal, now migratory, meanings combine with surrounding connectives as though still bearing their formerly incubinal meanings. This to the confounding of any simplehearted compositionality doctrine.
5 Mutations Usually, we may assume, the syntax produced by a speaker is the syntax received by the hearer. Sometimes, however, this is not so. On such occasions, one of two conditions must prevail: either the error is syntactically negligible, as in (39), or it is not. If the error is not syntactically negligible, then we might suppose that one of two conditions must obtain: either the error is satisfaction-conditionally negligible, or it is not. We need not set the standards of negligibility puristically high. If a speaker says “I don’t think she’s there yet,” and the hearer mistakenly takes this to be the claim “I think that she’s not there yet,” the satisfaction-conditional difference between the two, though not formally negligible, may nonetheless make no practical odds. This may sufficiently explain why the English language tolerates negation-raising verbs (though Griceans might insist on explanatory elaborations). If the difference is not satisfactionconditionally negligible, then one of two conditions must arise: either the syntactic error is eventually corrected, or the hearer persists for a while in satisfaction-conditional error as to what was said. This, I say, is how one might have thought the cases would bifurcate. In fact, there seems to be an intermediate case: namely that, roughly speaking, the syntactic error should be satisfaction-conditionally compensated for by a semantic one. A more precise account of what happens in the misconstrual of (39) might be made in these terms: the speaker’s syntax of “fallen (over here)” is imperfectly replicated as hearer’s syntax “(fallen over) here,” but the error is compensated for by a semantic error in which the otiose over of the construction
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over here is understood as the non-otiose over of the construction fallen over (as distinct from fallen in, fallen through, and so on). Under certain conditions, when the syntactic error is compensated for by a novel or nonstandard semantic construal, new meanings can be introduced, which are appropriately thought of as mutations in something very close to the molecular biological sense of the word: The replacement of a codon specific for a given amino acid by another codon specific for another amino acid is called a missense mutation. On the other hand, the change to a codon that does not correspond to any amino acid is called a nonsense mutation. The existence of extensive degeneracy means that most mutations are likely to cause missense rather than nonsense. Missense mutations produce proteins changed in only one location, and so the altered proteins which they produce frequently possess some of the biological activity of the original proteins. The abnormal hemoglobins are the result of missense mutations. (Watson 1965, 374) Mistakes in reading the genetic code also occur in living cells. These mistakes underlie the phenomenon of suppressor genes. Their existence was for many years very puzzling and seemingly paradoxical. Numerous examples were known where the effects of harmful mutations were reversed by a second genetic change. (378) Those mutations which can be reversed through additional changes in the same gene often involve insertions or deletions of single nucleotides. These shift the reading frame so that all the codons following the insertion (or deletion) are completely misread. (379)
Now some of the nonsense mutations produced by such “reading frame” errors of English have been recognized as nonsense by sensitive listeners without having been diagnosed as mutations. Consider this exchange between the naive and immature Catherine and the better educated Henry Tilney (Northanger Abbey) . . . ‘Have you had any letter from Bath since I saw you?’ ‘No, and I am very much surprized. Isabella promised so faithfully to write.’ ‘Promised so faithfully!—A faithful promise!—That puzzles me.—I have heard of a faithful performance. But a faithful promise—the fidelity of promising! It is power little worth knowing however, since it can deceive and pain you.’ (Austen 1993[1818], 209–210)
There need be no doubt (since Henry has put his finger on it) that Austen could see how this nonsense use of faithfully has come into English: through some earlier misreading of the adverb as applying to the finite verb where it had applied to the succeeding infinitive. To promise faithfully to write makes some sort of pleonastic sense; to promise faithfully to write makes none. Nevertheless, the legacy of this syntactic misconstrual is the idiomatic coupling of faithfully and promise as (45) I promise faithfully not to explore. (Milne 1980[1922], 143)
It would seem that, in the case of notional vocabulary, the distinct meaning that arises through such an error persists as an idiom only within the very restricted environment that gave rise to the error, and it does not propagate through migration to others. In this case, the reason is perhaps that faithfully does not seem to have any nonperplexing new meaning when attached to forms of promise. Something along the same lines could be said about negation-raiser verbs. Suppose the verb think were to acquire a distinct succubinal meaning through the construal of (46) as (47): (46) I don’t think she’ll come.
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(47) I think she won’t come.
The succubinal think would bear the relation to the standard think represented in the equivalence ‘I think that a iff I do not think that not a’. That there is no such noncommittal meaning of think in English is sufficient proof that no such development has taken place. And we might suppose a priori that any such development would be unlikely. One reason might be that positive verbs of attitude are too well established in their range of uses for such a noncommittal use to persist uncorrected in negation-free environments; another is that the negation-raising reading is sufficiently robust that I do not think that not-a will be read as I think that a. Again, one might look to some such development to explain the anomalous doubt but as (48) I do not doubt but that the Viet Cong will be defeated. (Richard Nixon)
This venerable construction was already current in Jacobean English: (49) No doubt but ye are the people, and wisdom shall die with you. (Job 12:2)
But the anomaly is explained by the presence in English of a use of doubt having approximately the force of fear or suspect as in (50) There I found as I doubted Mr. Pembleton with my wife (Pepys 1663-5-26) (51) . . . she could not forbear telling me how she had been used by them and her mayde, Ashwell, in the country, but I find it will be best not to examine it, for I doubt she’s in fault too . . . (1663-8-12) (52) . . . he is not so displeased with me as I did doubt he is (1663-12-8)
and so on. In fact, for most of the biblical occurrences of doubt, there is sufficient contextual evidence, sometimes quite explicit, to support some such “middle voice” reading as be in perplexity about or weigh the evidence for and against, rather than the “active voice” reading as think improbable: in fact, at least seven distinct Greek verbs and nouns are translated as ‘doubt’ in the King James Version of the New Testament. And the preferred construction doubt whether is itself evidence that a distinct middle voice reading, now largely superseded, was once standard. If the doubt but construction is explained as an isolated survival of an earlier weak positive doubt, then it may be that the standard (suspect-that-not) use of doubt is the product of just the sort of mutation that stronger positive verbs of attitude so robustly resist; for the standard use approximates the use that one would predict as likely to arise, through mutation, from negated negation-raising uses of the Pepysian doubt. A strong verb’s modus tollens is perhaps a weaker verb’s modus ponens.
5.1
Metanalysis
Jespersen (1922) introduced the term metanalysis as a label for a phenomenon in the process of word formation: Each child has to find out for himself, in hearing the connected speech of other people, where one word ends and the next one begins, or what belongs to the kernel and what to the ending of a word, etc. In most cases he will arrive at the same analysis as the former generation, but now and then he will put the boundaries in another place than formerly, and the new analysis may become general. (174)
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Thus we have an umpire from a numpire, an apron from a naperon, a nickname from an ickname, and so on. In such cases the mutation comes about through a misapprehension of the divisions between words. Jespersen is rather vague in the matter of how such a mutated form survives, but we can note here at least the prime condition for such a survival—that the discrepancy between speakers and audience in alternating roles should go for a time undetected, and therefore that it should make no or sufficiently little difference in the satisfaction-conditions of sentences in which the discrepancy occurs. And of course, as the difference is undetected, the metanalytic population has a chance to become established.3 5.2
Scope evasion
The term metanalysis, transposed to the level of syntactic structure, would serve equally well to label the initial stage of the development that I label scope evasion, for it, too, springs from a misapprehension of divisions within sentences, though at the clausal level. The more important difference is a dimensional one. For Jespersen the significance of metanalysis lies in the introduction of a new verbal expression of an existing meaning: in the course of the development umpire came to mean what numpire had meant. For us, its significance lies in the introduction of a meaning that did not previously exist. In the physicalist idiom adopted here, Jespersen’s observation can be couched in semantic language as well, since, for example, umpire comes to have a meaning where previously it had none. But in all but one of the cases we consider, the outcome of the metanalysis is that a word that previously had n meanings comes to have n + 1. I begin with the exception. Unless is a striking example of a connective for which the original meaning, which had a conjunctive component, has become extinct in favor of a disjunctive one, and apparently through evasion of the scope of negative sentence elements. The evidence for this lies in two features of its early development. The first is that its earliest uses are found exclusively in negative constructions; the second is that it represents the surviving coalesced core of on [a] less [condition than that]. Setting aside the scalar feature, the ancestral meaning of a unless b is a with the condition that b unmet, that is a without b—that is, a and not b.4 Thus the ancestral, elementary meaning of not . . . unless . . . is that of not(. . . and not _______)}. The ancestral, elementary meaning of that construction, of course, gives the truth-conditional meaning of not . . . unless _______ in its current use, but its elementary meaning is not(. . .) if not_______. or not(. . .) or _______, the unless being represented by the if not or the or. The establishment of a reading in which the negative element has foreshortened scope sponsored uses in which the negative element was absent. And over that enlarged field of use we may regard unless as univocal, provided that the negating elements, when they occur, are always given a short-scope reading. The disjunctive reading of unless is sufficiently robust to withstand repositionings and the introduction of negators such as It’s not the case that, with long scope intonationally made explicit. It is plausible to suppose that the conditional and of middle and Jacobean English, the and that, in Shakespeare, early editors clipped to an, had been speciated by an earlier parallel development in which in certain constructions not(. . . and . . .). was read not(. . .) and . . . , the and being construed conditionally to make up the construal of the whole: (53) Ich nolde cope me with thy catell ⋅ ne oure kirke amende, Ne take a meles mete of thyne ⋅ and myne herte hit wiste That thow were such as thow seist; ⋅ ich sholde rathere sterue. (Langland. C Passus VII. 288–290)
Compare such a construction as (54)–(56): (54) I do not think that you should go and she stay behind.
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(55) Could he have come out and we didn’t see him? (Wingfield 1995, 261) (56) Why am I a redhead and you have dark hair? (@discovery.ca, 1995-12-26)
Here the structure of the clause following the and is such as to permit a foreshortening of the scope of the negation or the modal could or interrogative why with substitution of if for and, a transformation skeletally recognizable in the PL equivalence: ¬(a ∧ b) ¬a ← b. It seems likely that the adversative but including its arrogative use (as in not black but dark blue) was engendered from the propositionally exceptive but by scope evasion. At the initial stage we would expect to find despatialized but in its propositionally restricted use inside the scope of a negative or modal sentence element: (57) He had not been long upon the scout but he heard a noise. (Defoe 1908[1722], 147)
Here what is denied is that the subject had been long on the scout without hearing a noise. If the scope of the negation is foreshortened and the sentence taken to imply absolutely that the subject had not been long upon the scout, then the sentence as a whole can have approximately the same conversational effect if it is taken, in virtue of its second clause, to imply that the subject heard a noise, and this quite independently of any understanding of the force of its but on this reading. Once a nonexceptive use is introduced, it can shelter beneath the exceptive use for all verbs that can be made nontrivially subject to exceptive clauses, but it must force a nonexceptive reading for verb phrases not plausibly so subject. Thus, for example, the but of (58) He wasn’t given to literary exercises, but he was neat and methodical. (Snow 1974, 252)
Even without the comma, this would have no plausible exceptive reading. The foreshortened scope made explicit, the nonexceptive reading, however to be understood, persists even in the presence of preceding negations and exceptively modifiable verb phrases: (59) In the mystery itself there is not the slightest interest. But the mysteriousness of it is charming. (Trollope 1967[1867], 398)
The exceptive but of this development, as we have so far discussed it, is a multivalent one: the exceptive clause limits the range of some multivalent magnitude or manner of engagement of some activity. Exceptive but has also a bivalent use in certain conditional constructions: (60) I should not now have spoken to you at all, but that since we left England I have had letters from a sort of partner of mine (Trollope 1983[1867], i, 236)
Here a number of elements are individually significant. First, the exceptive reading is reinforced by the subordinating that. Second, the sentence is reliably factive at its second clause; that is, it invites (through the perfect tense of its verb) the inference that the content of the second clause is being asserted. In the presence of the second of these factors, the omission of that might generally prompt a nonexceptive reading, though even in the absence of that an exceptive reading, at least for an audience of any but recent literary experience, will be prompted by an indefinite present tense. My informal surveys of introductory logic students find very few who need not struggle to understand the central example disjunctively: (61) It never rains but it pours.
The puzzling character of the adversative coordinator is the product of the scope foreshortening of the negative or modal sentence element. Certainly, the effect is as in other similar
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developments—that the connective loses its disjunctive reading in favor of a conjunctive one— but the historical connection with the despatialized, outside reading of but is rather obscured than lost. That that connection shapes the conjunctive use of but is, I think, undeniable. With a properly attuned theoretical language we can account for the puzzling adsentential character of the new use. But a fine-grained account of how speech production adjusts to such new uses requires a detailed neurotheoretical understanding that we simply have not got. Inspection reveals a similar development in the case of for which, from an earlier ‘because’ meaning, (62) The crew were beginning to get very much the worse for drink. (Dexter 1989, 53)
has evolved a later ‘in spite of’ reading: (63) And yet she was alert, for all the vagueness of her manner. (Potter 1986, 149)
But as a final example, I observe that English has a dualized if that seems to have come about by this process of scope evasion. The diathetic condition that rendered propositional if susceptible of this kind of mutation seems to have been the difficulty in English of negation placement in ifconstructions, and possibly the obscurity of satisfaction conditions for conditionals, an obscurity inherited by their denials. In general, dualized if can be marked by even, but just as frequently it is marked only prosodically. The A if, we think of conveniently as the sufficiency if. The B if, we can label the insufficiency if. The two following examples illustrate them in that order. Contrast (64) with (65): (64) If he wins the lottery, he’ll be MISERABLE. (Winning will make him miserable.) (65) If he wins the LOTTERY, he’ll be miserable. (Winning won’t cure his misery.)
Even in their material representation, the two are distinct, the material representative of the latter being deductively stronger than that of the former. That is: ¬(a → ¬b) PL a → b, but a → b PL ¬(a → ¬b). The conjectured origin of this if is the misapprehended scope of a negation placed in the main clause as if in (66) I wouldn’t do that, if the QUEEN (herself) asked me. (Her asking me would be insufficient.)
a short-scope sufficiency if with long-scope negation (n’t) is read as a short-scope negation with long-scope if. The satisfaction-conditions being kept constant, the if must be given an insufficiency reading. From a formal point of view, the dualized, insufficiency if (sometimes marked as even if, sometimes only prosodically) has the appearance of a sort of hybrid. The reason seems to involve the triggering phenomenon mentioned earlier. In the production of speech, the choice of conjunctive connective, whether and or or is determined by habituation rather than the anticipations of interpreted manipulation. Since sufficiency if-clauses with or are effectively conjunctive, so are those of insufficiency if-clauses. But since English sufficiency conditionals distribute conjunctively over a disjunctive if-clause, a negated conditional ought, at least by the standards of logic, to be read as a disjunction. Nevertheless, insufficiency conditionals also distribute conjunctively over disjunctive if-clauses. So, for example,
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(67) If the king OR the queen asked me I wouldn’t do it.
will be read as (68) If the king asked I wouldn’t, and if the queen asked I wouldn’t.
but does not commit us to: (69) If the king AND the queen asked me I wouldn’t do it
since though they might be insufficient severally, their requests might be jointly sufficient. So dualized if is left-downward nonmonotonic.
6 The stages of mutation In appropriating the language of mutation, I claim only an abstract connection with the microbiological phenomenon. That there should be such a connection is striking only to those who have not attended to the most obvious feature of language, namely that it is a biological phenomenon transmitted through successive biological populations. The nature of specifically linguistic mutation must be a study in its own right. The following represent something like an average account of its stages, of which at least six seem to be distinguishable. 1. Genesis. In the case of mutation by scope evasion, the first stage in the production of a new connective meaning is the initiating scope misapprehension (by members of population B), typically involving negative and modal sentence elements (in the speech of population A), with the resulting combination of approximately correct (or at least indetectably incorrect) apprehension of satisfaction conditions on the one hand and undetected incorrect processing of syntax on the other, which forces an incorrect (or at least novel) apprehension of the use of the connective. 2. Incubation. The primary association intended by the label as used here is with the period during which a population of viruses establishes itself in a host organism, rather than with the hatching of a single organism from an egg. But there is a respect in which the process resembles the second: if we regard the novel reading as a misconstrual, then it is a misconstrual that is protected from correction by the practical overall synonymy of the proper and improper construals of the sentence as a whole. The new construal is in this way sheltered by the old one, and is conversely dependent on it, since there is no guarantee at this stage that the connective in the incorrectly apprehended use is viable in environments outside those of the highly specific kind in which it was engendered. 3. Autonomy. At this stage the newly engendered reading can be obtained for the connective even in the absence of a sentence element of the kind given a scopeforeshortened reading at an earlier stage. At this stage, we find occurrences of conjunctive unless, or suppositional and in the absence of negation, but otherwise in roughly the same sentence position, as, (70)
He shall be glad of men, and he can catch them. (Dekker 1933[1600], II, iii)
4. Migration. Among the early sites to which one would expect the connective in its new construal to migrate from the environment that engendered it to sites nor-
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mally occupied by the connectives with which it has been newly construed as synonymous. In this stage, suppositional and migrates to other if positions, as: (71) Faith, and your foreman go, dame, you must take a journey to seek a new journeyman; if Roger remove, Firk follows. (Ibid.)
In such a migration, the new reading is still protected, but now by the presence of positional and modal cues which defeat a conjunctive and force a suppositional reading. 5. Ambiguity. When a meaning engendered by scope evasion is fully established, the reintroduction of the connective into a construction of the kind that engendered the new meaning will give rise to a semantic ambiguity, either clause of which is expressible by either of the dual readings of the connective. 6. Marking. In the fifth stage, the new meaning is disambiguated from the old by order or by the addition of markers generalized from particular cases or types. At this stage we find the ‘in spite of’ for at this stage marked by the addition of all, detached from content, and attached to the connective: (72) To him Zeus handed over the power, ‘for all he was young and but a greedy infant’ (Guthrie 1952[1935], 82)
We find universal any and anticipative in case marked by just: (73) I’ve never had any time for these women who go out and leave their children all day with just anyone. (Barnard 1986[1980], 18) (74) There was a path up to the summit he felt sure, but it might be as well to keep off it, just in case the men were looking in that direction, expecting someone else. (Barnard 1983[1977], 153)
7 The general idea I say nothing more in defense of the evolutionary approach to the study of connectives that I have been advocating. It is essentially an Aristotelian approach, which W. K. C. Guthrie sums up pretty well: (75) Since motion and change are the most characteristic marks of nature, it is precisely these that have to be understood and explained—not run away from. (1981, 102)
But having said that, I must confess that the investigation of the principles of linguistic change would not be of such interest to me if it did not also dissolve puzzles about the present state of things. This, I think, this approach does accomplish: it explains both the fact and the details of the diversity of connective uses, of which I have here offered only a few examples. And where folk-semantical accounts are difficult to give, as in the case of but, this approach also explains the difficulty. That, of course, speaks only to that aspect of the account that treats of the logicalization of connectives. It says nothing of that aspect of the theory with which I began—its being, as far as possible, a physical theory, rather than a semantical one. Since I seem to have made free with semantical notions such as satisfaction and satisfaction-conditions and so on throughout the exposition, it will be as well to say something about them here. I have said that acts of speech are physical interventions and that they typically have what I have called inferential effects. It should be added that, typically, acts of speech are interventions in situations in which many features of the environs have inferential effects, in which features have already had effects and in which
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effects of expected change are anticipated. It would, therefore, be equally correct to say that acts of speech are typically operations on effects. That is, they present dynamic modifications of the effects of other occurrences—spoken, gestural, and nonlinguistic. And it is part of the picture that parts of acts of speech are dynamic alterations and adjustments of the effects of other parts of the same acts of speech. Within that general viewpoint, we are able to hypothesize the roles of connectives understood as discriminating distinct operations on effects. Here I mention, as an illustration, only one connective, conjunctive but. Conjunctive but is subtractive with respect to inferential effects. The effect of the but-clause (the subtrahend clause) of “He got here, but he got here late” to cancel or nullify or reserve some of the expected effects of what could be called the minuend clause. This explains the noncommutativity of such constructions—that is, why “He got here, but he got here late” is not intersubstitutable in conversation with “He got here late, but he got here.” This last subtracts, by the reminder that he got here, from the effects of the utterance of “He got here late.” Notice that such constructions are not compositional as that term is usually understood. The effect of the subtrahend is the subtraction of effects, but the effects to be subtracted are not determinable from the subtrahend clause independently of particularities of the minuend. Notes 1. For example, see Jennings (1994), pp. 70–71. 2. For a more extensive sampling, see Jennings (1994). 3. Canadian English furnishes a charming example of metanalysis. The drawing up of a writ is constitutionally dictated preliminary to the holding of an election. The draw up of the formulaic announcement has been heard as ‘drop’, with the result that it is now standard usage to speak of the prime minister as in course of dropping the writ or as having finally dropped the writ. The absurdity of the construction is evidently sufficiently masked by the presumption of antique obscurity that attends parliamentary language generally. 4. In fact, without has undergone a similar mutation, except that in the case of without both uses survive. Compare she’ll die without medical attention and she’ll die without betraying her friends.
34 JAMES HIGGINBOTHAM
Interrogatives
1 Introduction It is a pleasure to be able to present this paper as part of a volume to honor Sylvain Bromberger. My subject, interrogative sentences and the questions that they express, is one on which he has thought and written deeply and at length. I am specifically indebted to Sylvain for discussion in our seminar from some time back, and for many conversations over the years. Above all, however, I am grateful to him for his support early on of my hybrid research into language and philosophy, and I hope he may think that this work justifies it at least in part. In this paper I advance some parts of a view of interrogative sentences and their interpretations, with reference to English examples. The details of this view depend upon assumptions about the semantics of embedded indicative sentences that I use but do not defend here. I therefore distinguish at the beginning the major theses I advance about interrogatives, which I would urge even apart from these assumptions, from others that will show up in the details of execution. The major theses are these: 1. The semantics of interrogative sentences is given by associating with them certain objects, which I will call abstract questions: I will say that the interrogative expresses an abstract question. To utter the interrogative is to ask the abstract question that it expresses. 2. Pairs of direct questions, as in (1), and their corresponding indirect questions, as in the italicized complement of (2), are related in this way: the direct question expresses what the indirect question refers to: (1) (2)
Is it raining? John knows whether it is raining.
James Higginbotham (1993) Interrogatives. In Kenneth Hale and Samuel Jay Keyser (eds.), The View from Building 20: Essays in Linguistics in Honor of Sylvain Bromberger. Reprinted by permission of MIT Press.
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3. Indirect questions are singular terms, and they occupy quantifiable places of objectual reference. Thus, for example, the argument (3) is valid: (3)
John is certain (about) whether it is raining; Whether it is raining is Mary’s favorite question; therefore, John is certain about (the answer to) Mary’s favorite question.
4. Elementary abstract questions (what is expressed by simple interrogatives, or referred to by simple indirect questions) are partitions of the possible states of nature into families of mutually exclusive (and possibly jointly exhaustive) alternatives. Complex abstract questions (the result of quantifying into interrogatives, or conjoining them, as explained below) are constructed out of elementary ones. These form a hierarchy of orders, with abstract questions of order n being sets of sets of abstract questions of order n – 1. 5. Abstract questions can be constructed by generalizing along any of several different semantic dimensions and can be referred to by appropriate syntactic means even when their dimensions of generality are not domains of quantification in the indicative fragment of a language; such categories include those of predicates, quantifiers, and even parts of words. However, most abstract questions are not the reference of any interrogative sentence at all. In sections 2–5 I present informally a number of definitions and illustrations of the point of view I advance. In section 6 I turn to a defense of theses 1 and 2. In the final section, which I have labeled an appendix because it involves more material from logic and linguistics than the others, I argue that an explanation of the licensing of negative polarity items in interrogatives can be seen to follow from the proposal I develop here and in other work.
2 Preliminary definitions and illustrations An abstract question, what is expressed by an interrogative form, is not itself a linguistic form (although it is in a sense constructed from linguistic forms, in a way explained more fully below), but on the present view a nonempty partition P of the possible states of nature into cells Pi for i ∈ I, having the property that no more than one cell corresponds to the true state of nature (i.e., the cells are mutually exclusive). If in addition at least one cell must correspond to the true state of nature, then P is a proper partition (i.e., the cells are jointly exhaustive). The elements of a cell Pi can be thought of as statements, so that Pi corresponds to the true state of nature if and only if all the statements that it contains are true. Partitions are used in probability theory, and I will freely adapt terminology from there. If P is a partition, and S is a set of statements, let P + S be the result of adjoining S to each Pi. Thus, if P = {Pi}i ∈ I, then P + S = {P'i}i ∈ I, where, for each i, P'i = Pi ∪ S. Since P is a partition, so is P + S; but P may be proper, while P + S is improper. A cell of a partition may be satisfiable or unsatisfiable. Let F be some designated unsatisfiable set, fixed throughout the discussion, for example, F = {p & ¬p}. F is the degenerate set, and the improper partition {F} is the degenerate partition. If P is a partition, let P– be the result of deleting the unsatisfiable cells from P (or {F} if all are unsatisfiable). If S is a set of sentences, let P/S, or the conditionalization of P on S, be (P + S)–. Then P/S is a partition. Also, we evidently have (P/S1)/S2 = (P/S2)/S1 = P/(S1 ∪ S2)
An answer to a question P is a set S of sentences that is inconsistent with one or more cells in P. If P is the degenerate partition {F}, then S answers P for every S. S is a proper answer if it is an answer and P/S is not {F}.
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The notions introduced by the above definitions may be illustrated through a fabricated example. Let P be a partition whose cells are statements about the possible outcomes of rolling two dice A and B, where the outcomes are distinguished according to the total shown by the dice. There are eleven cells, which will be represented by the numbers 2 through 12, each of which stands for a complex disjunctive statement giving the outcomes that would add up to those totals; thus, cell 6 is (Die A: 1 & Die B: 5) or (Die A: 2 & Die B: 4) or . . . . . . or (Die A: 5 & Die B: 1)
Then P is a partition, since the outcomes are regarded as functions of A and B, and it is proper given the background information that the values of these functions are integers between 1 and 6. The above proper partition P is one way of construing the question expressed by (4), (4)
What was the total of the dice?
incorporating further information about how totals in a throw of two dice may be obtained. A person who asks (4) will be said, following Belnap (1963), to have put the question P. Consider now the statements in (5) as responses to (4): (5)
a. b. c. d.
(The dice totaled) 12. (I don’t know but) one came up 4. The sun is shining. The dice were never thrown.
In much of the literature on interrogatives, it is answers like (5a) that have been chiefly considered. Their relation to the interrogative sentence is particularly intimate: they provide instances of the matrix the total of the dice was (the number) _______, instances that are also in a sense canonical to the type of question asked: that is, they are numerical instances, rather than nonnumerical instances like the total of the dice was the number of the apostles. Objects themselves, rather than their standard names, can also be taken as filling the blank in the matrix above. Following this course, I regard the instances arising from substitution of names as presentations of the instances arising from assignment of the objects themselves. In discussions including Karttunen 1977 and Hamblin 1973, the question expressed by an interrogative was simply the totality of its instances (Hamblin) or, alternatively, the totality of its true instances (Karttunen). The totality of instances for (4), which might be indicated by abstracting over the empty matrix position as in (6), (6)
lx (the total of the dice was x)
is a natural candidate for the abstract question expressed by (4), and the question arises whether the further step to partitions does not create a needless complexity. My belief is that the definition of answerhood requires the more complex structure. Besides canonical and noncanonical instances, there are answers that give only partial information, as illustrated by (5b). Partial answers give information by being inconsistent with some, but not with all but one, of the possibilities enumerated in the partition. Obviously, they must be distinguished from irrelevant remarks like (5c). Not that (5c) is necessarily irrelevant. If it is known that the dice are crooked, loaded somehow to show double-six when the sun shines on them, it may be just as informative as (5a). Such knowledge, and background information more generally, is appealed to in seeing that P
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really is a partition (thus, the more general notion is that of a partition relative to background B). An answer that contravenes background conditions violates the presuppositions of a question, in an appropriate sense of this term.1 Technically, if X is a presupposition of P, then every cell of P implies X, and so if S is inconsistent with X, then S is inconsistent with every cell of P, so that P/S = {F}. The response (5d) thus violates the presupposition of (4) that the dice were thrown. Summing up, I have suggested that simple interrogatives express partitions (relative to background assumptions), and that complete and partial answers, nonanswers, and responses that violate presuppositions can all be appropriately characterized on that assumption. Consider now some examples or interrogatives. The partitions corresponding to yes-no questions are the simplest possible. They have two cells—one representing the affirmative, the other the negative. The elements of these cells need not be contents, in any sense over and above that of the sentences themselves, as interpreted in the indicative part of the language. Thus, for the question Did John see Mary? we have the partition (7): (7) {{John saw Mary} | {John did not see Mary}}
(I use a bar rather than a comma to separate the cells of a partition.) For a simple wh-question, as in (8), (8) Who did John see?
I assume the logical form (9): (9) [WHa: person(a)]? John saw a
The cells or the partition expressed by (8) run through all the possibilities for John’s seeing of persons. If in contexts there are just two persons in question—say, Fred and Mary—then a typical cell is {John saw Fred, ¬ (John saw Mary)}, representing the possibility that John saw Fred but not Mary. The question (8) with its quantification restricted to persons must be distinguished from the question (10), involving unrestricted quantification: (10) Which things are such that John saw them and they are persons?
This can be seen by noting that (11) is a (partial) answer to (10), but is in response to (8) simply an irrelevant remark. (11) Fido is not a person.
It is also seen, rather more vividly, in pairs like (12)–(13): (12) Which men are bachelors? (13) Which bachelors are men?
The unrestricted question corresponding to both of these examples is (14): (14) Which things are both bachelors and men?
But of course (12) and (13) are very different.
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The generalization that the quantifications which N must be understood as restricted, with the variable ranging over things that in fact satisfy N, is supported by examples like (15), (15) Which philosophers would you be annoyed if we invited?
where we never have an interpretation that would “reconstruct” the noun within the scope of the modal, giving a meaning like that of (16): (16) For which things x would you be annoyed if x was a philosopher and we invited x?
See Reinhart 1992 for similar examples. Higginbotham and May (1981) showed how to characterize presuppositions of singularity, as in (17): (17) Which person did John see?
An utterance of (17) in virtue of its form carries the presupposition that John saw one and only one of Fred and Mary. Its partition will carry the presupposition in question by having only two cells—one affirming that John saw Mary and not Fred, and the other that John saw Fred and not Mary. The cells for affirming that John saw both and that he saw neither will not be represented. Similar remarks hold for presuppositions that are expressed by words rather than morphologically, as in (18): (18) Which two articles did Mary read?
Nothing prevents our asking wh-questions ranging over infinite domains, or domains for which we could not possibly have a singular term for every object in the range. Thus, the question expressed by (19) is perfectly in order, although we shall be powerless to give it a complete answer: (19) Which real numbers are transcendental?
The partition expressed by this interrogative will have cells on the order of the set of all subsets of the real numbers. Multiple questions call for more refined partitions, as in (20): (20) Which people read which books?
The elements of the cells of these partitions will be sentences like “John read War and Peace” and their negations.2 The account of single and multiple wh-questions extends to the case where the position interrogated is not in the main clause, but in one or another embedded position or positions, as in (21): (21) Which people did he say like to read which books?
Finally, it should be noted that many wh-forms incorporate prepositions or subordinating conjunctions, as where incorporates at, and is effectively equivalent to at which place, and why incorporates either because or in order to. The latter gives a simple example of interrogatives that generalize over predicate positions, so that (22), in one of its interpretations, should be taken up as in (23).
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(22) Why did John go to the refrigerator? (23) [WHF] ? John went to the refrigerator in order to F
Questions like (24) have long been noted ambiguous: (24) What did everybody say?
Intuitively, (24) asks, for each person in the range of the quantifier everybody, what that person said. There are some syntactic limitations on expressing questions of this form.3 Our interest here, however, is quite general: What is the question expressed by an interrogative as in (25), where Q is a restricted quantifier, f is the restriction on Q, and q is another interrogative? (25) [Qv: f] q
The answer is that the question should be composed of sets of questions, one set for each way in which the quantifier, construed as a function from pairs of extensions to truth values, gives the value true.4 A simple example like (26) will generate the basic idea: (26) Where can I find two screwdrivers?
A person who asks (26) may mean to inquire what place is an x such that there are two screwdrivers at x. But she may also mean just to get hold of information that will enable her to locate two screwdrivers, and in this sense of the question it arises from the interrogative (27): (27) [Two x: screwdriver(x)] [What a: place(a)] x at a
The partition for the embedded interrogative [What a: place(a)] x at a
is given by our previous semantics: ‘x’ is simply a free variable here. Now, the numeral two, construed as a restricted quantifier, is such that Two f are q
is true if and only if at least two things satisfy both f and q. So the question expressed by (27) will be the class of all classes of partitions each of which, for at least two screwdrivers a and b as values of x (and for no other objects than screwdrivers as values of x), contains the partition for the interrogatives [What a: place(a)] a at a [What a: place(a)] b at a
The classes of partitions I call blocs, and classes of them questions of order 1. To answer a question of order 1 is to answer every question in one of its blocs. It follows that to answer (26) is to answer both the question where a is and the question where b is, for at least two screwdrivers a and b. The above method of quantifying into questions extends to all quantifiers, since it is completely determined by their extensional meanings. A scrutiny of actual cases shows that any quantifier that is not monotone-decreasing (in the sense of Barwise and Cooper (1981: chapter
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23 in this volume; see the discussion in section 5 below) can in principle get wide scope in an interrogative, including even the existential quantifier, as in one interpretation of (28): (28) What does somebody here think?
Intuition suggests that a speaker of (28) would expect from whoever elects to be his respondent the answer “I think so-and-so,” and that any such answer would be sufficient for the question. The theory accords with this intuition, since the abstract question expressed by the interpretation of (28) shown in (29) consists of all nonempty sets of sets of abstract questions of the form in (30), where a is a person in the domain of quantification: (29) [∃x] [WHa] ? x thinks a (30) [WHa] ? a thinks a
Truth-functional and and or are recruited for conjunction and disjunction of interrogatives, as in (31) and (32): (31) Will it be nice tomorrow, and will you go on a picnic if it is? (32) Is Mary happy or is John happy?
Their role is clarified by the analogy between connectives and quantifiers. Conjunctive interrogatives, as in (31), are obviously answered only by statements that answer both conjuncts. In the present terminology, (31) expresses a question of order 1, whose sole bloc consists of the partitions expressed by the conjuncts. Disjunctive interrogatives, as in one interpretation of (32), will have the meaning, “Choose your question, and answer it.” They express questions of order 1 whose blocs consist of one or both of the partitions expressed by the disjuncts. The more common type of disjunctive question is the free-choice type, exemplified by (33) in an airline setting: (33) Would you like coffee, tea, or milk?
My view of the role of disjunction in these cases, as explained in Higginbotham 1991a, is that they represent universal quantification into a yes-no question, as in (34): (34) ∀x: x = coffee ∨ x = tea ∨ x = milk]? you would like x
Thus, the steward who asks (33) is asking for each of coffee, tea, and milk whether you would like it (subject to the understood condition that you will have at most one of these). Finally, multiple quantification into questions is possible and will generalize so as to produce questions of arbitrary finite order. Such questions include (35), (35) What did everybody say to everybody?
with both quantifiers taking wide scope. Thus far I have considered partitions and abstract questions of higher orders with respect to domains of quantification that have not been incorporated into the abstract questions themselves. Consider (8), repeated here: (8) Who did John see?
The proper representation of the abstract question that it expresses must include the information that the property of having been seen by John is under consideration only for persons as values.
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Let K be the class of persons, and let P = p(John saw a[K]) be the partition obtained by assigning just the objects in K as values of a. If the abstract question expressed by (8) is to be distinguished from the extensionally equivalent one expressed by Which rational animals did John see?, then information about how the class of values is determined must be incorporated somehow. We have already seen that domain restrictions cannot be represented by conjuncts within a question—for example, that (8) must be distinguished from Which things are persons such that John saw them? However, we could include in each cell of the abstract question expressed by (8) the information, about each thing in K, that it is a person. If [person(a)[K]] is the class of atomic sentences person(a) for a ∈ K, we can propose the partition P' = P + [person(a)[K]] as answering to (8), thus distinguishing it from extensional equivalents. However, P' still fails to contain the information that the class K comprises all persons. This further information can be added where feasible, but is not finitely representable when the restriction is to an infinite class, for instance as in (36): (36) Which natural numbers are prime numbers?
Similarly, a set of instances constituting a complete true answer cannot always be replaced by a finite list L, together with the information that all the positive (negative) instances are to be found on L. Such is already the case for (36) since the set of prime numbers is neither finite nor cofinite.5
3 Indirect questions An indirect question is an interrogative sentential form used as an argument. In general, I believe no distinction except a syntactic one should be made between the sentential argument S and the nominal argument the question S: both are singular terms. Thus, we have both (37) and (38): (37) I asked whether it was raining. (38) I asked the question whether it was raining.
Now, certain verbs that take interrogative complements cannot take nominal complements: thus, (39) is ungrammatical: (39) *I wondered the question whether it was raining.
Pesetsky (1982) observes, however, that this fact may be reduced to an issue of abstract Case (the verb wonder does not assign Case to its complement, which therefore cannot be nominal); and that the introduction of morphemes, normally prepositions, for the purpose of assigning Case gives grammatical sentences whose meaning is just that of the corresponding sentence with a sentential complement. Thus, we have both (40) and (41): (40) I wondered whether it was raining. (41) I wondered about the question whether it was raining.6
Inversely, the verbs that take both nominal and sentential complements can appear with Noun Phrase complements whose interpretation is that of interrogatives. These are the so-called concealed questions, exemplified by (42): (42) I asked the time (what the time was).
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In all the above cases, in the view developed here, the complements refer to the abstract questions that they would refer to if used in isolation (with the necessary superficial syntactic adjustments). Thus, to ask whether p is to ask {p | ¬p}.7 With the epistemic verbs—and, indeed, with all verbs whose arguments are naturally taken to refer to propositions or to facts—interrogative complements are mediated by relations to answers to the abstract questions that they refer to. Thus, I assume that (43) is interpreted as in (44): (43) Mary knows who John saw. (44) Mary knows the (or an) answer to the question who John saw.
Berman (1989) has called attention to sentences with indirect questions in conjunction with quantificational adverbs, as in (45) and (46): (45) Mary mostly knows who John saw. (46) With some exceptions, Mary knows who John saw.
Examples are not limited to epistemic verbs, as (47), modeled after examples in Lahiri 1990, 1992, attests: (47) John and Mary mostly agree on who to invite.
I look upon these adverbs (differently from Berman) as qualifying the nature of the answers said to be known, or as in the case of (47), agreed upon; for example, (47) will be true if, out of a potential guest list of 20, John and Mary have agreed for (say) 15 on whether or not to invite them. See Lahiri 1992 for further discussion. Finally, there are interrogative arguments to verbs that have nothing to do with acts of speech or mental states. Karttunen (1977) noted indirect questions in contexts such as (48): (48) What will happen depends on who is elected.
Predicates like depend on express relations between abstract questions, and the notion of dependence at stake, applied to (48), comes to something like: Answers to the question who is elected, together with other facts, imply answers to the question what will happen. There are many other similar locutions, such as is influenced by, is relevant to, and, of course, their negations. It is worth observing that (48) leaves open the exact nature of the dependency, or the ways in which who is elected will influence what happens. In the parallel and simpler example (49), it may be that rising temperature causes rain or prevents it, and you may know (49) without knowing which it is: (49) Whether it will rain depends on whether the temperature will rise.
4 Extensions to higher types The basic apparatus developed here can be applied to construct abstract questions with respect to expressions of any syntactic category, independently of whether they occupy quantifiable places in the indicative fragment of a language. The sense in which the variables bound by wh-expressions have a range then dwindles toward the substitutional. For instance, interrogatives like (50) are likely to be put forth only where a fairly narrow range of linguistic alternatives is envisaged:
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(50) What (profession) is John?
Even questions expressed with which are often best answered simply by filling in appropriate material in the site of syntactic movement. So for (19), repeated here, an answer might be as in (51): (19) Which real numbers are transcendental? (51) Those real numbers that are not solutions to any equation are transcendental.
Engdahl (1986) has called attention to interrogatives like (52), (52) Which of his poems does no poet want to read?
where, understanding the pronoun as a variable bound to no poet, the answer might be as in (53): (53) His earliest poems.
I accept Engdahl’s view that these interrogatives likewise involve quantification over nonarguments, in this case over functions. Thus, their logical forms might be represented as in (54): (54) [Which ƒ:(∀x)ƒ(x) is a poem by x][For no poet y] y wants to read f (y)
The need for functional interpretations of this kind is not confined to questions, since it occurs also with relative clauses, and even with definite NPs, as in (55): (55) John made a list of the dates no man should forget.
John’s list might read as follows: children’s birthdays own wedding anniversary Independence Day .....................
The list is a list of those ƒ whose domain is the class of men and whose range is included in the class of dates ƒ(x) such that no man x should forget ƒ(x).8 The recent discussion by Chierchia (1991) shows that for many purposes quantification into interrogatives can be replaced by the functional interpretation. I illustrate using the example (24), repeated here: (24) What did everybody say?
Suppose we understand what as having a functional interpretation, as in Engdahl 1986, and incorporate an appropriate description of the functions over which it ranges, as in (56): (56) [WHƒ : (∀x) x says ƒ(x)] ? (∀y) y said ƒ(y)
Example (56) must be allowed as possible anyway, because of possible answers to (24) such as (57): (57) The speech she had memorized.
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But now we might regard the listiform answer (58) as simply one way of specifying a desired function ƒ: (58) Mary said this, and Susan that, and Margaret the other.
The representation of (24) as (59) appears then to become redundant: (59) (∀y) [WHa] ? y said a
There are several points that would have to be clarified before (56) and (59) could be declared equivalent. As I have defined the interpretation of (59), true and complete answers to it must exhaustively specify for each person y what y said and also what y did not say. If this view is carried over to (56), then exhaustive information about the functions ƒ would be required to answer it, and not merely the specification of some ƒ. On the other hand, in any context in which (58) is a complete and true answer to (59), it is a complete and true answer to (56) as well. The logical limitations of functional interpretation surface when the exported quantifier binds a variable within a larger wh, as in (60): (60) Which picture of each student should we put in the yearbook?
A complete answer to (60) might be listiform, as in (61), or involve pronouns as bound variables, as in (62): (61) (We should put) this picture of Jones, and that picture of Smith, and . . . , and that picture of Robinson. (62) The picture in which he is wearing a hat.
From (60) we have the representation (63): (63) [∀x: student(x)] [WHa: a a picture of x] ? we should put a in the yearbook
For a functional interpretation of (60), we can no longer apply the routine exemplified in (56) but would instead have to posit something like (64): (64) [WHƒ : domain(ƒ) = the students & (∀x)ƒ(x) is a picture of x] ? (∀y)(∀z) [y is a picture of z → (we should put y in the yearbook ↔ y = ƒ(z))]
There are also a number of cases where listiform answers are unavailable, which nevertheless admit functional interpretation. Among these are (65) and (66): (65) Who did President Vest shake hands with after each student introduced him to? (66) Which of his relatives does every student really love?
Only functional answers like His or her mother are appropriate for (65) and (66).9 On the assumption that listiform answers are salient only where there is quantification into questions, these data follow from known conditions on scope of quantifiers and pronominal binding. Thus, in (65) we do not expect to be able to assign each student wide scope, since it is not interpretable with wide scope in (67): (67) President Vest shook hands with his mother after each student introduced him to her.
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Taken all together, then, these problems indicate that, besides functional interpretations of wh, genuine quantification into questions is possible in rather basic sentences of English. And in any case there is no difficulty in constructing sentences with explicit quantification into questions, as in (68): (68) I want to know for each person what that person said.
I return now to some final points about higher types for wh. One can sweep out positions for whole clauses (with why) or adverbs (with how) and even quantifiers, with how many, as in (69): (69) How many books have you decided to read?
Note that (69) is ambiguous, having either the interpretation indicated in (70) or that in (71): (70) [WHQ] ? You have decided to read [Q books] (71) [WHQ] ? [Qx: book(x)] you have decided to read x
All of the cases just discussed seem to fall under the theory presented here.10
5 The presentation of questions The semantics of questions, as I have presented it above, abstracts completely from the ways in which the objects, or the things in ranges of higher types that are values of the interrogative variables, are given to us, or may be given to a questioner or respondent. It furthermore abstracts from the questioner’s motives, if any, and other pragmatic matters. It seems to me that semantic theory, and especially the theory of truth for sentences with interrogative complements, requires this abstraction. We can raise questions that we do not know how to answer, and for which, as Bromberger (1966 and elsewhere) has pointed out, we do not even know what an answer would look like. There is, thus, no requirement in the general case that we have an effective procedure for determining whether a statement is a complete answer to a question—or, indeed, whether it is an answer at all. The distinction between abstract questions and the ways they are presented to us is clearest when the questions are about objects, which may be given from many different perspectives. Thus, to the question Who did John see?, the response John saw Bill is, technically, not even a partial answer, since we are not given which object as value of the interrogative variable a is the reference of Bill. In context, however, matters are not so bleak. We can conceive that the values of the variable are referred to by antecedently given singular terms and thus regard the response as a partial answer after all. More generally, given an abstract question P = p(q(a)[K]) + [f(a)[K]], where f is the restriction on the values of a, K is the class of objects satisfying it, and q(a) is the matrix predicate over which the partition is constructed, and given a class C of closed singular terms in 1–1 correspondence with the members of K, if [f(a)[C]] is {f(c/a): c ∈ C} and p(q(a)[C]) is the partition obtained from p(q(a)[K]) by replacing the objects in K by the respective terms in C that refer to them, we may define Pc = p(q(a)[C]) + [f(a)[C]] as the presentation Pc of P with respect to the substitution class C. A presentation of an abstract question is an abstract question in its own right. In practice we are interested in presentations. If Jones asks me who is playing which position in the outfield, and I respond that the left fielder is playing left field, the right fielder is playing right field, and the center fielder is playing center field, I have understood his question all right, and feign not to
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understand his presentation. It should not be inferred, however, that we can take the presentations and let the questions of which they are presentations go. We can, for example, ask questions whose presentations we know we would not recognize or for which we have no particular presentations in mind. Furthermore, by relating abstract questions to their presentations, we clarify, for instance, the sense in which we say two persons may ask the same question, perhaps without realizing it. Special attention must still be paid to questions [WHa: f(a)] ? q(a) where in fact nothing satisfies f at all. Their abstract questions will be {F}, and so not distinct from any number of other questions expressing {F}. Going intensional does not ameliorate the situation, since there are also restrictions f(a) that are not even possibly satisfied by anything. These cases underscore the fact that in practice the presentations are more nearly what matters to us than the questions they represent. I do not see this consequence as a difficulty of principle, but it does show that a full pragmatic theory must consider the case where, for instance, a person thinks she is asking a nondegenerate question but fails to do so. A further pragmatic and computational issue that is clarified by the conception of abstract questions as partitions, and of partial answers as statements or sets of statements that eliminate certain of the possibilities that the cells of the partitions represent, is that of interpreting what Hintikka (1976) has called the desideratum of a question, or the quantity of information that is wanted by the person asking it. A simple wh-question such as example (8), repeated here, may be associated with different desiderata: (8) Who did John see?
On the view that I have defended, (8) has the logical form (9), (9) [WHa: person(a)] ? John saw a
and the partition it expresses runs through all the possibilities for John’s seeing of persons in the domain of quantification, or at least all that are left open by the background theory. The desideratum of (8) is, therefore, not represented in the question expressed. But desiderata can be so expressed, and among these (as Belnap and Hintikka have pointed out) the existential, represented by (72), and the universal, represented in Southern American English by (73), are quite common: (72) Who for example did John see? (73) Who-all did John see?
Question (72) asks for an example, and (73) for an exhaustive list, of persons John saw. But intermediate desiderata are possible, as in (74): (74) Who are two or three people John saw?
The desideratum of an abstract question may be regarded as a set of statements—namely, those that are “sufficiently informative” (even if possibly false) with respect to that abstract question. Each abstract question comes with its own minimal desideratum—namely, those statements that are partial answers to it. But not all partial answers meet even the existential desideratum; thus, (75) is a partial answer to (9) but would not meet the desideratum that at least one value of a be supplied that is a person John saw: (75) John saw Mary or Bill.
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This desideratum, signaled explicitly in (72), is the class of those S implying, for some person a, John saw ca. Similarly, the desideratum of (73) is {S: For all persons a, S implies John saw ca or ¬(John saw ca)}
Note that (74) has a desideratum in between the universal and the existential. Desiderata may also involve substantive conditions not limited to quantity, as in (76): (76) What is a surprising/routine example of popular novel?
In general, a partial answer to an abstract question Q with desideratum D is a statement in D that is a partial answer to Q; and the ordering of desiderata by stringency corresponds to an ordering of partial answers by informativeness. I return now to some points about quantifying into questions. First of all, with which naturallanguage quantifiers can one quantify in? Certainly, I think, with all of those that are not monotonedecreasing in the sense of Barwise and Cooper (1981: chapter 23 in this volume), where a quantifier Q, interpreted via a map fQ from ordered pairs of subsets of the domain A of quantification into truth values, is monotone-decreasing if fQ(X,Y) = truth and X' ⊆ X then fQ(X',Y) = truth. Examples of quantifiers not monotone-decreasing have been used in the illustrations above. Monotone-decreasing quantifiers, such as at most two people (77) or (at an extreme) no one (78), can never take wide scope: (77) What do at most two people have to say? (78) Is no one at home?
The reason is intuitively clear: it is that, when a question [WHa: f(a)] ? q(x,a) is to be answered for at most two values of x, as in (77), or for none of them, as in (78), then it may be answered by answering for none—that is, by saying anything at all. This intuition corresponds to the feature of our construction that since there is a bloc for each set of persons consisting of at most two of them (for (77)) or none of them (for (78)), there is in each case a bloc for each set of persons consisting of none of them—that is, a bloc {{F}}. Answerhood then becomes degenerate. From the definition, S answers either of the questions expressed by (77) or (78) with the quantifier taking wide scope of S answers {F}, the sole question in the bloc {{F}}, and it answers {F} if inconsistent with F, an unsatisfiable sentence. Then S answers F, and so answers the question, no matter what S may be.
6 Mood and reference My discussion thus far has gone forward on the assumption that theses 1 and 2 of my introduction are correct: namely, that interrogative sentences express abstract questions, and embedded interrogatives refer to the questions that would be expressed by their direct counterparts. There are three major alternatives to these assumptions. The first, which has been taken up in various forms, is that the interrogative, like the imperative, optative, and perhaps other moods, is constructed by attaching an indicator of mood to an indicative (moodless) core. The meaning of the mood indicator then becomes an issue, and the issue of the reference of indirect questions is left up in the air. However, the idea that the difference between It is raining and Is it raining? semantically speaking is only in their mood and not in their content is one that has enjoyed wide appeal, and I will therefore consider it in some detail. The second alternative, elaborated especially by Jaakko Hintikka, is that all questions, whether direct or indirect, dissolve upon analysis into the more ordinary apparatus of propositional atti-
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tudes and ordinary quantifiers. On this view, not only are there no moods but also there are ultimately no quantifications like wh distinctive of questions. This view faces serious difficulties once we move outside direct questions and the complements to epistemic verbs and propositional attitudes, as noted by Karttunen (1977); I will therefore say no more about it here. The third alternative, which has been prominent from time to time and is defended elegantly if briefly by Lewis (1970: chapter 11 in this volume), is that all questions are really indirect, and apparently direct questions amount to indirect questions as complements of an unexpressed performative prefix, with the meaning of “I ask” or “I ask you.” To the obvious objection that it seems absurd to call interrogatives true or false, it may be responded that we do not call performatives true or false, either. However, on the view I will defend, this alternative is not so much mistaken as it is redundant: of course it is true that whoever utters an interrogative asks a question, but we do not need the higher-performative analysis to explain this. A theory of meaning must explain why uttering an indicative sentence is saying something (not necessarily asserting it), and it must explain why uttering a that-clause is not saying anything but simply referring to a proposition. The explanation in truth-conditional semantics is that only sentences, or utterances of sentences, admit of truth and falsehood. That is why, in uttering a sentence, one may, in Wittgenstein’s words, “make a move in the language game,” and, inversely, why in uttering a that-clause in isolation, no move is made at all. This explanatory charge carries over to nonindicatives. In uttering the question whether it is raining, one merely refers to a question, but in uttering Is it raining? that question is necessarily asked. But since direct questions do not appear to have truth values, the sense in which utterances of them must ask things is not apparent. The higher-performative analysis reduces the problem of direct questions to the previous case of indicatives. Utterances of Is it raining? are regarded as notational variants of utterances of I ask (you) (the question) whether it is raining. Since the latter are indicatives, and say things, so do the former. The type of saying is asking, since that concept was built into the analysis. But in fact all of this is unnecessary. Just as the semantic value of an indicative is a truth value, so the semantic value of a direct yes-no question is an unordered pair of truth values—one for each cell of its partition. Just as the semantic value of a that-clause is a proposition, so the semantic value of an indirect yes-no question is an unordered pair of propositions. And just as the proposition that it is raining is expressed by It is raining, so the pair {the proposition that it is raining, the proposition that it is not raining} is expressed by Is it raining? It follows immediately, first, that interrogatives cannot be called true or false; and, second, if we assume that ask is nothing but that variant of say whose proper objects are questions, that whoever utters an interrogative asks a question. Care must be taken in not freighting up the notion of asking here with any of the motives for raising a question. English has say and assert, where to assert is to say with assertive force. The verb ask, however, is ambiguous. In one sense it amounts to say, but its objects must be questions. In another sense it involves what we might call interrogative force (and is so understood in the higher-performative analysis). One can raise questions to which one perfectly well knows the answer, or doesn’t care what the answer may be, and one can also raise questions nonseriously. An actor on a stage says things without asserting them and utters questions without interrogative force. I take it that the verb ask may be so understood that an utterance by a of (79) justifies the subsequent assertion by anyone of (80): (79) Is dinner ready? (80) a asked whether dinner was ready.
The position I have outlined may be clarified by being expressed in an extension of the language IL of intensional logic. In that language there are sentences of the syntactic type t of truth
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values and expressions for propositions, of syntactic type (s, t), corresponding semantically to propositions—that is, sets of possible worlds. Interrogatives as I have interpreted them here would call for an extension of the type theory so that there would be a type {t,t} of unordered pairs of type t, whose semantic interpretation would be unordered pairs of truth values, and a type {(s,t), (s,t)} of unordered pairs of propositions. Verbs like ask and wonder would take arguments of this type. In this setting, the extension of an interrogative is a pair of truth values, and its intension a pair of propositions. Indeed, the account of interrogatives given here can be expressed in its entirety in the setting envisaged. If we assume that the reference of indirect questions is as I have suggested, then the higherperformative analysis of direct questions becomes redundant. Whether that analysis is adopted or not, however, the semantics of interrogatives does not take us out of the truth-conditional arena. In particular, there are no moods in the semantics of questions, either because they are not represented at all or because any work they might have done is taken up by the higher performative verb. However, there is a weighty tradition of thinking of moods as semantically independent items, and I wish to turn briefly to the difficulties in making out just what this tradition has in mind. The question we were considering was, Why can saying an interrogative sentence such as (81) constitute asking a question—namely, the question whether (82)? (81) Is it raining? (82) It is raining.
An answer that suggests itself is that the syntactic element represented in English by inversion and a characteristic intonation pattern, and in other languages by other syntactic devices, is a sign that the speaker of the sentence is performing a speech act with interrogative force, whose content is given by the clause on which the syntactic element operated. Thus, the datum (83) is an application of a rule of English: (83) If u is an utterance of (2), then the speaker of u asks (with interrogative force) the question whether (82).
As Davidson (1984c) points out, however, the above and kindred conceptions of mood fail to make room for nonserious uses of language. Taken quite literally, this account of mood implies that when the minister at a wedding rehearsal says (84), (84) Do you take this woman for your wife?
then he (or she) is asking with interrogative force whether the man addressed takes that woman for his wife. But he is not, in the desired sense, asking anything; it is only a rehearsal. Note that the higher-performative analysis does not face counterexamples along these lines. Whether the minister is asking anything is determined by whether (85), which is what he in fact said, is true: (85) I ask you whether you take this woman for your wife.
But since we are only at a rehearsal, it is not true. My own view, which does not recognize a higher performative, has it that the minister in a sense asks a question, but without interrogative force. The theory of mood developed in Davidson 1984c is specifically designed to allow for nonserious uses of language. Davidson’s suggestion is that yes-no questions are a kind of portmanteau, where the indicator of mood—or, as he calls it, the mood-setter—functions as a comment on the indicative core. Thus, Is it raining? is understood as in (86):
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(86) It is raining. That was interrogative in force.
The minister at the wedding rehearsal says nothing with interrogative force, even though in a way he says he does. It is obvious that Davidson’s suggestion runs into difficulties with wh-interrogatives (as Davidson notes in 1984c, 115), although it might be suggested that the indicative core is in this case an open sentence or utterance. But does his view really explain why interrogatives cannot be assessed for their truth values? Hornsby (1986) suggests that the explanation offered—namely, that interrogatives are a portmanteau of two sentences—is rather weak; for the same problem in more detail, see Segal 1988. Hornsby herself proposes that the convention or rules of language governing interrogatives be expressed adverbially, as in (87): (87) By saying Is it raining? a speaker says interrogatively that (or: asks-whether) it is raining.
To say no more than this about interrogatives is to leave indirect questions in the lurch, as Hornsby recognizes. But her aim is to formulate a view according to which the speaker in asking a question is not, in contrast to Davidson’s view, tacitly describing with words what he is doing. Still, the expression says interrogatively is left as an unanalyzed term of art. If it were interpreted as says with interrogative force, then I do not see that we would have better than Davidson’s theory back again. Now, if I am right to say that yes-no questions express partitions, unordered pairs consisting of a proposition and its negation, then we have an explanation of why yes-no questions may but need not have interrogative force that is parallel to the explanation of why indicatives may but need not have assertive force. There is no need of mood indicators at all, for the semantic work done by syntactic inversion or the abstract question morpheme formalized above by the question mark is just to convert propositions into appropriate unordered pairs. Indeed, the view that I have advocated here is partly based on the following thought: any correct account of indirect questions must assign them a reference, and that reference will have the property that, when presented via a main clause, its presentation can, but need not, constitute asking about it. If so, then we needn’t suppose that an interrogative does not wear its whole logical syntax on its face.
Appendix: Licensing negative polarity The English negative polarity items any and ever are freely licensed in interrogative environments, as in (88) and (89): (88) Did anybody speak? John wonders whether anybody spoke. *Anybody spoke. (89) Have you ever been to France? Whether he has ever been to France is known to the police. *He has ever been to France. *That he has ever been to France is known to the police.
In this appendix I will offer an explanation of such licensing, drawing on the discussion above and on the fuller account of English choice questions developed in Higginbotham 1991a. Following the latter paper, I will assume without argument that English disjunction or is always to be construed as in construction with a possibly tacit occurrence of either, and that the latter is a quantifier admitting a universal interpretation. The data that support this view are exemplified by the ambiguity of modal sentences such as (90):
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John will play chess or checkers.
Besides the obvious interpretation that John will play chess, or else he will play checkers, (90) also has an interpretation equivalent to John will play chess and John will play checkers. The second interpretation, I will assume, arises because (90) has in fact a syntactic structure as in (91), (91)
[either]i [John will play [chess or checkers]i]
and at LF a structure as in (92). (92)
[either chess or checkersi [John will play ti]
The prefix is a universal quantifier, so that we have in effect (93): (93)
[∀x: x = chess or x = checkers] John will play x
Proceeding now beyond my earlier discussion, I will assume that the syntax of (90) puts either in the Spec position of its clause, so that we have at LF (94): (94)
[CP [Spec either chess or checkers]i [C’ C [IP John will play ti]]]
This assumption is more specific than I will actually require. What will be necessary is that there be an intervening position—here C—between the quantification and the sentence over which it quantifies, and that this position be interpreted as the “?” of the discussion above is interpreted— that is, as passing from the type of propositions to the type of partitions. It is obvious that English whether is wh + either, as when is wh + then, where is wh + there, and so on. Suppose now that this etymological point has semantic significance, so that whether is interpreted as a universal quantification in [Spec, CP], hence outside the scope of “?” in C. Unlike either, and unlike other wh-words, whether is restricted to this syntactic position. Thus, we do not have (95), in contrast to (96) or (97): (95) (96) (97)
*Who saw whether Mary or Bill? Who saw either Mary or Bill? Who saw who?
We may assume further that just as every occurrence of either must go together with an occurrence of the disjunction or, so must every occurrence of whether, the sole exception being the case where the disjunction is tacit, and over the whole indicative IP. Thus, (98) will have a structure as in (99), and (100) a structure as in (101), prior ellipsis: (98) (99) (100) (101)
whether John played chess or checkers [CP [Spec whether]i [C’[C ?] [IP John played [chess or checkers]i]]] whether John left (or not) [[whether] [? [John left or John did not leave]]]
Consider now the LF representation and the accompanying semantics of (101) on the assumptions given. The representation will be (102), and its interpretation will be that of (103): (102) (103)
[[whether John left or John did not leave]i [? ti]] [∀p: p = that John left or p = that John did not leave] ? p
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Applying the semantics, the constituent ‘?p’ expresses the partition {p | ¬p}
with ‘p’ a free variable. Quantification into this position by the universal quantifier gives the question of order 1: {{John left | John did not leave}, {¬(John left) | ¬(John did not leave)}}
Manifestly, the latter is equivalent, in the sense of having all the same partial and complete answers, to {John left | John did not leave}
so that the quantification has accomplished nothing, semantically speaking. On the assumptions stated, however, whether-questions in which the scope of whether is the whole clause all have the property at LF that the elements of the clause appear within the restriction of a universal quantification, and such appearance is known to license negative polarity items. For the licensing itself I will adopt the explanation proposed by Ladusaw ( 1983) and others, that negative polarity items may appear only within the scope of downwardentailing expressions (definitions and a theoretical discussion are provided below). It follows at once that negative polarity items are licensed within interrogatives, where the licenser is overt or tacit whether. A crucial point for the above analysis of the licensing of negative polarity items in interrogatives is seen in minimal pairs such as (104)–(105) and (106)–(107): (104) (105) (106) (107)
Mary knows whether John played chess or checkers. Mary knows whether anyone played chess or checkers. Did John play chess or checkers? Did anyone play chess or checkers?
Examples (104) and (106) are of course ambiguous. On the view taken here, the ambiguity derives from the possibility of construing the disjunctive constituent chess or checkers either with whether, giving the interpretation of the embedded clause as a choice question, or else with its own tacit either within that constituent, giving the interpretation of that clause as a yes-no question. But (105) and (107) are not ambiguous: the complement cannot be interpreted as a choice question about chess versus checkers. The explanation in terms of the analysis above is that for the choice question we have the representation (108): (108)
[[whether chess or checkers]i [? [John/anyone played ti]]]
But this representation fails to license the negative polarity item anyone. To license it, we require that the entire clause anyone played chess or checkers be within the scope of whether, as in (109): (109)
[[whether anyone played chess or checkers (or not)i [? ti]]
But then the disjunction of chess or checkers is not construed with whether, so that the possibility of a choice question is precluded.
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The interpretation of whether as universal quantification is not confined to the domain of interrogatives but is corroborated by the use of whether analogous to a free relative pronoun, as in (110): (110)
You’ll have a good time whether you go to London or Paris.
The sentence means that you’ll have a good time if you go to London and also if you go to Paris. This interpretation follows from the assignment of the LF representation (111), or, with variables explicit, (112). (111) (112)
[whether London or Paris]i [you’ll have a good time if you go to ti] [∀x: x = London or x = Paris] [you’ll have a good time if you go to x]
When negative polarity is licensed within the scope of some other wh-expression than whether, as in (113), we assume that a tacit whether is present anyway, giving the LF representation (114): (113) (114)
Who had anything to say? [WHa] [∀p: p = that a had anything to say or p = that ¬(a had anything to say)] ? p
The equivalences noted above carry over to this case, so that the interpretation is not disrupted. There are a number of further linguistic points relevant to the hypothesis presented here that I hope to expand upon in later work. To review: the hypothesis is that negative polarity items are licensed in interrogatives because the latter are governed by the disjunction-host whether. This word behaves like its counterpart either in admitting an interpretation as a universal quantification. When that quantification is over propositions, then the constituents of the interrogative clause will be within its scope and the environment will satisfy known conditions on the licensing of negative polarity in English. I turn now to some formal points that have been so far left in abeyance. Ladusaw’s notion of downward-entailingness is defined in terms of implication and thus applies in the first instance only to indicative sentences. A quantifier Q is downward-entailing (with respect to its restriction) if the schema in (115) is valid: (115)
[Qx: F(x)] G(x) [∀x: H(x)] F(x) [Qx: H(x)] G(x)
By analogy with the indicative case, an expression of generality Q (which may be a quantifier, wh, or perhaps a “mix” of the two, such as which two) will be said to be downward-entailing for interrogatives if, where Q is the question expressed by the result of prefixing ‘[Qx: F(x)]’ to ‘?G(x)’, and Q' is the question expressed by the result of prefixing ‘[Qx: H(x)]’ to ‘?G(x)’, then we have (116): (116)
If [∀x: H(x)] F(x), then if S is a partial (complete) answer to Q, then S is a partial (complete) answer to Q'.
In other words, speaking derivatively in terms of answers to sentences rather than to the questions they express, the schema (117) is valid: (117)
S partially (completely) answers [Qx: F(x)] ? G(x) [∀x: H(x)] F(x) S partially (completely) answers [Qx: H(x)] ? G(x)
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We shall need the observation about quantifiers in natural language that they are all intersective in the sense of Higginbotham and May (1978, 1981). I construe quantifiers Q as modeltheoretically interpreted by functions fQ from ordered pairs (X, Y ) of subsets of the domain of quantification A into truth values. Q is intersective if fQ(X,Y ) = fQ(X,X ∩ Y). From intersectivity it follows that a natural-language quantifier that is downward-entailing, or for purposes of this exposition downward-entailing (DE) for indicatives, is DE for interrogatives as well. For suppose that Q is DE for indicatives, and let S be a partial answer to (118): (118)
[Qx: F(x)] ? G(x)
Each question Qa expressed by ‘?G(x)’ when a is assigned to x will be of some given order n, the same for all a. If F| is the extension of ‘F’, then for every subset A' of F| such that fQ(F|)(A') = truth, there is a bloc BA' in the question Q of order n + 1 expressed by (118), and Q consists entirely of such blocs. Since S answers Q, there is a bloc B in Q and a subset A' of F| such that S answers Qa for every a ∈ A'. Consider the interrogative (119): (119)
[Qx: H(x)] ? G(x)
If H| is the extension of ‘H’, then since Q is DE for indicatives, if H| ⊆ F| then fQ(H|)(A') = truth. Since Q is intersective, fQ(H|)(H| ∩ A') = truth. Then S answers every Qa for a ∈ H| ∩ A', and is therefore an answer to (119); and S is a complete answer if it was a complete answer to (118). So if Q is DE for indicatives and Q is intersective, then Q is DE for interrogatives. Since all naturallanguage Q are intersective, this completes the proof. The converse inclusion—that if Q is DE for interrogatives it is also DE for indicatives— requires stronger assumptions than the intersectivity of Q. Following the customary terminology, say that Q is monotone-increasing (-decreasing) if fQ(X) (Y) = truth and Y ⊆ Z (Z ⊆ Y) implies fQ(X)(Z) = truth, and indefinite if fQ(X)(Y) = fQ(Y)(X), for all X, Y, and Z. All natural-language quantifiers are monotone-increasing, monotone-decreasing, or indefinite (including combinations of these). If Q is monotone-decreasing, then Q does not quantify into interrogatives, and we have seen pragmatic reasons why. For those same pragmatic reasons, we may assume that fQ(f)(Y) = falsehood, and, if Q is indefinite, that fQ(X)(f) = falsehood as well. Suppose then that Q is not DE for indicatives, and consider a model M where (120) and (121) are true and (122) is false: (120) (121) (122)
[Qx: F(x)] G(x) [∀x: H(x)] F(x) [Qx: H(x)] G(x)
Then the extension F| of ‘F’ is nonempty. Consider with respect to this model the interrogatives (123) and (124): (123) (124)
[Qx: F(x)] ? (G(x) & H(x)) [Qx: H(x)] ? (G(x) & H(x))
We are going to show that there is a true partial answer to (123) that is not a partial answer to (124), so that Q is not DE for interrogatives, either. Assume on the contrary that Q is DE for interrogatives. Because (120) is true in M, the question expressed by (123) in M will have a bloc for the nonempty subset F| ∩ G| of F|. Hence, if there is an object a in M that lies in F| and G| but not in H|, then (125) is a true partial answer to (123) that is not a partial answer to (124 ):
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(125)
G(a) & ¬H(a)
Hence, F| ∩ G| ⊆ H. Then Q cannot be indefinite; for it were, then since it follows from the truth of (121) in M that F| ∩ G| = G| ∩ H|, and the truth values of (120) and (122) depend only on the respective cardinalities of F| ∩ G| and G| ∩ H|, these formulas would have the same truth value in M, contrary to hypothesis. The only remaining possibility is that Q is monotone-increasing, but not indefinite. The blocs of the question expressed by (124) in M correspond to those subsets S of H| for which fQ(H|,S) = truth. If we could choose S ⊆ G ∩ H, then since Q is monotone-increasing, (122) would be true in M. If there are no S for which fQ(H|,S) = truth, then the question expressed by (124) in M is degenerate, and so has no proper partial answers. But otherwise there are elements in G| that are not in H|; and by the previous argument (125) is then a partial answer to (123) but not to (124). The proof above can be strengthened to show that there are complete answers to (123) that are not complete answers to (124). I omit the details here. Notes Most of this paper is expanded from the less technical parts of one presented at a meeting of the Ockham Society, Oxford, March 1990, Roger Teichmann commenting; at the Workshop on Logical Form, University of California, Irvine, April 1990; and at the meeting of the Association for Symbolic Logic, CarnegieMellon University, Pittsburgh, January 1991. Other material is new, and some of it would not have been possible without class discussion in a seminar at MIT in the spring term of 1992 taught jointly with Irene Heim. For a technical supplement on direct questions, see Higginbotham 1991b:secs. 6 and 7. I have incorporated some remarks prompted by Teichmann’s comments, and discussions with a number of persons, including especially Utpal Lahiri, Gabriel Segal, and Robert Stainton, have also been very helpful. I note here the background to this paper. My first work on the topic of interrogatives was carried out jointly with Robert May, and some was published in Higginbotham and May 1978, 1981. I presented a more extended view at the CUNY Graduate Center, New York, October 1978, and at MIT, November 1979. This work was influenced particularly by Levi (1967); May (1989) has also carried out some of the further development. Further research was done at the University of Texas at Austin in 1980 under grant BNS 76-20307 A-01 from the National Science Foundation. I am grateful to Stanley Peters for this opportunity, and to him, Hans Kamp, and Lauri Karttunen for comments and discussion. The views that I then arrived at, and presented in a seminar at MIT in 1982 together with Sylvain Bromberger, I subsequently found to overlap in part with the research report Belnap 1963, some of the material from which was published as Belnap and Steel 1976. Discussion with Belnap at a conference sponsored by the Sloan Foundation at McGill University, 1982, confirmed that the method he and Michael Bennett envisaged for adding quantification over questions was similar to mine as well. (I have noted below where I follow Belnap’s terminology, but have not in general cited specific parallels to his work.) Finally, Groenendijk and Stokhof (1984, 1989) have independently arrived at a view of what simple interrogatives express that is similar to what I advance here in section I. 1. Belnap (1969) observes that interrogatives may be expected to have presuppositions even for a language whose indicatives do not. 2. The presuppositions of multiple singular wh-questions are examined in Barss 1990. 3. See May 1985. 4. For a different implementation of the same basic idea, see Belnap 1982, following work by Michael Bennett. 5. If the background theory is w-incomplete, even finiteness (or emptiness) of the set of positive instances is not enough to guarantee that an answer is attainable. For example, let the background theory be Peano arithmetic, where P represents provability and g+ is the numeral for the Gödel number of a sentence g provably equivalent to its own unprovability, and consider (i), representing the question What is a proof of g? (i)
[WHa] ? P(a,g+)
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In the standard model, only the cell containing ‘¬P(a+,g+)’ for each numeral a+ is consistent with the background theory, but the true and complete answer ‘(∀x) ¬P(x,g+)’ is not provable. 6. There is another, irrelevant interpretation of (41), parallel to the natural interpretation of I wondered about school. 7. In the interest of readability I omit extra curly brackets when no ambiguity threatens. Thus, what is displayed in the text would be fully articulated as {{p} : {¬p}}; similarly for a number of later examples. 8. I believe that the functional interpretation also provides the proper mechanism for the examples in Geach 1969 such as (i) (p. 121): (i)
The one woman whom every true Englishman honors above all other women is his mother.
9. Examples like (66) are due to Engdahl 1986; (65) is modeled after an example in Collins 1992. 10. See Kroch 1989, Cinque 1990, and Szabolcsi and Zwarts 1990 for a discussion of ambiguities of this type.
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35 DANIEL VANDERVEKEN
Success, Satisfaction, and Truth in the Logic of Speech Acts and Formal Semantics
There has been much controversy about the role and place of speech act theory in the study of language. Following Morris (1975), semiotics is traditionally divided into three branches: syntax, semantics, and pragmatics. Syntax deals with relations that exist only between linguistic expressions (e.g., the rules of formation of sentences), semantics with relations that exist between linguistic expressions and their meanings (e.g., their senses or their denotations), and pragmatics with relations that exist between linguistic expressions and their meanings and uses in contexts of utterance. Because speakers use language to perform speech acts, most philosophers and linguists, following Carnap, have first tended to place speech act theory in pragmatics rather than in semantics. Moreover, up to the present time, the contemporary philosophy of language has been largely divided into two trends. The logical trend—founded by Frege and Russell and later developed by Carnap, Montague, and others—studies how language corresponds to the world. It concentrates on the analysis of truth conditions of declarative sentences. The ordinary language analysis trend—founded by Wittgenstein and Austin and later developed by Searle and Grice—studies how and for which purposes language is used in discourse. It concentrates on speech acts that speakers perform by uttering all types of sentences. As Austin (1962) pointed out, by uttering sentences under appropriate conditions, speakers characteristically perform illocutionary acts such as assertions, promises, requests, declarations, and apologies. Moreover, when their utterances have effects on the audience, they also occasionally perform perlocutionary acts. For example, they can convince, influence, please, amuse, or embarrass the hearer. Like Austin and Searle, I think that the primary units of meaning in the use and comprehension of language are not propositions or isolated truth conditions but are complete illocutionary acts. By making a meaningful utterance, a speaker always attempts to perform an illocutionary act. This is part of what he means and intends to communicate to the hearer.
This is an original chapter for this volume.
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In the case of a literal utterance, the speaker means to perform the illocutionary act expressed by the sentence that he uses in the context of his utterance. As Searle (1969) pointed out, most elementary illocutionary acts are of the form F(P): they consist of an illocutionary force1 F with a propositional content. Austin discovered illocutionary forces by paying attention to the fact that certain sentences—for example, “I order you to come,” “I swear to tell the truth”—can be used performatively: their literal utterances in appropriate conditions constitute the very performance of the action named by their verb. Austin called these sentences performative sentences in opposition to others that he called constative sentences. However Austin came soon to notice that all kinds of sentences whether performative or not serve to perform illocutionary acts. So the study of illocutionary acts turned out to be needed not only for the analysis of performative sentences but also for the general theory of meaning and communication. If it is not possible to express a propositional content without an illocutionary force, then most elementary sentences whose logical form is completely analyzed contain an illocutionary force marker in addition to a clause expressing a proposition. As linguists and grammarians had long acknowledged in their classification of sentential types, verb mood, word order, and punctuation signs are the most common features of illocutionary markers. Thus declarative sentences serve to make assertions; imperative sentences to give directives to the hearer; interrogative sentences to ask questions; and exclamatory sentences to express the speaker’s attitudes. Using logical formalisms, philosophers of the logical trend have greatly contributed to the theory of sentence meaning. They have analyzed the logical form and truth conditions of propositional contents of utterances, and they have formulated a general logic of sense and denotation. In particular, they have explicated the meanings of important words and syncategorematic expressions such as truth, modal, and temporal connectives and quantifiers, all of which serve to determine the truth conditions of propositional contents. However, because they have ignored illocutionary aspects of meaning, they have failed to analyze the meaning of expressions such as force markers and performative verbs that serve to determine the illocutionary forces of utterances. Morris’s division of semiotics was mainly programmatic. The need for a more precise characterization of the delimitations between semantics and pragmatics has become clear in recent years. New philosophical logics such as the logic of demonstratives and illocutionary logic have analyzed the logical form of expressions whose linguistic meaning is systematically related to use. First, contexts of utterance and moments of time were introduced in semantic interpretations of the logic of demonstratives and temporal logic in order to analyze the linguistic meaning of indexical expressions like the pronouns “I” and “you” and adverbs of time and location like “now” and “here,” whose senses and denotations are systematically dependent on contextual features such as the identity of the speaker and hearer and the time and place of utterance. Since Kaplan (1978b) worked on demonstratives, the study of indexical expressions which was first assigned by Bar-Hillel (1954) and Montague (1968) to pragmatics is now commonly assigned to semantics. Similarly, the systematic analysis by Searle and myself (1985) of English performative verbs and illocutionary force makers has shown that their meaning contributes systematically to the determination of the forces of utterances in which they occur. Thus, the identification of sentence meaning with truth conditions is now challenged in the philosophy of language. Many philosophers and linguists no longer accept the thesis that the meaning of linguistic expressions only contributes to determining the propositional content and truth conditions of utterances.
Section 1 Principles of illocutionary logic I have formulated such principles in various papers and with Searle in Foundations of Illocutionary Logic (1985). I have used proof and model theory in Meaning and Speech Acts (1990; 1991b) in
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order to proceed to the formalization. As Searle and I pointed out, language use not only consists in the performance of elementary illocutionary acts with a force and a propositional content; it also consists in the performance of more complex illocutionary acts whose logical form is not reducible to that of elementary speech acts. Illocutionary denegations, conditional speech acts, and conjunctions of illocutionary acts are the three basic kinds of complex illocutionary acts. From a logical point of view, acts of illocutionary denegations are of the form ¬A; their linguistic aim is to make explicit the nonperformance by the speaker of an illocutionary act A. For example, a rejection is the illocutionary denegation of the acceptance of an offer. Conditional speech acts are of the form (P ⇒ A); their linguistic aim is to perform an illocutionary act A not categorically but on the condition that a proposition P be true. Thus, an offer is a promise that is conditional on the hearer’s acceptance. Finally, conjunctions of illocutionary acts are of the form (A & B); their aim is to perform simultaneously two illocutionary acts A and B. For example, an alert is the conjunction of an assertion that some imminent potential danger exists and of a warning to the hearer to prepare for action against that danger. Sentences containing illocutionary connectives serve to perform such complex illocutionary acts. For example, “if ” and the semicolon play the role of illocutionary connectives of conditional and conjunction in the two sentences “If it is difficult, help me!” and “Paul is leaving; are you going with him?” By nature illocutionary acts are intentional actions. Speakers who perform illocutionary acts always attempt to perform these acts by making meaningful utterances. As is the case for human actions in general, attempts to perform illocutionary acts can succeed or fail. First, speakers must use appropriate sentences in order to express their attempted illocutionary act in the context of their utterance. Second, that context must be appropriate for the performance of that illocutionary act. For example, an attempt to threaten someone is not successful when the speaker speaks to the wrong person or when he is in a situation where it is obvious that he has not the least intention to do what he threatens to do. Moreover, illocutionary acts are directed at objects and states of affairs, and, even when they are successful, they can still fail to be satisfied, when the world does not fit their propositional content. Thus successful assertions can be false, successful promises can be broken, and successful requests can be refused. The conditions of success of an illocutionary act are the conditions that must obtain in a context of utterance in order that the speaker succeed in performing that act in that context. Thus, a condition of success of a promise is that the speaker commit himself to carrying out a future course of action. Failure to perform an illocutionary act is a special case of lack of performance which occurs only in contexts where the speaker makes an unsuccessful attempt to perform that illocutionary act. The conditions of satisfaction of an illocutionary act are the conditions that must obtain in a possible context of utterance in order that the act be satisfied in the world of that context. For example, a condition of satisfaction of a promise is that the speaker carry out in the world the promised course of action. The notion of a condition of satisfaction is a generalization of the notion of a truth condition that is necessary to cover all illocutionary forces. Just as an assertion is satisfied when it is true, a command is satisfied when it is obeyed, a promise when it is kept, a request when it is granted, and similarly for all other illocutionary forces. According to Searle and me, one cannot understand the nature of illocutionary acts without understanding their success and satisfaction conditions. Moreover, the two types of success and satisfaction conditions of elementary illocutionary acts are not reducible to the truth conditions of their propositional contents. Consequently, the two single most important objectives of the logic of speech acts and semantics of ordinary language are to develop new theories of success and of satisfaction integrating the classical theory of truth for propositions. One reason why earlier attempts to formally analyze nondeclarative sentences and performatives have failed is that they have tended to identify illocutionary acts with their conditions of satisfaction and to reduce satisfaction to truth. However, as I have argued repeatedly, one cannot leave out the general notion of success in the analysis of the logical form of actions in general
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and of speech acts in particular. Moreover, as we will see later, the notion of satisfaction is richer than the notion of truth. The fundamental philosophical concepts of success, satisfaction, and truth are logically related. On the one hand, the satisfaction of elementary illocutionary acts requires the truth of their propositional content; there is no satisfaction without correspondence. On the other hand, the successful performance of declaratory illocutionary acts brings about the truth of their propositional content; any successful declaration constitutes the performance by the speaker of the action represented by the propositional content. Searle and I have analyzed each performative utterance as being a declaration by the speaker that he performs by virtue of his utterance the illocutionary act that he represents. In this view, any successful literal utterance of a performative sentence is performative because a successful declaration makes its propositional content true, and the propositional content in this case is that the speaker performs the illocutionary act expressed by the performative verb. Thus by a successful literal utterance of “1 request your help,” a speaker requests help by way of primarily declaring that he make that request. As one can expect, speakers whose utterances constitute successful, nondefective, and satisfied illocutionary acts are felicitous. So in Austin’s terminology, illocutionary acts have felicity conditions. Searle and I did not analyze the logical form of propositional contents in Foundations. We contributed to the theory of success of illocutionary acts. Our main objective was to study illocutionary commitment as it is determined by types of illocutionary act. By virtue of their logical form, certain illocutionary acts strongly commit the speaker to others: it is not possible to perform them without eo ipso performing the others. Thus supplications and invitations contain requests. However, sometimes illocutionary commitment is weaker. The successful performance of the illocutionary act weakly commits the speaker to another act that he does not openly perform. For example, someone who gives an order to a hearer is committed to giving him the corresponding permission even if he does not openly give that permission. Such a weak illocutionary commitment shows itself in the fact that one cannot simultaneously give an order and denegate the permission. It is paradoxical to say “I order you and I do not permit you to go away .” Most propositions are true or false, no matter whether or not they are expressed. All depends on whether the things are in the world as they represent them. In contrast, an illocutionary act cannot be performed unless a speaker attempts to perform it and expresses his intention in an utterance. A performed illocutionary act is always an illocutionary act that the speaker succeeds in performing. Unlike truth, success is then inseparable from thought. For that reason, the theory of success of illocutionary logic is much more effective (finite and decidable) and innate than that of truth and satisfaction. Certain illocutionary acts are unperformable in the sense that they cannot be performed in any possible context of utterance. We know that a priori by virtue of competence, and we never attempt to perform them. So we never speak literally when we use an illocutionarily inconsistent sentence like “I order and forbid you to come,” which expresses a nonperformable illocution. We mean something other than what we say. However many unsatisfiable illocutionary acts (for example, many necessarily false assertions) are performable. So we can use with success truth conditionally inconsistent sentences like “Whales are fishes” expressing unsatisfiable illocutions. As Wittgenstein pointed out, meaning is well determined: “It seems clear that what we mean must always be sharp” (Notebooks p. 68).2 So each speaker always knows which illocutionary act he primarily attempts to perform by his utterance. Moreover, each speaker also knows which other illocutionary acts he would perform if his utterance were successful. He knows to which illocutionary acts he is strongly committed in each context of utterance. Whenever an illocutionary force Fl contains another force F2 (for example, the force of prediction contains that of assertion), we know that by virtue of competence so that each speech act of the form F1(P) commits us to performing the corresponding act F2(P). Similarly, whenever we know by virtue of competence that a proposition P cannot be true unless another proposition Q is also true, illocutionary acts of the form F(P) whose force is primitive and nonexpressive strongly
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commit us to performing corresponding acts of the form F(Q). Thus we cannot assert a conjunction P ∧ Q without asserting each conjunct P and Q. So the speaker’s strong illocutionary commitments are well known and, for that reason, well founded, decidable, and finite. Here are brief explanations of the basic principles of illocutionary logic. Components of illocutionary force Each illocutionary force can be divided into six types of component which serve to determine the conditions of success and satisfaction of the illocutionary acts with that force. The notion of illocutionary force is too complex to be taken as a primitive notion. In illocutionary logic, it is derived from a few simpler notions. Thus, each force is divided into six types of components: an illocutionary point, a mode of achievement of illocutionary point, propositional content, preparatory conditions, sincerity conditions, and a degree of strength. Two illocutionary forces Fl and F2 with the same components are identical, for all illocutionary acts of the form F1 (P) and F2 (P) serve the same linguistic purposes in the use of language. Illocutionary point The principal component of each illocutionary force is its illocutionary point, for that point determines the direction of fit of utterances with that force. There are exactly five illocutionary points that speakers can attempt to achieve in expressing a propositional content with an illocutionary force: the assertive, commissive, directive, declaratory, and expressive points. They correspond to the four possible directions of fit that exist between words and things in language use: The words-to-things direction of fit. When the force has the words-to-things direction of fit, the illocutionary act is satisfied when its propositional content fits a state of affairs existing (in general independently) in the world. Illocutionary acts with the assertive point (e.g., conjectures, assertions, testimonies, and predictions) have the words-to-world direction of fit. Their point is to represent how things are. Thus, in the case of assertive utterances, the words must correspond to the objects of reference as they stand in the world. The things-to-words direction of fit. When the force has the things-to-words direction of fit, the illocutionary act is satisfied when the world is transformed to fit the propositional content. Illocutionary acts with the commissive or directive point have the thingsto-words direction of fit. Their point is to have the world transformed by the future course of action of the speaker (commissives) or of the hearer (directives) in order to match the propositional content of the utterance. In this case, the things in the world have to be changed to correspond to the words uttered in the performance of the illocutionary act. Promises, threats, vows, and pledges are commissive illocutions. Requests, questions, invitations, orders, commands, and advice are directives. The double direction of fit. When the force has the double direction of fit, the illocutionary act is satisfied when the world is transformed by an action of the speaker to fit the propositional content by virtue of the fact that the speaker represents it as being so transformed. Illocutionary acts with the declaratory illocutionary point (e.g., resignations, definitions, condemnations, and blessings) have the double direction of fit. Their point is to get the world to match the propositional content by saying that the propositional content matches the world. In successful declarations, objects of reference are then changed to correspond to words in the very utterance of these words. As Austin pointed out, in such utterances, we do things with words.
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The empty direction of fit. For some illocutionary acts, there is no question of success or failure of fit, and their propositional content is in general presupposed to be true. Such are the illocutionary acts with the expressive point—for example, thanks, apologies, congratulations, and boasts. They have the empty direction of fit. Their point is just to express a mental state of the speaker about the state of affairs represented by the propositional content. Thus, in expressive utterances, speakers do not attempt to establish a correspondence between words and things. They just want to manifest their feelings about the ways in which objects are in the world. Each illocutionary point serves one linguistic purpose in relating propositions to the world, so different illocutionary points have different conditions of achievement. For that reason, the type of an illocutionary point P is that of a function which associates with each possible context of utterance c and proposition P the value success when the speaker achieves the illocutionary point P on proposition P in context c, and the value unsuccess otherwise. All forces with the same illocutionary point do not play the same role in the use of language. For example, orders, commands, requests, supplications, questions, recommendations, and demands are directives to be made in different conditions. Mode of achievement Illocutionary points, like most purposes of our actions, can be achieved in various ways. The mode of achievement of an illocutionary force determines how its point must be achieved on the propositional content where there is a successful performance of an act with that force. For example, in a command the speaker must invoke a position of authority over the hearer, whereas in a request he must give the option of refusal to the hearer. Such modes of achievement are expressed in English by adverbs such as “please” and “whether you like it or not” in imperative sentences. From a logical point of view, the mode of achievement of a force restricts the conditions of achievement of its point by requiring certain specific means or ways of achievement. Formally, a mode of achievement m is a restriction function which has the same type as illocutionary points. Propositional content conditions Many illocutionary forces impose conditions on the set of propositions that can be taken as propositional contents of acts with that force in a context of utterance. For example, the propositional content of a prediction must represent a fact which is future with respect to the moment of utterance. Such conditions are propositional content conditions. The type of a propositional content condition q is that of a function which associates with each possible context a set of propositions. Some propositional content conditions are determined by illocutionary point. For example, all commissive illocutionary forces have as a condition that their propositional content represent a future course of action of the speaker. Other propositional content conditions are specific to certain illocutionary forces. For example, a proposal is a directive speech act with a special propositional content condition. To propose that a hearer carry out an action is to suggest that he accept doing that action. Propositional content conditions are expressed by syntactic constraints on the grammatical form of the clauses of elementary sentences. For example, the main verb of imperative sentences must be in the second person and in the future tense. Preparatory conditions By performing an illocutionary act, the speaker also presupposes that certain propositions are true in the context of the utterance. For example, a speaker who promises to do something
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presupposes that his future action is good for the hearer. The preparatory conditions of an illocutionary force determine which propositions the speaker would presuppose if he were performing acts with that force in a possible context of utterance. So the logical type of a preparatory condition S is that of a function which associates with each context c and proposition P a set of propositions. Many, but not all, preparatory conditions are determined by illocutionary point. “Yes” and “No” are often used in English to express preparatory conditions regarding the fact that the speaker gives a positive or negative answer to a previous question. Sincerity conditions By performing an illocutionary act, the speaker also expresses mental states of particular modes about the fact represented by the propositional content. For example, a speaker who makes a request expresses a desire, and a speaker who offers thanks expresses gratitude. The sincerity conditions of each illocutionary force F determine the particular psychological modes of the mental states that the speaker would have if he were sincerely performing an illocutionary act with that force. Thus, a sincerity condition is just a set of modes of propositional attitudes. Some sincerity conditions are common to all forces with the same illocutionary point. For example, each commissive force has the sincerity condition that the speaker intends to do what he commits himself to doing. But other sincerity conditions are independent of illocutionary point. For example, to agree to do something is to accept to do it with the special sincerity condition to the effect that one is in agreement with the person who has requested that action. In English, adverbs like “alas” and “O.K.” express sincerity conditions. As I have pointed out (1990; 1991b), the sets of modes of achievement, propositional content, and preparatory and sincerity conditions have the formal structure of a Boolean algebra. Thus there are a neutral and an absorbent component of these types of components.3 Degree of strength The mental states that enter into sincerity conditions are expressed with different degrees of strength, depending on the illocutionary force. For example, the degree of strength of the sincerity conditions of a promise is greater than that of an acceptance. A speaker who promises to do something expresses a stronger intention than a speaker who simply agrees to do it. Degree of strength is often orally expressed by intonation contour. The formal structure of the set of degrees of strength is that of an Abelian group. The existence of preparatory and sincerity conditions is illustrated linguistically by Moore’s paradox: it is paradoxical to attempt to perform an illocutionary act and to deny simultaneously one of these conditions. Thus utterances like “It is raining and I do not believe it” and “I promise to help you and I am absolutely unable to do it” are paradoxical and self-defeating. Recursive definition of the set of illocutionary forces The set of illocutionary forces of possible utterances is recursive. There are five primitive illocutionary forces. These are the simplest possible illocutionary forces: they have an illocutionary point, no special mode of achievement of that point, a neutral degree of strength, and only the propositional content and the preparatory and sincerity conditions that are determined by their point. The five primitive forces are as follows: 1. The illocutionary force of assertion, which is named by the performative verb “assert” and realized syntactically in the declarative sentential type 2. The primitive commissive illocutionary force, which is named by the performative verb “commit”
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3. The primitive directive force, which is realized syntactically in the imperative sentential type 4. The illocutionary force of declaration, which is named by the performative verb “declare” and expressed in performative utterances 5. The primitive expressive illocutionary force, which is realized syntactically in the type of exclamatory sentences. All other illocutionary forces are derived from the primitive forces by a finite number of applications of five simple logical operations on forces which consist in adding new components or in changing the degree of strength. Four of these operations on forces add components; they consist in restricting the mode of achievement of the illocutionary point by imposing a new mode and in adding new propositional content or preparatory or sincerity conditions. (From a logical point of view, these operations are Boolean operations of intersection or of union.) The fifth operation on forces consists in increasing or decreasing the degree of strength. (It is like addition in an Abelian group.) Here are some examples of derived illocutionary forces: The illocutionary force of promise is obtained from the primitive commissive force by imposing a special mode of achievement of the commissive point involving the undertaking of an obligation. The illocutionary force of a renunciation has the special propositional content condition to the effect that it is a negative commitment. In the commissive use of renouncing, to renounce something is to commit oneself to pursue no longer certain activities. The illocutionary force of a pledge is obtained from the primitive commissive force by increasing the degree of strength of the sincerity conditions. The illocutionary force of a threat is obtained from the primitive commissive force by adding the preparatory condition that the future course of action represented by the propositional content is bad for the hearer. Finally, to consent to do something is to accept to do it with the added sincerity condition that one is reluctant to do it. As one can expect, it is possible to make a systematic analysis of illocutionary verbs of natural languages on the basis of this recursive definition of the set of possible forces. The same holds for force markers. Some syntactic types of sentence—for example, the declarative, imperative, and exclamatory types—express primitive forces. Others, like the conditional and interrogative types, express derived forces. For example, conditional sentences like “I could do it, if you want” and “He would like that” are used to assert with reserve and a weak degree of strength how things will be later if specified or unspecified future facts happen. Basic definition of success The conditions of success of elementary illocutionary acts are a function of the components of their illocutionary force and of their propositional content. Thus an illocutionary act of the form F(P) is successfully performed in the context of an utterance if and only if, firstly in that context, the speaker succeeds in achieving the illocutionary point of force F on proposition P with the mode of achievement of F , and P satisfies the propositional content conditions of F; secondly, the speaker succeeds in presupposing the propositions determined by the preparatory conditions of F; and, finally, he also succeeds in expressing with the degree of strength of F the mental states of the modes determined by the sincerity conditions of F about the fact represented by the propo-
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sitional content P. Thus a speaker makes a promise in a context of utterance when (1) the point of his utterance is to commit himself to doing an act A (illocutionary point); (2) in his utterance, the speaker puts himself under an obligation to do act A (mode of achievement); (3) the propositional content of the utterance is that the speaker will do act A (propositional content conditions); (4) the speaker presupposes that he is capable of doing act A and that act A is in the interest of the hearer (preparatory conditions); and (5) he expresses with a strong degree of strength an intention to accomplish such an act (sincerity conditions and degree of strength). A speaker can presuppose propositions that are false. He can also express mental states that he does not have. Consequently, successful performances of illocutionary acts may be defective. For example, a speaker can mistakenly make a promise that is not beneficial at all to the hearer. A speaker can also make an insincere promise that he does not intend to keep. In such cases, the performed promise is defective. The hearer could reply by pointing out such mistakes. From a logical point of view, an illocutionary act is nondefectively performed in a context of utterance when it is successfully performed and its preparatory and sincerity conditions are fulfilled in that context. Austin with his notion of felicity conditions did not distinguish clearly between utterances that are successful but defective and utterances that are not even successful. In our terminology, we can say that an illocution is felicitous when it is successful, nondefective, and satisfied. Basic definition of satisfaction The notion of a condition of satisfaction is based on the traditional correspondence theory of truth for propositions.4 Whenever an elementary illocutionary act is satisfied in an actual context of utterance, there is a success of fit, or correspondence, between language and the world, because the propositional content of the illocutionary act corresponds to an actual fact in the world. Thus, an elementary illocutionary act of the form F(P) is satisfied in an actual context of utterance only if its propositional content P is true in that context. However, there is more to the notion of a condition of a satisfaction than the notion of truth-condition. In order that an elementary illocutionary act be satisfied, the correspondence between words and things must be established following the proper direction of fit of its illocutionary force. When an illocutionary act has the words-to-things direction of fit, it is satisfied in a context of utterance when its propositional content is true in that context. In such a case, the success of fit between language and the world is achieved by the fact that its propositional content represents a fact which exists (in general independently) in the world. In contrast, when an illocutionary act has the things-to-words or the double direction of fit, it is satisfied in a context of utterance when its propositional content P is true in that context because of its performance. Unlike assertive utterances, commissive and directive utterances have self-referential conditions of satisfaction. An assertive speech act is true when its propositional content corresponds to an existing fact no matter how that fact came to exist. But strictly speaking, a pledge is kept or a command is obeyed only if the speaker or hearer carries out in the world a future course of action stemming from the pledge or the command. Thus truth predicates cannot be used to evaluate the satisfaction of speech acts with the world-to-words direction of fit like pledges or commands can. A pledge or a command is not true or false. A pledge is either kept or broken. Similarly, a command is either obeyed or disobeyed. It is a mistake to attempt to reduce the theory of satisfaction of illocutionary acts to the theory of truth of propositions.5 Success conditions of complex illocutionary acts Any successful performance of an illocutionary act in a context somehow restricts the set of possible contexts of utterance which are illocutionarily compatible with that context. By definition two contexts are illocutionarily compatible when all illocutionary acts performed in one could
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be performed in the other. As Searle and I pointed out, this accessibility relation is Brouwerian: reflexive and anti-symmetrical. A speaker succeeds in performing an illocutionary denegation of the form ¬A in a context when he attempts to perform that act and A is not performed in any possible context that is illocutionarily compatible with that context. Similarly, a speaker succeeds in performing a conditional illocutionary act of the form P ⇒ A in a context when he attempts to perform that conditional illocutionary act and he performs illocutionary act A in all possible contexts which are illocutionarily compatible with that context where proposition P is true.
Section 2 The logical form of propositional contents In my approach, propositions have a double nature. On the one hand, propositions are units of sense of a fundamental logical type that are expressed by sentences and have truth values. On the other hand, propositions are also the contents of conceptual thoughts such as illocutionary acts and attitudes which are representations rather than presentations of facts. As Frege already noticed, the two constitutive aspects of propositions are not logically independent. Thus, every proposition which is the sense of a sentence in a possible context of utterance is also the propositional content of the illocutionary act that the speaker would attempt to perform if he were literally using that sentence in that context. For example, the proposition which is the common sense of the sentences “John will help me” and “Please, John, help me” in a context of utterance is also the propositional content of the assertion or request that the speaker of that context would mean to make if he were using literally one of these sentences in that context. Until now contemporary logicians have paid attention to the role that propositions play as senses of sentences rather than as contents of thought. Moreover, they have tended under the influence of Carnap to reduce propositions to their actual truth conditions in reality. Thus the type of a proposition in classical logic is that of a function from the set of possible circumstances (the term comes from Kaplan) to the set of truth values. (Circumstances can be moments of time, possible worlds, contexts, histories, etc., depending on the logic under consideration.) On this view, strictly equivalent propositions, which are true in the same possible circumstances are identified. However it is clear that most strictly equivalent propositions are not substituable salva felicitate within the scope of illocutionary forces. For example, the assertion that Paris is a city is different from the assertion that it is a city and not an irrational number, even if their contents are strictly equivalent propositions. One can make the first assertion without making the second. Illocutionary logic requires, then, a finer propositional logic. For this purpose I have formulated in Meaning and Speech Acts and later essays a natural logic of propositions in terms of predication so as to take into account the fact that propositions are always in principle expressible in the performance of illocutionary acts. My propositional logic is predicative in the very general sense that it mainly takes into consideration the acts of predication that we make in expressing and understanding propositions. My main objective was to construct a theory of truth that would be appropriate for enriching the theory of success and satisfaction of illocutionary acts. I have analyzed the logical form of propositions on the basis of the following principles. Structure of constituents Propositions have a structure of constituents. As Frege, Russell, Strawson, and others pointed out, understanding a proposition consists mainly of understanding which attributes (properties or relations) certain objects of reference must possess in the world in order that this proposition be true. In expressing propositions speakers refer to objects under concepts and predicate attributes
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of these objects. The speakers have in mind atomic propositions whose truth in a circumstance depends on whether these objects have in that circumstance the predicated attribute. Each proposition is then composed out of atomic propositions corresponding to predications. For example, the proposition that the pope is in Rome or Venice is composed of two atomic propositions: the first predicates of him the property of being in Rome, the second the property of being in Venice. It is true if and only if at least one is true. Senses, not objects Propositional constituents are senses and not objects. As Frege pointed out, we cannot refer to objects without subsuming them under senses and without predicating of them attributes. Thus the formal ontology of propositional logic is realist and not nominalist. Referential and predicative expressions have a sense in addition to a possible denotation. Frege’s argument against direct reference remains conclusive if one accepts that propositions are contents of thought. As Kaplan nowadays admits quite frankly, Kripke’s puzzle for belief is much more a puzzle for the theory of direct reference than for propositional attitudes. From the true premise that Babylonians did not believe that Hesperus is Phosphorus, the theory of direct reference concludes that the Babylonians did not believe that Hesperus is Hesperus. Such an absurd conclusion is incompatible with the minimal rationality of competent speakers. Finite structure Propositions are complex senses whose structure is finite. As is well known, human beings have restricted cognitive abilities. We can only use finitely long sentences in a context of utterance. Similarly, we only can refer to a finite number of different objects and we can only predicate of them a finite number of attributes. Consequently, propositions that are the senses of sentences have a finite number of propositional constituents. Upon reflexion, this requirement of finiteness has important consequences for both illocutionary and intensional logics. A human being can only express a finite number of propositions in an act of thought. So a speaker can only perform a finite number of illocutionary acts in a possible context of use of a natural language. Furthermore, one must reject the standard objectual or substitutional analyses of quantification in propositional logic. For we do not refer to all the values that can be assigned to bound variables when we make generalizations. lnadequacy of Carnap’s explication of truth conditions Carnap’s explication of truth conditions is not adequate. It does not take into account the effective way in which we understand such conditions. To understand the truth conditions of a proposition is not to know its truth value in each possible circumstance, as most logicians tend to believe. It is, rather, to understand that it is true according to some possible truth conditions of its atomic propositions and false according to all others. We understand the proposition that whales are fishes without knowing eo ipso that it is necessarily false. It is a historical discovery that whales are mammals. In my view, to understand an elementary proposition is just to understand that it is true in a circumstance if and only if the denotations of its attribute and concepts are such that its unique atomic proposition is true in that very circumstance; it is not to know whether or not it is true in that circumstance. We often express senses without knowing their denotation in the context of utterance. We can speak of Jane’s children without knowing who they are. From a cognitive point of view, atomic propositions have a lot of possible truth conditions: they can be true in all circumstances, they can be false in all circumstances, they can be false in one circumstance and true in all others, they can be false in two circumstances and true in all others, and so
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on. The type of possible truth conditions is that of functions from the set of all possible circumstances into the set of truth values. Among all possible truth conditions of each atomic proposition, there are, of course, its actual Carnapian truth conditions, which give as value the true in a circumstance if and only if the objects that fall under its concepts satisfy its attribute in that circumstance. I propose to inductively analyze truth conditions by associating with each proposition (with respect to any circumstance) the unique set of possible truth conditions of its atomic propositions that are compatible with its truth in that very circumstance. As we will see, this explicates better the mechanism of truth understanding. Thus the truth of an elementary proposition in a circumstance is compatible by definition with all and only the possible truth conditions of its unique atomic proposition under which it is true in that very circumstance. As one can expect, the truth of propositional negation ¬P is compatible with all and only the possible truth conditions of its atomic propositions that are incompatible with the truth of P. And the truth of the modal proposition that “it is universally necessary that P” is compatible with all and only the possible truth conditions of its atomic propositions, which are compatible with the truth of P in all circumstances. As Wittgenstein pointed out in the Tractatus, there are two limit cases of truth conditions. Sometimes the truth of a proposition is compatible with all possible ways in which objects could be; in this case, it is a tautology. Sometimes it is incompatible with all of them; in this case, it is a contradiction. In my approach, tautologies are propositions whose truth is compatible with all the possible truth conditions of their atomic propositions, and contradictions are propositions whose truth is compatible with none. Recursive definition of the set of propositions The set of propositions is recursive. Elementary propositions are the simplest propositions. All other propositions are more complex: they are obtained by applying to simpler propositions operations that change atomic propositions or truth conditions. Truth functions are the simplest propositional operations: they only rearrange truth conditions. Thus the conjunction P ∧ Q and the disjunction P ∨ Q of two propositions P and Q have all and only the atomic propositions of P and Q. Such propositions only differ by their truth conditions. The truth of the disjunction is compatible with all the possible truth conditions of their atomic propositions, which are compatible with the truth of at least one of the two arguments P and Q. But the truth of the conjunction is only compatible with all these possible truth conditions, which are compatible with the truth of both P and Q. Unlike truth functions, quantification and modal, temporal and agentive operations on propositions change constituent atomic propositions, as well as truth conditions. Thus by way of saying that it is necessary that God does not make mistakes, we predicate of God not only the property of not making mistakes but also the modal property of infallibility—namely, that, in all possible circumstances, He does not make mistakes. Law of propositional identity In order to be identical, two propositions must be composed of the same atomic propositions and their truth in each circumstance must be compatible with the same possible truth conditions of their atomic propositions. This criterion of propositional identity is stronger than that of classical logics such as modal, temporal, and intensional logics and the logic of relevance. Strictly equivalent propositions composed out of different atomic propositions are no longer identified. We do not make the same predications in expressing them. Unlike Parry (1933) I do not identify all strictly equivalent propositions whose atomic propositions are the same. Such propositions whose truth is not compatible with the same possible truth conditions of their atomic propositions do indeed not have the same cognitive value. For we understand in a different way their
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truth conditions. For example, we can believe the necessarily false proposition that whales are fishes. But we never believe the contradiction that whales are and are not fishes. We know a priori that it is false. Notice that my criterion of propositional identity is less rigid than that of intensional isomorphism of Cresswell (1975a)’s hyperintensional logic. For all Boolean laws of idempotence, commutativity, distributivity, and associativity of truth functions remain valid laws of propositional identity. A new concise definition of truth In the philosophical tradition from Aristotle to Tarski true propositions correspond to reality. Objects of reference stand in certain relations in possible circumstances. Atomic propositions have then a unique truth value in each circumstance depending on the denotation of their attributes and concepts and the order of their predication. Their actual truth conditions are then well determined. However things could stand in many other relations in each circumstance. In addition to the ways in which things are, there are the possible ways in which they could be. We are not omniscient. In interpreting propositional contents of utterances we consider then a lot of possible truth conditions other than the actual truth conditions of their atomic propositions. We know a priori the actual truth conditions of few propositions. The truth of most propositions in most circumstances is compatible with many possible ways in which objects could be in them and incompatible with many others. Think about disjunctions, material implications, historic possibilities, future propositions, and so on. However, in order that a proposition P be true in a given circumstance, things must be in that circumstance as P represents them. Otherwise there would be no correspondence. Along these lines, I define truth as follows: a proposition is true in a circumstance i, according to an interpretation if and only if its truth in that circumstance is compatible with the actual truth conditions of all its atomic propositions in that very interpretation. One can derive from that simple definition classical laws of truth theory. A new relation of strong implication between propositions Human beings are not perfectionally rational. We are often inconsistent. For example, we sometimes assert propositions whose truth is impossible. Furthermore, our illocutionary commitments are not as strong as they should be from the logical point of view. Thus, we assert propositions without asserting all their logical consequences. We are not omniscient, and we even do not know all necessary truths. We therefore need in propositional logic a finer logical implication than C. I. Lewis’s strict implication: a proposition strictly implies all others which are true in all possible circumstances where it is true. As we do not know which propositions are strictly implied by the propositional contents of our thoughts, our illocutionary and psychological commitments based on truth conditions are not explainable in terms of strict implication. Hintikka’ s epistemic logic according to which the set of propositional contents of our beliefs is closed under strict implication predicts far too many commitments. Given my predicative analysis of the logical form of propositions, one can define a new relation of strong implication between propositions which is finer than Lewis’s strict implication: a proposition P strongly implies another proposition Q when, first, all the atomic propositions of Q are in P and, second, the proposition P tautologically implies proposition Q—that is to say: all possible truth condition assignments to atomic propositions that are compatible with the truth of proposition P in a circumstance are also compatible with the truth of proposition Q in that very circumstance. Unlike strict implication, strong implication is cognitive. Whenever a proposition P strongly implies another proposition Q, we cannot express that proposition P without knowing a priori that it implies that other proposition Q. For in expressing P, we have in mind by hypothesis all atomic propositions of Q. We make all the corresponding acts of refer-
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ence and predication. Furthermore, in understanding the truth conditions of proposition P, we have in mind all possible truth conditions of its atomic propositions that are compatible with its truth in any circumstance. The same possible truth conditions of atomic propositions of P which are in Q are by hypothesis compatible with the truth of proposition Q in the same circumstance. Thus we know in expressing P that ‘if P then Q’.
Section 3 A new formulation of illocutionary logic Thanks to the new predicative propositional logic, I have enriched the theory of success and satisfaction of elementary illocutionary acts. I have first formulated (1991b; 1995) an illocutionary logic incorporating the minimal predicative logic of elementary propositions and of their truth functions. Next (forthcoming a, b) I have incorporated predicative logics of quantification (1997), historic modalities, action (2003; 2004b), and time (2004a) in illocutionary logic. So we can now better explicate commissive, directive, and declaratory illocutionary forces whose propositional content, preparatory, and sincerity conditions are relative to time, action, and abilities—and thereby prove new valid laws governing the success conditions of elementary illocutionary acts having such forces. We can also develop the theory of satisfaction, thanks to the new theory of truth and derive illocutionary commitments based on strong implication. Because illocutionary acts are by nature actions, the new logic of action of illocutionary logic applies to illocutionary acts, as well as to the actions represented by their propositional content. I (1991b; 1994; forthcoming b) have adopted new principles in the formulation of illocutionary logic. The speaker’s minimal rationality Competent speakers are minimally rational. As Greek and classic philosophers had anticipated, language is the work of reason. First, competent speakers are minimally consistent. They never attempt to achieve an illocutionary point with a nonempty direction of fit on a contradictory propositional content. They know a priori that such attempts would fail. Declarative, imperative, performative sentences whose clauses express a contradiction (e.g., “Come and do not come!”) are both illocutionarily and truth conditionally inconsistent. They express illocutionary acts that are both unperformable and unsatisfiable. Similarly, competent speakers never attempt to achieve an illocutionary point with the things-to-words direction of fit on a tautology. They know a priori that tautologies are true, no matter what they do and, consequently, that such attempts are pointless. So imperative and performative sentences like “Come or do not come!” and “I promise or do not promise to come” are illocutionarily inconsistent. Second, whoever attempts to achieve an illocutionary point with a nonempty direction of fit on a proposition P also attempts to achieve that point on all other propositions Q strongly implied by P which satisfy the propositional content conditions of that point. For he knows a priori that there would not be satisfaction otherwise. Thus, by way of promising to serve red or white wine, a speaker eo ipso commits himself to serve wine. Such a promise, he knows, could not be kept otherwise. Well-foundedness Illocutionary commitment is well founded. Human agents have restricted abilities. They can only make a finite number of attempts in each circumstance. So they only attempt to achieve illocutionary points on a finite number of propositional contents in each context. And they can only succeed in carrying out a finite number of intentional (verbal and nonverbal) actions at each
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moment. Furthermore, they carry out all their successful actions at a moment by way of making at that moment a basic attempt that generates (causally, conventionally, or by extension) all these actions.6 Thus speakers succeed in performing all their illocutionary acts in each context of utterance by way of attempting to perform a single primary illocutionary act in that context. In the use of language, they make that basic attempt by way of uttering a sentence. Their basic speech act is then an utterance act that generates all their successful illocutionary acts given the meaning of their words and the facts that exist in the proper circumstance of their context of utterance. In the case of a literal utterance, where speaker meaning is identical with sentence meaning, the primary illocutionary act that the speaker attempts to perform is by hypothesis the literal illocutionary act expressed by the uttered sentence. Whenever an utterance is successful, it is in performing the primary act that he performs all others in the context of utterance. In such a case, the speaker then performs all illocutionary acts to which the primary illocutionary act strongly commits him. So if he primarily makes a testimony, then he also makes an assertion. But he can also perform other illocutionary acts—for example, a speaker who makes an assertion about the future also makes a prediction. A successful literal utterance today of the declarative sentence “It will rain tomorrow” is both an assertion and a prediction. However, the primary literal assertion does not strongly commit the speaker to the prediction, for tomorrow one can still make the same assertion by saying “It is raining today.” But one cannot make the prediction any more, for tomorrow that assertion will be about the present and not the future. Law of identity for illocutionary acts Two types of elementary illocutionary acts are identical when they have the same propositional content and the same conditions of success. Two illocutionary denegations are identical when they are denegations of the same speech act. And two conditional speech acts are identical when their aim is to perform the same illocutionary act on the same condition. Illocutionary acts are natural kinds of use of language. They serve linguistic purposes in relating propositions to the world with a direction of fit. Now different illocutionary acts should have different linguistic purposes, and different linguistic purposes should be either achievable under different conditions or directed at facts represented or obtainable under different conditions. Thus an elementary illocutionary act can be identified formally with the pair containing its propositional content and the set of possible contexts in which it is performed. And the logical type of a force F is that of a function that associates with each proposition P the pair corresponding to illocutionary act F(P). Given these remarks, there are three essential features in every illocutionary act: first, the (possibly empty) set of its antecedent propositions; second, the nonempty set of its constituent elementary illocutionary acts; and third, the set of all contexts where it is successfully performed. So, for example, each conditional speech act of the form (P ∨ Q) ⇒ A is identical with the conjunction (P ⇒ A) & (Q ⇒ A). In order to formulate illocutionary logic I (1991b; 1994; forthcoming b) have used an artificial ideographical object language where the logical form of illocutionary acts is shown clearly on the surface by the grammatical form of the formulas that express them. So one can see on the surface whether one illocutionary force marker expresses a stronger force than another. And one can also determine effectively on the basis of their syntactic forms which clauses express propositions related by strong implication. The number of proper primitive notions of first-order illocutionary logic is small. Its theoretical vocabulary contains a few new logical constants and syncategorematic expressions expressing universals of language use.7 Some of these universals are illocutionary: the five illocutionary points, the basic degree of strength, and, for each other type of force component, the neutral and absorbent components of that type and the various operations on components of illocutionary force. Other primitive notions of illocutionary logic
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are relative to propositions: identity, presupposition, expression of attitudes, functional application, truth functions, necessity, quantification, and the rest. Many important notions of illocutionary and propositional logics like force, illocutionary acts, success and satisfaction conditions, performability, satisfiability, and strong and weak illocutionary commitment are derived from the few primitive notions by a series of rules of abbreviation. As one might expect, the syntactic form of a force marker is complex: it contains six constituents expressing the six different components of that force. Markers whose syntactic forms are the simplest express primitive forces: they only contain logical constants expressing an illocutionary point; the neutral mode of achievement of illocutionary point; the neutral degree of strength; and the neutral propositional content, preparatory, and sincerity conditions. Other force markers contain longer constituent expressions expressing complex propositional content, preparatory or sincerity conditions, or a greater or weaker degree of strength. Each formula expressing an elementary illocutionary act is a force marker followed by a clause. The new illocutionary logic that I have formulated on the basis of these principles contains a unified theory of success, satisfaction, and truth. It explains why speakers are not perfectly rational and in which way they are always minimally rational. It also explains why some unsatisfiable illocutionary acts are performable and why others are unperformable but satisfiable. There are four important logical relations of implication between speech acts: • Some illocutionary acts have more conditions of success than others: they strongly commit the speaker to these other illocutionary acts. For example, one cannot implore help and protection without making a request for help. • Some illocutionary acts have more conditions of satisfaction than others: they cannot be satisfied unless the others are also satisfied. For example, whenever an elementary illocutionary act is satisfied, any assertion of its propositional content is eo ipso true. • Some illocutionary acts have conditions of success that are stronger than the conditions of satisfaction of others: they cannot be successfully performed unless the others are satisfied. For example, by virtue of its double direction of fit, a successful declaration is eo ipso satisfied. • Some speech acts have conditions of satisfaction that are stronger than the conditions of success of other speech acts: they cannot be satisfied in a context unless the others are performed in that context. For example, given the self-referential nature of the conditions of satisfaction of illocutionary acts with the things-towords direction of fit, the satisfaction of directives and commissives requires their successful performance. Thus if a promise is kept, it has been made. Similarly, if an order is obeyed, it has been given. Illocutionary logic can prove all the fundamental laws governing these four kinds of relations of implication between speech acts.8 Contrary to what was commonly believed before, the set of illocutionary acts is much more logically structured by these logical relations of implication than the set of propositions is structured by material or even strict implication. For example, given the general definition of success and the recursive definition of the set of all illocutionary forces, there are a few valid laws of comparative strength for illocutionary forces that explain strong illocutionary commitments due to force: • First, any force F2, which is obtained from another force F1 by the application of an operation, is either stronger or weaker than that force. By definition, a force F1 is stronger than another force F2 when any illocutionary act of the form Fl(P) strongly
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commits the speaker to the corresponding illocutionary act of the form F2(P). For example, the forces of a prediction and of a testimony are stronger than the force of an assertion. Conversely, a force F is weaker than another force F' when F' is stronger than F. All the Boolean operations (which consist in adding a new mode of achievement or a new propositional, preparatory, or sincerity condition) and the Abelian operation (which consists in increasing the degree of strength) generate stronger illocutionary forces. • Second, the order of application of operations on forces is not important; it does not affect the success conditions. • Third, when an illocutionary force is stronger than another force, it can always be obtained from that force by a finite number of applications of such operations. The set of propositions is not structured so strongly by implication in standard logic. First, the applications of logical operations on propositions such as truth functions do not always generate implication. Second, the order of application of these operations is important; it often affects the truth conditions. Furthermore, illocutionary logic has contributed to the theory of truth. It has discovered that the set of propositions is logically structured by a logical relation of strong implication much finer than all other relations of implication. Unlike strict implication, strong implication is antisymmetrical. Two propositions that strongly imply each other are identical. Unlike Parry’s analytic implication, strong implication is always tautological. Natural deduction rules of elimination and introduction generate strong implication when all atomic propositions of the conclusion belong to the premises. So a conjunction P ∧ Q strongly implies each conjunct P and Q. But a proposition P does not strongly imply any disjunction of the form P ∨ Q. Strong implication is paraconsistent. A contradiction does not strongly imply all propositions. Tautologies (and contradictions) are a special kind of necessarily true (and false) propositions. Unlike other necessarily true propositions, we know a priori that tautologies are true (and that contradictions are false). Finally, strong implication is finite and decidable.
Section 4 General semantics of success and satisfaction Contemporary logicians like Church (1951), Carnap (1956), Prior (1967), Belnap (Belnap and Perloff 1992; Belnap and Green 1994), Kripke (1963), Kaplan (1978b), and Marcus (1993) have used the resources of logical formalisms such as proof and model theory to formulate philosophical logics like modal, intensional, and temporal logic and the logic of demonstratives and agency which are important for the analysis of propositional contents. Such logicians have contributed to the theory of truth and meaning. Moreover, some like Montague (1974) and Cresswell (1973) contributed to the foundations of the formal syntax and semantics of natural languages. Thus logical formalisms, which were originally conceived by Frege, Russell, and Tarski for the sole study of formal languages, were successfully used and improved to generate and interpret important fragments of ordinary language. Like Montague, I think that there is no important theoretical difference between formal and natural languages. Mathematical formalisms are most useful to explicate meaning and understanding. However, unlike Montague, Davidson, and many others, I do not believe that the single most important objective of semantics is to develop a recursive theory of truth. As I have explained, the primary units of meaning in the use and comprehension of language are not isolated propositions (or truth conditions) but complete illocutionary acts whose success and satisfaction conditions are not reducible to truth conditions. On my view, the primary objectives of semantics, then, are to formulate a theory of success and of satisfaction for illocutionary acts and not
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just to develop the theory of truth for propositions. For that purpose, formal semantics must integrate a unified illocutionary and intensional logic. Until now, traditional formal semantics has tended to construct the linguistic competence of speakers as their ability to understand the propositional contents of utterances. For that reason, until Meaning and Speech Acts, most applications of formal semantics to actual natural languages have been restricted solely to the interpretation of declarative sentences. Thanks to illocutionary logic, formal semantics can now analyze other kinds of expressions like force markers and performative verbs whose meaning contributes to the determination of success and satisfaction conditions. For the first time in the history of logic, we now have formal means for interpreting without reduction all syntactic types of sentences (imperative, optative, conditional, exclamatory, and subjunctive, as well as declarative) expressing speech acts with any possible illocutionary force. In my approach, the semantic theory of truth advocated by Montague and Davidson for ordinary language is just the special subtheory for assertive speech acts of the more general theory of satisfaction for speech acts with an arbitrary illocutionary force. On my account, linguistic competence is not separable from performance, as Chomsky thinks. On the contrary, it is essentially the speaker’s ability to perform and understand illocutionary acts which are meanings of utterances. Natural languages have a vast vocabulary for specifying illocutionary act types and propositions. But they are ambiguous, and their grammatical conventions are so complicated that it is difficult to analyze directly the underlying logical form of attempted illocutionary acts. First, there is no one-to-one correspondence between illocutionary forces and performative verbs or force markers of natural languages: “Illocutionary forces are, so to speak, natural kinds of use of language, but we can no more expect the vernacular expressions to correspond exactly to the natural kinds than we can expect vernacular names of plants and animals to correspond exactly to the natural kinds.”9 Thus, some possible illocutionary forces are not actual today in English. One can no longer repudiate one’s wife and break off one’s marriage by uttering words, as one could do in past civilizations in certain ways fixed by custom. Some possible illocutionary forces are actual in English but are not realized syntactically or lexicalized. For example, there is no marker in English for commissive illocutionary forces. One cannot directly commit oneself to doing something in English. One must speak nonliterally (by saying, for example, “I will do it”) or performatively (“I promise to do it”). (In the first case, the speaker commits himself indirectly to an action by making a literal assertion. In the second, by making a literal declaration.) Moreover, actual forces such as “to boast” are named by speech act verbs that have no performative use. Certain forces have an implicit mode of achievement of their point. Notice also that performative verbs like “tell” and “swear” are ambiguous between different illocutionary points. One can assertively tell that something is the case, just as one can make a directive in telling someone to do something. A second reason for distinguishing carefully between illocutionary forces, on the one hand, and performative verbs and illocutionary force markers, on the other hand, is that natural languages are not perspicuous. Many sentences of the same syntactic type (for example, declarative sentences like “They lost,” “Frankly, they lost,” “Of course, they lost,” “Unfortunately, they lost,” and ” Alas, they lost”) express illocutionary acts whose assertive forces are different. The same holds for illocutionary force markers. Sentential types like the declarative, imperative, and exclamatory types express primitive forces. But others like the conditional and interrogative types express derived forces. To ask a question is to request the hearer to perform a future speech act that would give a correct answer to that question. Many performative verbs with a superficially similar syntactic behavior (for example, “order,” “forbid, ” and “permit”) do not name illocutionary acts with the same logical form. The verb “order” names a derived directive illocutionary force, but there is no force of forbidding. For an act of forbidding something is just an order not to do it. Furthermore, an act of granting permission is the illocutionary denegation of an act of forbidding.
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As Russell and the first Wittgenstein argued, one should not trust too much the surface structure of ordinary language in order to describe its logical structure. It is better to analyze indirectly the deep structure of ordinary sentences via their translations into a logically perfect perspicuous and disambiguous formal object language. For that purpose, I have used in the formal semantics of success and satisfaction10 the ideographic language of a higher-order unified illocutionary and intensional logic containing a revisited predicative propositional logic where strictly equivalent propositions are distinguished. All the logical constants and syncategorematic expressions of the ideographic object language of illocutionary logic express universal features of language, such as identity, success, truth, satisfaction, abstraction over contexts, functional application, and l abstraction. Because of this, the syntactic rules of formation and abbreviation of the ideal object language, the meaning postulates governing its expressions in possible interpretations and the axioms and rules of inference of the corresponding axiomatic system make universal claims about the deep structure of language. Thanks to the new ideography, richer fragments of natural languages containing sentences of all syntactic types {both declarative and nondeclarative) can now be interpreted indirectly in logic. The first advantage of using an ideographic language is to have at one’s disposal a theoretical vocabulary thanks to which any expressible illocutionary act can in principle be analyzed in a canonical way and be put into relationships with others. Another advantage is that, contrary to what is the case in ordinary language; the grammatical forms of its sentences reflect clearly on the surface the logical forms of the illocutionary acts that they express. As Montague (1970a, b, c) pointed out, by way of translating clauses of ordinary sentences into the ideal object language of intensional logic; formal semantics clarifies the logical form of propositions and proceeds to a better explication of their truth conditions. Similarly, by way of translating force markers and performative verbs into the ideographic object language of illocutionary logic, formal semantics can exhibit the logical form of illocutions and proceed to a better explication of their success and satisfaction conditions. I have developed the foundations of a formal semantics of success and satisfaction for elementary illocutionary acts in Meaning and Speech Acts. The first volume, Principles of Language Use, introduces the theory; the second volume, Formal Semantics of Success and Satisfaction, uses proof and model theories to formalize the theory. I am now writing a new book, The Logic of Discourse, where I formulate a richer illocutionary logic capable of expressing historic modalities, time, and action and studying complex illocutionary acts like denegations and conditional speech acts and conversations with a discursive purpose such as consultations, interviews, deliberations, and eulogies. I have adopted the following principles in my formal theory of meaning. 1. There are two types of meaning. Most sentences contain expressions whose sense can vary in different contexts. They can serve to perform different illocutionary acts in different contexts. For example, each literal utterance of the sentence “Today it is raining” serves to assert the proposition that it is raining on the day of that utterance. So different assertions are made by uttering that sentence on different days. In my conception of semantics, the linguistic meaning of a sentence in a semantic interpretation is then a function from the set of possible contexts of utterance into the set of illocutionary acts. On the other hand, the meaning of a sentence in a context is the particular illocutionary act that it expresses in that context. (It is the value that the linguistic meaning of that sentence associates with that context.) Thus, linguistic meanings apply to sentence types, whereas illocutionary acts apply to sentences in contexts or sentence tokens. 2. Illocutionary act types (and not tokens) are the units of sentence meaning in contexts. The illocutionary act type expressed by a sentence in a context of utterance can be defmed counterfactually as the primary illocutionary act that the speaker would mean to perform in that context if he were using that single sentence and speaking literally. Such an illocutionary act type exists even if the speaker does not use that sentence or if he uses it unsuccessfully in that context. Just as syntax and semantics are primarily concerned with the formation and interpreta-
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tion of sentence types, speech act theory is primarily concerned with the analysis of illocutionary act types. Linguistic competence is creative. We only use and understand finitely many sentence tokens during our lifetime. However, we are able to use and understand an infinite set of sentences, including new sentences, which have never been used before. Similarly, we are able to perform and understand infinitely many illocutionary acts, including new illocutionary acts never performed before. 3. Possible contexts of utterance consist of various features. For the purposes of general semantics, a possible context of utterance of a semantic interpretation consists of one or several speakers and hearers, a finite set of sentences (uttered by the speaker(s) in that context), a moment of time and a place (which are the moment and place at which utterances are made in that context), a history containing moments of time before and after the moment of utterance,11 and a background12 relative to the forms of life and conversation in which are engaged protagonists of the utterance. The force and propositional content of literal illocutionary acts can depend on conversational background. Thus two utterances of the sentence “Cut the grass!” express different directives in contexts where speaker and hearer are talking of a different grass lawn. Moreover, as Searle (1980) pointed out, different denotations can correspond to the same senses in circumstances with different backgrounds. For example, in order to cut the same grass lawn, a hearer can use a lawnmower in an ordinary background where the purposes of contextual forms of life are esthetical (to make the lawn more beautiful). But he has to act differently when the purposes are to sell the lawn. (In that case he must transplant the grass.) 4. Speaker meaning is reduced to sentence meaning. In semantics one assumes insofar as possible that speakers speak literally and mean what they say. Thus the primary illocutionary act that the speaker means to perform in a context according to a semantic interpretation is always the conjunction of all literal illocutionary acts expressed by the sentences that he utters in that context, when all such illocutionary acts are simultaneously performable. For example, if the speaker says “Can you pass the salt?” he refers to the salt and not the sugar, and he means to ask a question about the hearer’s abilities and not to indirectly request him to pass the salt. Speakers who use an illocutionarily inconsistent sentence like “I am not myself today” know by virtue of competence that it is impossible to perform the literal illocutionary act. So they do not mean what they say. They mean something else. In the present formal semantics of literal meaning, I will consider that they do not mean anything.13 5. There is a double semantic indexation in the understanding of meaning. Just as the same sentence can express different illocutionary act types in different contexts of utterance, the illocutionary act, which is the meaning of a sentence in a context, can have different success and satisfaction values in different circumstances. For example, the present utterance “I am awake right now” is a successful and true assertion about Daniel Vanderveken in the present circumstance. But that particular assertion about me is not true in other circumstances where I am sleeping. Moreover, it is not often made in the use of English. In my view, we interpret sentences and assign to them a meaning in two steps: 1. In the first step, we interpret a sentence as expressing certain literal illocutionary acts in various contexts of utterance. In our interpretation, we determine the nature of literal speech acts from the linguistic meaning of that sentence and the relevant aspects of each context. Sometimes, we understand the linguistic meaning of a sentence. But that sentence contains an expression such as “yesterday” or “he” whose sense is context-dependent. And we do not know the relevant feature of the context of utterance. In that case, we are not able to fully understand the illocutionary act that is the meaning of that sentence in that particular context. Expressions whose linguistic meaning is sensitive to contextual aspects of the same type (e.g., “tomorrow,” “today,” and “yesterday”) can have the same sense
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in different contexts (taking place in following days). Thus nonsynonymous sentences of ordinary language can express literally the same illocutionary act in different contexts whose contextual aspects are related in certain ways. For example, the three sentences “It will rain tomorrow,” “It is raining today,” and “It has rained yesterday” serve to make the same assertion whenever they are used in three days running. By virtue of linguistic competence, we are aware of such meaning similarities. 2. In the second step of our interpretation, each illocutionary act, which is the meaning of a sentence in a context, is then evaluated in its turn as having a success and a satisfaction value in various contexts of utterance. From a philosophical point ofview, the success and satisfaction values of an illocutionary act in a context are dependent on particular aspects like the moment of time, history, and background that constitute the particular circumstance of that context. Success and satisfaction values of an illocution can then vary from one circumstance to another in an interpretation. For example, the assertion that Paul will win is true in a circumstance if and only if Paul wins in another circumstance at a posterior moment in the same history and background. As Searle (1981) pointed out, the truth value of propositions and satisfaction values of illocutionary acts are relative to the background of contexts. The same holds for success values. However, as Kaplan anticipated, these values are always the same in contexts occurring in the same circumstance. Just as we can understand an expressed proposition without knowing whether it is true in the context of utterance, we can understand the illocutionary act that a speaker attempts to perform in a context without knowing whether or not it is successful or satisfied. We often do not know whether the relevant facts exist in the circumstance of that context. 6. There is a general ramification of the fundamental semantic notions of analyticity, consistency, and entailment. As I said earlier, one must distinguish the two notions of illocutionary and truth-conditional consistency in language. Similarly, one must distinguish the notions of illocutionary and truth-conditional analyticity. Some sentences—for example, Moore’s paradoxical sentence “It is raining and I do not believe it”—are analytically unsuccessful: they can never be used literally with success. Others like “I do not exist” are analytically insatisfied: they can never be used literally with satisfaction. Such notions do not have the same extension. Utterances of Moore’s paradoxical sentence are not analytically insatisfied. Just as illocutionary acts are related by four different kinds of implication, sentences are related by four different kinds of entailment in the deep structure of language: 1. Illocutionary entailment: A sentence such as “I request your help” illocutionarily entails the sentence “Please, help me!”: it expresses in each context of use an illocution that the speaker could not perform in that context without also performing the illocution expressed by the second sentence. 2. Truth-conditional entailment: A sentence like “Please, eat!” truth-conditionally entails the sentence “You are able to eat”: it expresses in each context of use an illocution that could not be satisfied in that context unless the illocution expressed by the second sentence is also satisfied. 3. Illocutionary entailment of satisfaction: A sentence illocutionarily entails the satisfaction of another sentence when it expresses in each context an illocution whose successful performance in that context implies the satisfaction of the illocution expressed by the other sentence. For example, performative sentences illocutionarily entail their own satisfaction.
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4. Truth-conditional entailment of success: Finally, a sentence truth conditionally entails the success of another sentence when it expresses in each context an illocution whose satisfaction in that context implies the successful performance of the illocution expressed by the second sentence. For example, imperative and performative sentences truth-conditionally entail their own success. The four preceding relations of entailment exist between sentences when the illocutionary acts that they express in a possible context of utterance always have in that very context related success or satisfaction values. However illocutionary acts that are the meanings of two sentences in a given context of utterance also have success and satisfaction values in all other possible contexts. And one can quantify over all these values. So there are four strong relations of entailment of each type in the logic of language—for example, strong illocutionary and strong truthconditional entailment. A sentence strongly illocutionarily entails (or strongly truth-conditionally entails) another sentence when it expresses in any context an illocutionary act that has the same or more success (or satisfaction) conditions than the illocutionary act expressed by the other sentence in the same context. As one can expect from Kaplan’s logic of demonstratives, not all cases of illocutionary or truth-conditional entailment are strong. For example, the sentence “John asserts that he won yesterday” both illocutionarily and truth-conditionally entails (but not strongly) the sentence “John reports that he won yesterday.” Notions of illocutionary consistency, analyticity, and entailment had been completely ignored until now by formal semantics. However, as I pointed out in Meaning and Speech Acts, all the ramified notions that I have defined exist for all kinds of sentences (whether declarative or not) in ordinary language. And they do not coincide in extension. For example, performative sentences illocutionarily entail (but not truth-conditionally) corresponding nonperformative sentences. By assigning entire illocutionary acts as semantic values to sentences in contexts, semantics can better describe the logic of language. On the basis of the principles that I have just explained, I have pursued Montague’s program and developed in volume 2 of Meaning and Speech Acts a general formal semantics of success and satisfaction that is a generalization and extension of Montague’s intensional logic. For my purposes, I have enriched the conceptual apparatus of intensional logic in various ways. I have used as ideal object language the ideographic object language of a higher-order illocutionary logic that contains that of intensional logic. As I said earlier, all logical constants or syncategorematic expressions express primitive notions that are material or formal linguistic universals relative to force or propositions. I have defined all other fundamental illocutionary and intensional notions by rules of abbreviation. I have explained how to translate the different syntactic types of declarative, conditional, imperative, performative, exclamatory, optative, subjunctive, and interrogative sentences into the ideal language. To stratify the universe of discourse, I have enriched formal ontology by admitting the new primitive type of success values in addition to those of truth values, individuals, and attributes. I have changed the definition of the logical type of propositions in the predicative way. Furthermore, I have adopted the double semantic indexation advocated above. So illocutionary acts are the meanings of sentences in contexts of interpretations. I have defined recursively truth, success, and satisfaction by induction on the length of clauses and sentences in canonical notation. And I have axiomatized all generally valid laws of my illocutionary logic. Incidentally, the axiomatic system is a conservative extension of that of Gallin for Montague’s intensional logic. Unlike Montague, who tended to consider formal semantics and universal grammar as parts of mathematics, I think—like Searle, Chomsky, and others—that philosophy, linguistics, and psychology have to take an important role in their development. Natural languages are human languages whose speakers have creative and restricted abilities. We are able to learn them and to understand rapidly the meanings of their sentences. We know by virtue of linguistic competence
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the logical forms of sentences whose utterances are analytically unsuccessful. We also know just by understanding them which sentences are related by illocutionary entailment. So we need a very constructive formal theory of meaning that accounts for such facts. I have formulated general semantics so as to make decidable innate notions. Here are a few important laws of the logic of language that I have stated. There are sentences whose utterances are analytically successful and satisfied: for example, “I am speaking” and Descartes’ Cogito “I am thinking now.” But these sentences do not express necessarily and a priori true propositions. Contrary to what was commonly believed in logical positivism, the notions of analytic, a priori, and necessary truth do not coincide in extension. Kaplan (1978b) has noticed that analytically true sentences like “I am here now” are not necessarily true, and Kripke (1971) pointed out that necessarily true sentences like “Water is H20” are not a priori true. All their distinctions hold and can be generalized at the illocutionary level and for all types of sentences. Kaplan also discovered the existence of analytically false sentences— for example, “I do not exist”—which are, however, truth-conditionally consistent. Similarly, Moore’s paradoxical sentence “It is raining today and I do not believe it” is analytically unsuccessful, but it is illocutionarily consistent. Nothing prevents my making that assertion tomorrow by saying “It was raining yesterday and I did not believe it.” Because of the minimal rationality of competent speakers, semantic paradoxes like the liar paradox do not really occur in the use of language. Contrary to what Russell and Tarski believed, natural languages are not inconsistent because they contain paradoxical sentences like “This assertion is false” and, let me add, “I will not keep this promise,” “Disobey this order,” et cetera. It is not necessary to prevent the formation of such sentences in logic in order to avoid paradoxes. As I have shown, one can translate without inconsistency these paradoxical sentences in the object language of general semantics. For their self-referential utterances are not both satisfied and insatisfied, as logicians wrongly believe. When their logical form is well analyzed, it appears that in order to be satisfied such utterances would have to be successful. And this is impossible given the law of minimal consistency of speakers stated above. As Prior (1971) anticipated, the liar’s paradox is of the form “There exists a proposition P such that I assert P and P is not true and P is that very proposition, namely that there is a proposition P such that I assert P and P is not true.” Whenever the logical form of the liar’s paradox is so analyzed, one discovers that it is a false assertion that no one can make. For its propositional content is a pure contradiction incompatible with all possible truth conditions. Sentences expressing that paradox are then both illocutionarily and truth-conditionally inconsistent. The general semantics of success and satisfaction studies inferences from a new point of view. An inference is valid whenever it is not possible for its premises to express illocutionary acts with certain success or satisfaction values unless its conclusion also expresses an illocutionary act with the same or other success or satisfaction values. So general semantics can formulate valid laws of inference for all types or sentences. It can study practical inferences whose conclusion has the things-to-words direction of fit, as well as theoretical inferences whose conclusion has the words-to-things direction of fit. Until now, contemporary logic and formal semantics have been confined to the study of the sole assertive use of language and to the interpretation of declarative sentences. They have studied the valid forms of theoretical inferences whose premises cannot be true unless their conclusion is also true. However, we are not able to make all such valid theoretical inferences by virtue of linguistic competence. For we understand propositions without knowing how they are related by strict implication. Moreover, there are many other kinds of inference relative to success and satisfaction conditions. From the point of view of universal grammar, the most interesting principles of valid inferences are those that speakers have necessarily internalized in learning their mother tongue. They reflect the very nature of human reason and constitute a decidable natural logic that is part of linguistic competence. The logical semantics of speech acts is able to study these principles. For example, we are all able by virtue of
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competence to make practical and theoretical inferences whose premises cannot be successful and satisfied unless their conclusion is also successful and satisfied. For example, when we understand the request expressed by a literal utterance of the imperative sentence “Please, come and see me tomorrow at home or in the office!” we infer automatically that the speaker also means to request “Please, come and see me tomorrow!” For we know by virtue of our competence that it is not possible to make the request expressed by the premise without making that expressed by the conclusion. And we also know by competence that it is not possible to grant the first request without also granting the second. Here are a few characteristic laws of the semantics for speech acts. A sentence of the form [d]f(p) strongly entails both illocutionarily and truth conditionally the shorter sentence f(p) when its complex marker [d]f contains an additional expression d naming a force component or serving to increase the degree of strength. Thus, sentences like “Come, please!” “Frankly, come!” “Come urgently!” and “O.K. come!” strongly illocutionarily and truth conditionally entail “Come!” The interrogative type of sentence contains the imperative type. So any interrogative sentence (e.g., “Is it raining?”) is synonymous with the corresponding imperative sentence (“Please, tell whether or not it is raining!”). Exclamatory sentences are the weakest type of sentences. For every successful performance of an illocutionary act is an expression of the attitudes determined by its sincerity conditions. So every elementary sentence (e.g., “Alas, he is dead”) strongly illocutionary entails corresponding exclamatory sentences (e.g., “How sad that he be dead!”) But the converse is not true. For there is more in the performance of an illocution with a nonempty direction of fit than a simple expression of attitudes. Performative sentences are the strongest type of sentence. For every successful declaration is felicitous. So performative sentences like “I ask you if it is raining” strongly illocutionarily entail corresponding nonperformative sentences “Is it raining?” But the converse is not true. For we need not make a declaration in order to perform an illocutionary act. We can directly perform it. So the so-called performative hypothesis is false. Performative sentences are not synonymous with corresponding nonperformative sentences. Every explicit performative sentence (e.g., “I hereby condemn you to death”) strongly entails both illocutionarily and truth conditionally the corresponding declarative sentence (“You are condemned to death.”). For any successful declaration is an assertion. But the converse is not true. So performative utterances are not assertions to the effect that the speaker performs an illocutionary act, as G. J. Warnock (1973) and others claim. Only the rules of introduction and elimination of natural deduction whose premises contain the clauses of their conclusion generate strong illocutionary entailment between sentences whose marker expresses a nonexpressive force. Thus “Do it today or tomorrow!” illocutionarily and truth-conditionally entails “Do it!” But “Do it today!” does not illocutionarily entail “Do it today or tomorrow!” (Such laws had been formulated in an ad hoc way in Foundations.) Unlike applied semantics of empirical linguistics, general semantics is above all a logicophilosophical theory of language. It deals mainly with the logical form of meanings of possible utterances of sentences of possible natural languages and only incidentally with particular actual realizations of these possibilities in living languages. Its primary objective is to articulate and exhibit the deep logical structure common to all possible natural language. As Cocchiarella (1997,
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72) pointed out, my program is also an attempt to articulate what classical philosophers called a priori forms of thought: “In any case, the notion of a lingua philosophica containig both an intensional and illocutionary logic is no longer merely a program but has already in many respects been realized.” As Searle and I pointed out, illocutionary logic is transcendental in Kant’s sense. Any conceptual thought is in principle expressible by means of language in the performance of an illocutionary act. Consequently, necessary and universal semantic laws determining the conditions of possibility of successful meaningful utterances reflect a priori forms of thought. It is impossible to have a thought whose expression would ever violate such laws. General semantics aims to do more than stating empirical laws governing meaning and understanding. In the tradition of transcendental philosophy, it also aims to fix limits to thought. According to Wittgenstein (1961[1922]), the logic of language fixes limits to thought indirectly by fixing limits to their expression in language. In general semantics, limits of thought show themselves in language in the fact that sentences of certain logical forms can never be used literally with success. We can of course refer to impossible thoughts, describe their forms, and even attribute them to others. But we can never really entertain these impossible thoughts in the first person, just as we cannot speak and think literally when we make analytically unsuccessful utterances. Along the same lines, the fact that sentences of certain logical forms illocutionarily entail others shows that we cannot have certain thoughts without having others. So language reflects the a priori order of thought. Notes 1. The term of force was first used by Frege (1972; 1977). 2. See also the Tractatus logico-philosophicus 3.251 and section 99 of his Philosophical Investigations. 3. The neutral propositional content condition associates with each context of utterance the set of all propositions and the absorbent propositional content condition the empty set. 4. One can find a first formulation of the classical theory of truth by correspondence in Aristotle’s Metaphysics. See also G. Frege (1977) and A. Tarski (1944). 5. Logicians and philosophers like Rescher (1966) and Belnap and Steel (1976) who have constructed earlier logics of speech acts such as the logic of commands and the logic of questions have neglected success and satisfaction in favor of truth in their analyses. 6. See Goldman (1970) for the terminology of generation of actions and my paper (Vanderveken 2004b) on the basic logic of action. 7. See Vanderveken (2001a), “Universal Grammar and Speech Act Theory.” 8. See Vanderveken (1991b; volume 2 of Meaning and Speech Acts) and my paper (1994). 9. Searle and Vanderveken (1985), p. 179. 10. See Vanderveken 1991b. 11. Speech act theory requires a logic of branching time that is compatible with indeterminism and the liberty of human agents. In the logic of branching time, a moment is a possible state of the world at an instant and the temporal relation of anteriority/posteriority is partial rather than linear. On the one hand, each moment is immediately preceded by at most one moment. On the other hand, several incompatible moments might immediately follow upon a given moment. A history is a maxjmal chain of moments of time. See Belnap and Green (1994) and Vanderveken (2001; 2004a). Unlike Belnap, I believe that contexts of utterance occur not only at a moment but also in a history. For the utterances and illocutionary acts which are made in a context are in general part of a discourse or conversation which occur during an interval of time containing past and future moments of utterances. The discourse to which the speaker contributes by asking a question is not the same if the hearer answers one way or another. Furthermore, the interpretation of an utterance can depend on a future exchange between protagonists of the discourse. For considerations on the logical structure of discourses see Vanderveken (forthcoming a). 12. The term and notions of background are from Searle (1979; 1981). 13. It is the purpose of formal pragmatics to study nonliteral meaning. See Vanderveken (1991a) and (1997b) for considerations on nonliteral illocutionary acts.
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trange goings on! Jones did it slowly, deliberately, in the bathroom, with a knife, at midnight. What he did was butter a piece of toast. We are too familiar with the language of action to notice at first an anomaly: the “it” of “Jones did it slowly, deliberately, . . .” seems to refer to some entity, presumably an action, that is then characterized in a number of ways. Asked for the logical form of this sentence, we might volunteer something like “There is an action x such that Jones did x slowly and Jones did x deliberately and Jones did x in the bathroom, . . .” and so on. But then we need an appropriate singular term to substitute for ‘x’. In fact, we know Jones buttered a piece of toast. And, allowing a little slack, we can substitute for ‘x’ and get “Jones buttered a piece of toast slowly and Jones buttered a piece of toast deliberately and Jones buttered a piece of toast in the bathroom . . .” and so on. The trouble is that we have nothing here we could ordinarily recognize as a singular term. Another sign that we have not caught the logical form of the sentence is that in this last version there is no implication that any one action was slow, deliberate, and in the bathroom, though this is clearly part of what is meant by the original. The present paper is devoted to trying to get the logical form of simple sentences about actions straight. I would like to give an account of the logical or grammatical role of the parts or words of such sentences that is consistent with the entailment relations between such sentences and with what is known of the role of those same parts or words in other (non-action) sentences. I take this enterprise to be the same as showing how the meanings of action sentences depend on their structure. I am not concerned with the meaning analysis of logically simple expressions insofar as this goes beyond the question of logical form. Applied to the case at hand, for example, I am not concerned with the meaning of “deliberately” as opposed, perhaps, to “voluntarily”; but I am interested in the logical role of both these words. To give another illustration of the distinction I have in mind: we need not view the difference between “Joe believes that there is life on Mars” and “Joe knows that there is life on Mars” Donald Davidson (1966) The logical form of action sentences. In Nicholas Rescher (ed.), The Logic of Decision and Action (© 1966 by the University of Pittsburgh Press). Reprinted by permission of the University of Pittsburgh Press.
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as a difference in logical form. That the second, but not the first, entails “There is life on Mars” is plausibly a logical truth; but it is a truth that emerges only when we consider the meaning analysis of “believes” and “knows.” Admittedly, there is something arbitrary in how much of logic to pin on logical form. But limits are set if our interest is in giving a coherent and constructive account of meaning: we must uncover enough structure to make it possible to state, for an arbitrary sentence, how its meaning depends on that structure, and we must not attribute more structure than such a theory of meaning can accommodate. Consider the sentence: (1)
Jones buttered the toast slowly, deliberately, in the bathroom, with a knife, at midnight.
Despite the superficial grammar we cannot, I shall argue later, treat the “deliberately” on a par with the other modifying clauses. It alone imputes intention, for of course Jones may have buttered the toast slowly, in the bathroom, with a knife, at midnight, and quite unintentionally, having mistaken the toast for his hairbrush which was what he intended to butter. Let us, therefore, postpone discussion of the “deliberately” and its intentional kindred. “Slowly,” unlike the other adverbial clauses, fails to introduce a new entity (a place, an instrument, a time), and also may involve a special difficulty. For suppose we take “Jones buttered the toast slowly” as saying that Jones’s buttering of the toast was slow; is it clear that we can equally well say of Jones’s action, no matter how we describe it, that it was slow? A change in the example will help. Susan says, “I crossed the Channel in fifteen hours.” “Good grief, that was slow.” (Notice how much more naturally we say “slow” here than “slowly.” But what was slow, what does “that” refer to? No appropriate singular term appears in “I crossed the Channel in fifteen hours.”) Now Susan adds, “But I swam.” “Good grief, that was fast.” We do not withdraw the claim that it was a slow crossing; this is consistent with its being a fast swimming. Here we have enough to show, I think, that we cannot construe “It was a slow crossing” as “It was slow and it was a crossing” since the crossing may also be a swimming that was not slow, in which case we would have “It was slow and it was a crossing and it was a swimming and it was not slow.” The problem is not peculiar to talk of actions, however. It appears equally when we try to explain the logical role of the attributive adjectives in “Grundy was a short basketball player, but a tall man,” and “This is a good memento of the murder, but a poor steak knife.” The problem of attributives is indeed a problem about logical form, but it may be put to one side here because it is not a problem only when the subject is action. We have decided to ignore, for the moment at least, the first two adverbial modifiers in (1), and may now deal with the problem of the logical form of: (2)
Jones buttered the toast in the bathroom with a knife at midnight.
Anthony Kenny, who deserves the credit for calling explicit attention to this problem,1 points out that most philosophers today would, as a start, analyze this sentence as containing a fiveplace predicate with the argument places filled in the obvious ways with singular terms or bound variables. If we go on to analyze “Jones buttered the toast” as containing a two-place predicate, “Jones buttered the toast in the bathroom” as containing a three-place predicate, and so forth, we obliterate the logical relation between these sentences—namely, that (2) entails the others. Or, to put the objection another way, the original sentences contain a common syntactic element (“buttered”) which we intuitively recognize as relevant to the meaning relations of the sentences. But the proposed analyses show no such common syntactic element. Kenny rejects the suggestion that “Jones buttered the toast” be considered as elliptical for “Jones buttered the toast somewhere with something at some time,” which would restore the wanted entailments, on the ground that we could never be sure how many standby positions to
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provide in each predicate of action. For example, couldn’t we add to (2) the phrase “by holding it between the toes of his left foot”? Still, this adds a place to the predicate only if it differs in meaning from “while holding it between the toes of his left foot,” and it is not quite clear that this is so. I am inclined to agree with Kenny that we cannot view verbs of action as usually containing a large number of standby positions, but I do not have what I would consider a knock-down argument. (A knock-down argument would consist in a method for increasing the number of places indefinitely.2) Kenny proposes that we may exhibit the logical form of (2) in somewhat the following manner: (3)
Jones brought it about that the toast was buttered in the bathroom with a knife at midnight.
Whatever the other merits in this proposal (I shall consider some of them presently), is clear that it does not solve the problem Kenny raises. For it is, if anything, even more obscure how (3) entails “Jones brought it about that the toast was buttered” or “The toast was buttered” than how (2) entails “Jones buttered the toast.” Kenny seems to have confused two different problems. One is the problem of how to represent the idea of agency: it is this that prompts Kenny to assign “Jones” a logically distinguished role in (3). The other is the problem of the “variable polyadicity” (as Kenny calls it) of action verbs. And it is clear that this problem is independent of the first, since it arises with respect to the sentences that replace ‘p’ in “x brings it about that p.” If I say I bought a house downtown that has four bedrooms, two fireplaces, and a glass chandelier in the kitchen, it’s obvious that I can go on forever adding details. Yet the logical form of the sentences I use presents no problem (in this respect). It is something like “There is a house such that I bought it, it is downtown, it has four bedrooms, . . .” and so forth. We can tack on a new clause at will because the iterated relative pronoun will carry the reference back to the same entity as often as desired. (Of course we know how to state this much more precisely.) Much of our talk of action suggests the same idea: that there are such things as actions, and that a sentence like (2) describes the action in a number of ways. “Jones did it with a knife.” “Please tell me more about it.” The “it” here doesn’t refer to Jones or the knife, but to what Jones did—or so it seems. “It is in principle always open to us, along various lines, to describe or refer to ‘what I did’ in so many different ways,” writes Austin in “A Plea for Excuses.”3 Austin is obviously leery of the apparent singular term, which he puts in scare quotes; yet the grammar of his sentence requires a singular term. Austin would have had little sympathy, I imagine, for the investigation into logical form I am undertaking here, though the demand that underlies it, for an intuitively acceptable and constructive theory of meaning, is one that begins to appear in the closing chapters of How to Do Things with Words. But in any case, Austin’s discussion of excuses illustrates over and over the fact that our common talk and reasoning about actions is most naturally analyzed by supposing that there are such entities. “I didn’t know it was loaded” belongs to one standard pattern of excuse. I do not deny that I pointed the gun and pulled the trigger, nor that I shot the victim. My ignorance explains how it happened that I pointed the gun and pulled the trigger intentionally, but did not shoot the victim intentionally. That the bullet pierced the victim was a consequence of my pointing the gun and pulling the trigger. It is clear that these are two different events, since one began slightly after the other. But what is the relation between my pointing the gun and pulling the trigger, and my shooting the victim? The natural and, I think, correct answer is that the relation is that of identity. The logic of this sort of excuse includes, it seems, at least this much structure: I am accused of doing b, which is deplorable. I admit I did a, which is excusable. My excuse for doing b rests upon my claim that I did not know that a = b. Another pattern of excuse would have me allow that I shot the victim intentionally, but in self-defense. Now the structure includes something more. I am still accused of b (my shooting
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the victim), which is deplorable. I admit I did c (my shooting the victim in self-defense), which is excusable. My excuse for doing b rests upon my claim that I knew or believed that b = c. The additional structure, not yet displayed, would reveal the following as a logical truth: x = c → x = b: that is, if an action is my shooting the victim in self-defense, it is my shooting the victim. The story can be given another twist. Again I shoot the victim, again intentionally. What I am asked to explain is my shooting of the bank president (d), for the victim was that distinguished gentleman. My excuse is that I shot the escaping murderer (e), and, surprising and unpleasant as it is, my shooting the escaping murderer and my shooting of the bank president were one and the same action (e = d), since the bank president and the escaping murderer were one and the same person. To justify the “since” we must presumably think of “my shooting of x” as a functional expression that names an action when the ‘x’ is replaced by an appropriate singular term. The relevant reasoning would then be an application of the principle x = y → ƒx = ƒy. Excuses provide endless examples of cases where we seem compelled to take talk of “alternative descriptions of the same action” seriously—that is, literally. But there are plenty of other contexts in which the same need presses. Explaining an action by giving an intention with which it was done provides new descriptions of the action: I am writing my name on a piece of paper with the intention of writing a check with the intention of paying my gambling debt. List all the different descriptions of my action. Here are a few for a start: I am writing my name. I am writing my name on a piece of paper. I am writing my name on a piece of paper with the intention of writing a check. I am writing a check. I am paying my gambling debt. It is hard to imagine how we can have a coherent theory of action unless we are allowed to say here: each of these sentences describes the same action. Redescription may supply the motive (“I was getting my revenge”), place the action in the context of a rule (“I am castling”), give the outcome (“I killed him”), or provide evaluation (“I did the right thing”). According to Kenny, as we just noted, action sentences have the form “Jones brought it about that p.” The sentence that replaces ‘p’ is to be in the present tense, and it describes the result that the agent has wrought: it is a sentence “newly true of the patient.”4 Thus “The doctor removed the patient’s appendix” must be rendered “The doctor brought it about that the patient has no appendix.” By insisting that the sentence that replaces ‘p’ describe a terminal state rather than an event, it may be thought that Kenny can avoid the criticism made above that the problem of logical form of action sentences turns up within the sentence that replaces ‘p’: we may allow that “The patient has no appendix” presents no relevant problem. The difficulty is that neither will the analysis stand in its present form. The doctor may bring it about that the patient has no appendix by turning the patient over to another doctor who performs the operation—or by running the patient down with his Lincoln Continental. In neither case would we say the doctor removed the patient’s appendix. Closer approximations to a correct analysis might be “The doctor brought it about that the doctor has removed the patient’s appendix” or perhaps “The doctor brought it about that the patient has had his appendix removed by the doctor.” One may still have a few doubts, I think, as to whether these sentences have the same truth conditions as “The doctor removed the patient’s appendix.” But in any case it is plain that in these versions, the problem of the logical form of action sentences does turn up in the sentences that replace ‘p’: “The patient has had his appendix removed by the doctor” or “The doctor has removed the patient’s appendix” are surely no easier to analyze than “The doctor removed the patient’s appendix.” By the same token, “Cass walked to the store” can’t be given as “Cass brought it about that Cass is at the store,” since this drops the idea of walking. Nor is it clear that “Cass brought it about that Cass is at the store and is there through having walked” will serve; but in any case again the contained sentence is worse than what we started with. It is not easy to decide what to do with “Smith coughed.” Should we say “Smith brought it about that Smith is in a state of just having coughed”? At best this would be correct only if Smith coughed on purpose.
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The difficulty in Kenny’s proposal that we have been discussing may perhaps be put this way: he wants to represent every (completed) action in terms only of the agent, the notion of bringing it about that a state of affairs obtains, and the state of affairs brought about by the agent. But many action sentences yield no description of the state of affairs brought about by the action except that it is the state of affairs brought about by that action. A natural move, then, is to allow that the sentence that replaces ‘p’ in “x brings it about that p” may (or perhaps must) describe an event. If I am not mistaken, Chisholm has suggested an analysis that at least permits the sentence that replaces ‘p’ to describe (as we are allowing ourselves to say) an event.5 His favored locution is “x makes p happen,” though he uses such variants as “x brings it about that p” or “x makes it true that p.” Chisholm speaks of the entities to which the expressions that replace ‘p’ refer as “states of affairs,” and explicitly adds that states of affairs may be changes or events (as well as “unchanges”). An example Chisholm provides is this: if a man raises his arm, then we may say he makes it happen that his arm goes up. I do not know whether Chisholm would propose “Jones made it happen that Jones’s arm went up” as an analysis of “Jones raised his arm,” but I think the proposal would be wrong because although the second of these sentences does perhaps entail the first, the first does not entail the second. The point is even clearer if we take as our example “Jones batted an eyelash.” In this case I think nothing will do but “Jones made it happen that Jones batted an eyelash” (or some trivial variant), and this cannot be called progress in uncovering the logical form of “Jones batted an eyelash.” There is something else that may puzzle us about Chisholm’s analysis of action sentences, and it is independent of the question what sentence we substitute for ‘p’. Whatever we put for ‘p’, we are to interpret it as describing some event. It is natural to say, I think, that whole sentences of the form “x makes it happen that p” also describe events. Should we say that these events are the same event, or that they are different? If they are the same event, as many people would claim (perhaps including Chisholm), then no matter what we put for ‘p’, we cannot have solved the general problem of the logical form of sentences about actions until we have dealt with the sentences that can replace ‘p’. If they are different events, we must ask how the element of agency has been introduced into the larger sentence though it is lacking in the sentence for which ‘p’ stands; for each has the agent as its subject. The answer Chisholm gives, I think, is that the special notion of making it happen that he has in mind is intentional, and thus to be distinguished from simply causing something to happen. Suppose we want to say that Alice broke the mirror without implying that she did it intentionally. Then Chisholm’s special idiom is not called for; but we could say “Alice caused it to happen that the mirror broke.” Suppose we now want to add that she did it intentionally. Then the Chisholm-sentence would be: “Alice made it happen that Alice caused it to happen that the mirror broke.” And now we want to know, what is the event that the whole sentence reports, and that the contained sentence does not? It is, apparently, just what used to be called an act of the will. I will not dredge up the standard objections to the view that acts of the will are special events distinct from, say, our bodily movements, and perhaps the causes of them. But even if Chisholm is willing to accept such a view, the problem of the logical form of the sentences that can replace ‘p’ remains, and these describe the things people do as we describe them when we do not impute intention. A somewhat different view has been developed with care and precision by von Wright in his book Norm and Action.6 In effect, von Wright puts action sentences into the following form: “x brings it about that a state where p changes into a state where q.” Thus the important relevant difference between von Wright’s analysis and the ones we have been considering is the more complex structure of the description of the change or event the agent brings about: where Kenny and Chisholm were content to describe the result of the change, von Wright includes also a description of the initial state.
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Von Wright is interested in exploring the logic of change and action and not, at least primarily, in giving the logical form of our common sentences about acts or events. For the purposes of his study, it may be very fruitful to think of events as ordered pairs of states. But I think it is also fairly obvious that this does not give us a standard way of translating or representing the form of most sentences about acts and events. If I walk from San Francisco to Pittsburgh, for example, my initial state is that I am in San Francisco and my terminal state is that I am in Pittsburgh; but the same is more pleasantly true if I fly. Of course, we may describe the terminal state as my having walked to Pittsburgh from San Francisco, but then we no longer need the separate statement of the initial state. Indeed, viewed as an analysis of ordinary sentences about actions, von Wright’s proposal seems subject to all the difficulties I have already outlined plus the extra one that most action sentences do not yield a non-trivial description of the initial state (try “He circled the field,” “He recited the Odyssey,” “He flirted with Olga”). In two matters, however, it seems to me von Wright suggests important and valuable changes in the pattern of analysis we have been considering, or at least in our interpretation of it. First, he says that an action is not an event, but, rather, the bringing about of an event. I do not think this can be correct. If I fall down, this is an event whether I do it intentionally or not. If you thought my falling was an accident and later discovered I did it on purpose, you would not be tempted to withdraw your claim that you had witnessed an event. I take von Wright’s refusal to call an action an event to be a reflection of the embarrassment we found follows if we say an act is an event, when agency is introduced by a phrase like “brings it about that.” The solution lies, however, not in distinguishing acts from events, but in finding a different logical form for action sentences. The second important idea von Wright introduces comes in the context of his distinction between generic and individual propositions about events.7 This distinction is not, as von Wright makes it, quite clear, for he says both: that an individual proposition differs from a generic one in having a uniquely determined truth value, while a generic proposition has a truth value only when coupled with an occasion; and that, that Brutus killed Caesar is an individual proposition while that Brutus kissed Caesar is a generic proposition, because “a person can be kissed by another on more than one occasion.” In fact, the proposition that Brutus kissed Caesar seems to have a uniquely determined truth value in the same sense that the proposition that Brutus killed Caesar does. But it is, I believe, a very important observation that “Brutus kissed Caesar” does not, by virtue of its meaning alone, describe a single act. It is easy to see that the proposals we have been considering concerning the logical form of action sentences do not yield solutions to the problems with which we began. I have already pointed out that Kenny’s problem, that verbs of action apparently have “variable polyadicity,” arises within the sentences that can replace ‘p’ in such formulas as “x brought it about that p.” An analogous remark goes for von Wright’s more elaborate formula. The other main problem may be put as that of assigning a logical form to action sentences that will justify claims that two sentences describe “the same action.” A study of some of the ways in which we excuse, or attempt to excuse, acts shows that we want to make inferences such as this: I flew my spaceship to the Morning Star, the Morning Star is identical with the Evening Star; so, I flew my spaceship to the Evening Star. (My leader told me not to go to the Evening Star; I headed for the Morning Star not knowing.) But suppose we translate the action sentences along the lines suggested by Kenny or Chisholm or von Wright. Then we have something like “I brought it about that my spaceship is on the Morning Star.” How can we infer, given the well-known identity, “I brought it about that my spaceship is on the Evening Star”? We know that if we replace “the Morning Star” by “the Evening Star” in “My spaceship is on the Morning Star” the truth-value will not be disturbed; and so if the occurrence of this sentence in “I brought it about that my spaceship is on the Morning Star” is truth-functional, the inference is justified. But of course the occurrence can’t be truth-functional: otherwise, from the fact that I brought about one actual state of affairs it would follow that I brought about every actual state of affairs. It is no good saying that after the words “bring
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it about that” sentences describe something between truth-values and propositions, say states of affairs. Such a claim must be backed by a semantic theory telling us how each sentence determines the state of affairs it does; otherwise the claim is empty. Israel Scheffler has put forward an analysis of sentences about choice that can be applied without serious modification to sentences about intentional acts.8 Scheffler makes no suggestion concerning action sentences that do not impute intention and so has no solution to the chief problems I am discussing. Nevertheless, his analysis has a feature I should like to mention. Scheffler would have us render “Jones intentionally buttered the toast” as “Jones made-true a that Jones-butteredthe-toast inscription.” This cannot, for reasons I have urged in detail elsewhere,9 be considered a finally satisfying form for such sentences because it contains the logically unstructured predicate “is a that Jones-buttered-the-toast inscription,” and there are an infinite number of such semantical primitives in the language. But in one respect, I believe Scheffler’s analysis is clearly superior to the others, for it implies that introducing the element of intentionality does not call for a reduction in the content of the sentence that expresses what was done intentionally. This brings out a fact otherwise suppressed: that, to use our example, “Jones” turns up twice, once inside and once outside the scope of the intentional operator. I shall return briefly to this point. A discussion of the logical form of action sentences in ordinary language is to be found in the justly famed ch. 7 of Reichenbach’s Elements of Symbolic Logic.10 According to Reichenbach’s doctrine, we may transform a sentence like (4)
Amundsen flew to the North Pole
into: (5)
(∃x)(x consists in the fact that Amundsen flew to the North Pole).
The words “is an event that consists in the fact that” are to be viewed as an operator which, when prefixed to a sentence, forms a predicate of events. Reichenbach does not think of (5) as showing or revealing the logical form of (4), for he thinks (4) is unproblematic. Rather, he says (5) is logically equivalent to (4). [Example] (5) has its counterpart in a more ordinary idiom: (6)
A flight by Amundsen to the North Pole took place.
Thus Reichenbach seems to hold that we have two ways of expressing the same idea, (4) and (6); they have quite different logical forms, but they are logically equivalent; one speaks literally of events, while the other does not. I believe this view spoils much of the merit in Reichenbach’s proposal and that we must abandon the idea that (4) has an unproblematic logical form distinct from that of (5) or (6). Following Reichenbach’s formula for putting any action sentence into the form of (5), we translate (7)
Amundsen flew to the North Pole in May 1926
into: (8)
(∃x)(x consists in the fact that Amundsen flew to the North Pole in May 1926).
The fact that (8) entails (5) is no more obvious than that (7) entails (4); what was obscure remains obscure. The correct way to render (7) is: (9)
(∃x)(x consists in the fact that Amundsen flew to the North Pole and x took place in May 1926).
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But (9) does not bear the simple relation to the standard way of interpreting (7) that (8) does. We do not know of any logical operation on (7) as it would usually be formalized (with a three-place predicate) that would make it logically equivalent to (9). This is why I suggest that we treat (9) alone as giving the logical form of (7). If we follow this strategy, Kenny’s problem of the “variable polyadicity” of action verbs is on the way to solution; there is, of course, no variable polyadicity. The problem is solved in the natural way—by introducing events as entities about which an indefinite number of things can be said. Reichenbach’s proposal has another attractive feature: it eliminates a peculiar confusion that seemed to attach to the idea that sentences like (7) “describe an event.” The difficulty was that one wavered between thinking of the sentence as describing or referring to that one flight Amundsen made in May 1926, or as describing a kind of event, or perhaps as describing (potentially?) several. As von Wright pointed out, any number of events might be described by a sentence like “Brutus kissed Caesar.” This fog is dispelled in a way I find entirely persuasive by Reichenbach’s proposal that ordinary action sentences have, in effect, an existential quantifier binding the action-variable. When we were tempted into thinking a sentence like (7) describes a single event we were misled: it does not describe any event at all. But if (7) is true, then there is an event that makes it true. This unrecognized element of generality in action sentences is, I think, of the utmost importance in understanding the relation between actions and desires; this, however, is a subject for another occasion. There are two objections to Reichenbach’s analysis of action sentences. The first may not be fatal. It is that as matters stand the analysis may be applied to any sentence whatsoever, whether it deals with actions, events, or anything else. Even “2 + 3 = 5” becomes “(∃x)(x consists in the fact that 2 + 3 = 5).” Why not say “2 + 3 = 5” does not show its true colors until put through the machine? For that matter, are we finished when we get to the first step? Shouldn’t we go on to “(∃y)(y consists in the fact that (∃x)(x consists in the fact that 2 + 3 = 5))”? And so on. It isn’t clear on what principle the decision to apply the analysis is based. The second objection is worse. We have: (10) (∃x)(x consists in the fact that I flew my spaceship to the Morning Star)
and (11) the Morning Star = the Evening Star
and we want to make the inference to (12) (∃x)(x consists in the fact that I flew my spaceship to the Evening Star).
The likely principle to justify the inference would be: (13) (x) (x consists in the fact that S ↔ x consists in the fact that S')
where ‘S'’ differs from ‘S’ only in containing in one or more places some singular term where ‘S’ contains another singular term that refers to the same thing. It is plausible to add that (13) holds if ‘S’ and ‘S'’ are logically equivalent. But (13) and the last assumption lead to trouble. For observing that ‘S’ is logically equivalent to “y]](y = y & S) = y](y = y)” we get (14) (x)(x consists in the fact that S ↔ x consists in the fact that (y](y = y & S) = y](y = y))).
Now suppose ‘R’ is any sentence materially equivalent to ‘S’: then “y](y = y & S)” and “y](y = y & R)” will refer to the same thing. Substituting in (14) we obtain
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(15) (x)(x consists in the fact that S ↔ x consists in the fact that (y](y = y & R) = y](y = y)),
which leads to (16) (x)(x consists in the fact that S ↔ x consists in the fact that R)
when we observe the logical equivalence of ‘R’ and “y](y = y & R) = y](y = y).” [Example] (16) may be interpreted as saying (considering that the sole assumption is that ‘R’ and ‘S’ are materially equivalent) that all events that occur (= all events) are identical. This demonstrates, I think, that Reichenbach’s analysis is radically defective. Now I would like to put forward an analysis of action sentences that seems to me to combine most of the merits of the alternatives already discussed, and to avoid the difficulties. The basic idea is that verbs of action—verbs that say “what someone did”—should be construed as containing a place, for singular terms or variables, that they do not appear to. For example, we would normally suppose that “Shem kicked Shaun” consisted in two names and a two-place predicate. I suggest, though, that we think of “kicked” as a three-place predicate, and that the sentence be given in this form: (17) (∃x)(Kicked(Shem, Shaun, x)).
If we try for an English sentence that directly reflects this form, we run into difficulties. “There is an event x such that x is a kicking of Shaun by Shem” is about the best I can do, but we must remember “a kicking” is not a singular term. Given this English reading, my proposal may sound very like Reichenbach’s; but of course it has quite different logical properties. The sentence “Shem kicked Shaun” nowhere appears inside my analytic sentence, and this makes it differ from all the theories we have considered. The principles that license the Morning Star–Evening Star inference now make no trouble: they are the usual principles of extensionality. As a result, nothing now stands in the way of giving a standard theory of meaning for action sentences, in the form of a Tarski-type truth definition; nothing stands in the way, that is, of giving a coherent and constructive account of how the meanings (truth conditions) of these sentences depend upon their structure. To see how one of the troublesome inferences now goes through, consider (10) rewritten as (18) (∃x)(Flew(I, my spaceship, x) & To(the Morning Star, x)).
which, along with (11), entails (19) (∃x)(Flew(I, my spaceship, x) & To(the Evening Star, x)).
It is not necessary, in representing this argument, to separate off the To-relation; instead, we could have taken “Flew” as a four-place predicate. But that would have obscured another inference, namely that from (19) to (20) (∃x)(Flew(I, my spaceship, x)).
In general, we conceal logical structure when we treat prepositions as integral parts of verbs; it is a merit of the present proposal that it suggests a way of treating prepositions as contributing structure. Not only is it nice to have the inference from (19) to (20); it is also nice to be able to keep track of the common element in “fly to” and “fly away from,” and this of course we cannot do if we treat these as unstructured predicates.
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The problem that threatened in Reichenbach’s analysis—that there seemed no clear principle on which to refrain from applying the analysis to every sentence—has a natural solution if my suggestion is accepted. Part of what we must learn when we learn the meaning of any predicate is how many places it has, and what sorts of entities the variables that hold these places range over. Some predicates have an event-place, some do not. In general, what kinds of predicates do have event-places? Without pursuing this question very far, I think it is evident that if action predicates do, many predicates that have little relation to action do. Indeed, the problems we have been mainly concerned with are not at all unique to talk of actions: they are common to talk of events of any kind. An action of flying to the Morning Star is identical with an action of flying to the Evening Star; but equally, an eclipse of the Morning Star is an eclipse of the Evening Star. Our ordinary talk of events, of causes and effects, requires constant use of the idea of different descriptions of the same event. When it is pointed out that striking the match was not sufficient to light it, what is not sufficient is not the event, but the description of it—it was a dry match, and so on. And of course Kenny’s problem of “variable polyadicity,” though he takes it to be a mark of verbs of action, is common to all verbs that describe events. It may now appear that the apparent success of the analysis proposed here is due to the fact that it has simply omitted what is peculiar to action sentences as contrasted with other sentences about events. But I do not think so. The concept of agency contains two elements, and when we separate them clearly, I think we shall see that the present analysis has not left anything out. The first of these two elements we try, rather feebly, to elicit by saying that the agent acts, or does something, instead of being acted upon, or having something happen to him. Or we say that the agent is active rather than passive; and perhaps try to make use of the moods of the verb as a grammatical clue. And we may try to depend upon some fixed phrase like “brings it about that” or “makes it the case that.” But only a little thought will make it clear that there is no satisfactory grammatical test for verbs where we want to say there is agency. Perhaps it is a necessary condition of attributing agency that one argument-place in the verb is filled with a reference to the agent as a person; it will not do to refer to his body, or his members, or to anyone else. But beyond that it is hard to go. I sleep, I snore, I push buttons, I recite verses, I catch cold. Also others are insulted by me, struck by me, admired by me, and so on. No grammatical test I know of, in terms of the things we may be said to do, of active or passive mood, or of any other sort, will separate out the cases here where we want to speak of agency. Perhaps it is true that “brings it about that” guarantees agency; but as we have seen, many sentences that do attribute agency cannot be cast in this grammatical form. I believe the correct thing to say about this element in the concept of agency is that it is simply introduced by certain verbs and not by others; when we understand the verb we recognize whether or not it includes the idea of an agent. Thus “I coughed” and “I insulted him” do impute agency to the person referred to by the first singular term; “I caught cold” and “I had my thirteenth birthday” do not. In these cases, we do seem to have the following test: we impute agency only where it makes sense to ask whether the agent acted intentionally. But there are other cases, or so it seems to me, where we impute agency only when the answer to the question whether the agent acted intentionally is “yes.” If a man falls down by accident or because a truck knocks him down, we do not impute agency; but we do if he fell down on purpose. This introduces the second element in the concept of agency, for we surely impute agency when we say or imply that the act is intentional. Instead of speaking of two elements in the concept of agency, perhaps it would be better to say there are two ways we can imply that a person acted as an agent: we may use a verb that implies it directly, or we may use a verb that is noncommittal, and add that the act was intentional. But when we take the second course, it is important not to think of the intentionality as adding an extra doing of the agent; we must not make the expression that introduces intention a verb of action. In particular, we cannot use “intentionally
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brings it about that” as the expression that introduces intention, for “brings it about that” is in itself a verb of action, and imputes agency, but it is neutral with respect to the question whether the action was intentional as described. This leaves the question what logical form the expression that introduces intention should (must) have. It is obvious, I hope, that the adverbial form must be in some way deceptive; intentional actions are not a class of actions, or, to put the point a little differently, doing something intentionally is not a manner of doing it. To say someone did something intentionally is to describe the action in a way that bears a special relation to the beliefs and attitudes of the agent; and perhaps further to describe the action as having been caused by those beliefs and attitudes.11 But of course to describe the action of the agent as having been caused in a certain way does not mean that the agent is described as performing any further action. From a logical point of view, there are thus these important conditions governing the expression that introduces intention: it must not be interpreted as a verb of action, it is intentional, and the intentionality is tied to a person. I propose, then, that we use some form of words like “It was intentional of x that p” where ‘x’ names the agent, and ‘p’ is a sentence that says the agent did something. It is useful, perhaps necessary, that the agent be named twice when we try to make logical form explicit. It is useful, because it reminds us that to describe an action as intentional is to describe the action in the light of certain attitudes and beliefs of a particular person; it may be necessary in order to illuminate what goes on in those cases in which the agent makes a mistake about who he is. It was intentional of Oedipus, and hence of the slayer of Laius, that Oedipus sought the slayer of Laius, but it was not intentional of Oedipus (the slayer of Laius) that the slayer of Laius sought the slayer of Laius. Notes I have profited from discussion with Daniel Dennett, Paul Grice, Sue Larson, David Pears, Merrill Provence, and David Wiggins. John Wallace and I talked on topics connected with this paper almost daily walking through the Odyssean landscape of Corfu during the spring of 1965; his contribution to the ideas expressed here is too pervasive to be disentangled. My research was supported by the National Science Foundation. 1. Anthony Kenny, Action, Emotion, and Will (London: Routledge and Kegan Paul, 1963), ch. 7. 2. Kenny seems to think that there is such a method, for he writes, “If we cast our net widely enough, we can make ‘Brutus killed Caesar’ into a sentence which describes, with a certain lack of specification, the whole history of the world.” (1963, p. 160). But he does not show how to make each addition to the sentence one that irreducibly modifies the killing as opposed, say, to Brutus or Caesar, or the place or the time. 3. John Austin, “A Plea for Excuses,” in Philosophical Papers (Oxford: Oxford University Press, 1971), p. 148. 4. Kenny, 1963, p. 181. 5. Roderick Chisholm, “The Descriptive Element in the Concept of Action,” Journal of Philosophy, 61, no. 20 (1964a), 613–625. Also see Chisholm, “The Ethics of Requirement,” American Philosophical Quarterly, vol. 1, no. 2 (1964b), 147–153. 6. Georg Henrik von Wright, Norm and Action: A Logical Inquiry (London: Routledge and Kegan Paul, 1963). 7. Ibid., p. 23. 8. Israel Scheffler, The Anatomy of Inquiry (New York: Knopf, 1963). See especially pp. 104–105. 9. Donald Davidson, “Theories of Meaning and Learnable Languages,” in Y. Bar-Hillel (ed.), Logic, Methodology and Philosophy of Science (Amsterdam: North-Holland, 1965), pp. 390–391. 10. Hans Reichenbach, Elements of Symbolic Logic (New York: Macmillan, 1947), §48. 11. These, and other matters directly related to the present paper, are discussed in Davidson, “Actions, Reasons and Causes,” Journal of Philosophy, vol. 60 (1963), 685–700.
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CONTEXT DEPENDENCY
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37 DAVID KAPLAN
Demonstratives
Preface In about 1966 I wrote a paper about quantification into epistemological contexts. There are very difficult metaphysical, logical, and epistemological problems involved in providing a treatment of such idioms which does not distort our intuitions about their proper use and which is up to contemporary logical standards. I did not then, and do not now, regard the treatment I provided as fully adequate. And I became more and more intrigued with problems centering on what I would like to call the semantics of direct reference. By this I mean theories of meaning according to which certain singular terms refer directly without the mediation of a Fregean Sinn as meaning. If there are such terms, then the proposition expressed by a sentence containing such a term would involve individuals directly rather than by way of the “individual concepts” or “manners of presentation” I had been taught to expect. Let us call such putative singular terms (if there are any) directly referential terms and such putative propositions (if there are any) singular propositions. Even if English contained no singular terms whose proper semantics was one of direct reference, could we determine to introduce such terms? And even if we had no directly referential terms and introduced none, is there a need or use for singular propositions? The feverish development of quantified modal logics, more generally, of quantified intensional logics, of the 1960s gave rise to a metaphysical and epistemological malaise regarding the problem of identifying individuals across worlds—what, in 1967, I called the problem of “TransWorld Heir Lines.” This problem was really just the problem of singular propositions: those which involve individuals directly, rearing its irrepressible head in the possible-world semantics that were then (and are now) so popular.
David Kaplan (1977) “Demonstratives.” In J. Almog, J. Perry, and H. Wettstein (eds.), Themes from Kaplan, 481– 563. Reprinted by permission of David Kaplan. [eds. “Demonstratives” was copyrighted and circulated in manuscript in 1977. The bracketed comments within the printed text are the author’s own, added by him to the 1989 publication. See Kaplan (1989a).]
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It was not that according to those semantical theories any sentences of the languages being studied were themselves taken to express singular propositions, it was just that singular propositions seemed to be needed in the analysis of the nonsingular propositions expressed by these sentences. For example, consider ∃x(Fx ∧ ~ Fx). This sentence would not be taken by anyone to express a singular proposition. But in order to evaluate the truth-value of the component Fx (under some assignment of an individual to the variable ‘x’), we must first determine whether the proposition expressed by its component Fx (under an assignment of an individual to the variable ‘x’) is a necessary proposition. So in the course of analyzing ∃x(Fx ∧ ~ Fx), we are required to determine the proposition associated with a formula containing a free variable. Now free variables under an assignment of values are paradigms of what I have been calling directly referential terms. In determining a semantical value for a formula containing a free variable we may be given a value for the variable—that is, an individual drawn from the universe over which the variable is taken to range—but nothing more. A variable’s first and only meaning is its value. Therefore, if we are to associate a proposition (not merely a truth-value) with a formula containing a free variable (with respect to an assignment of a value to the variable), that proposition seems bound to be singular (even if valiant attempts are made to disguise this fact by using constant functions to imitate individual concepts). The point is that if the component of the proposition (or the step in the construction of the proposition) which corresponds to the singular term is determined by the individual and the individual is directly determined by the singular term—rather than the individual being determined by the component of the proposition, which is directly determined by the singular term—then we have what I call a singular proposition. [Russell’s semantics was like the semantical theories for quantified intensional logics that I have described in that although no (closed) sentence of Principia Mathematica was taken to stand for a singular proposition, singular propositions are the essential building blocks of all propositions.] The most important hold-out against semantical theories that required singular propositions is Alonzo Church, the great modern champion of Frege’s semantical theories. Church also advocates a version of quantified intensional logic, but with a subtle difference that finesses the need for singular propositions. (In Church’s logic, given a sentential formula containing free variables and given an assignment of values to the variables, no proposition is yet determined. An additional assignment of “senses” to the free variables must be made before a proposition can be associated with the formula.) It is no accident that Church rejects direct reference semantical theories. For if there were singular terms which referred directly, it seems likely that Frege’s problem—how can a = b , if true, differ in meaning from a = a —could be reinstated, while Frege’s solution: that a and b, though referring to the same thing, do so by way of different senses, would be blocked. Also: because of the fact that the component of the proposition is being determined by the individual rather than vice versa, we have something like a violation of the famous Fregean dictum that there is no road back from denotation to sense [propositional component]. (Recently, I have come to think that if we countenance singular propositions, a collapse of Frege’s intensional ontology into Russell’s takes place.) I can draw some little pictures (Figures 37.1 and 37.2) to give you an idea of the two kinds of semantical theories I want to contrast. (These pictures are not entirely accurate for several reasons— among them, that the contrasting pictures are meant to account for more than just singular terms and that the relation marked ‘refers’ may already involve a kind of Fregean sense used to fix the referent.) I won’t go into the pros and cons of these two views at this time. Suffice it to say that I had been raised on Fregean semantics and was sufficiently devout to wonder whether the kind of quantification into modal and epistemic contexts that seemed to require singular propositions really made sense. (My paper “Quantifying In” can be regarded as an attempt to explain away such idioms for epistemic contexts.)1 But there were pressures from quarters other than quantified intensional logic in favor of a semantics of direct reference. First of all there was Donnellan’s fascinating paper “Reference and Definite Descriptions.”2 Then there were discussions I had had with Putnam in 1968 in which he
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37.1 Fregean picture
argued, with respect to certain natural kind terms like ‘tiger’ and ‘gold’, that if their Fregean senses were the kind of thing that one grasped when one understood the terms, then such senses could not determine the extension of the terms. And finally Kripke’s Princeton lectures of spring 1970, later published as Naming and Necessity,3 were just beginning to leak out along with their strong attack on the Fregean theory of proper names and their support of a theory of direct reference. As I said earlier, I was intrigued by the semantics of direct reference, so when I had a sabbatical leave for the year 1970–71, I decided to work in the area in which such a theory seemed most plausible: demonstratives. In fall 1970, I wrote, for a conference at Stanford, a paper “Dthat.”4 Using Donnellan’s ideas as a starting point, I tried to develop the contrast between Fregean semantics and the semantics of direct reference, and to argue that demonstratives—although they could be treated on a Fregean model—were more interestingly treated on a direct reference model. Ultimately I came to the conclusion that something analogous to Donnellan’s referential use of a definite description could be developed using my new demonstrative, “dthat.” In the course of this paper I groped my way to a formal semantics for demonstratives rather different in conception from those that had been offered before. In spring 1971, I gave a series of lectures at Princeton on the semantics of direct reference. By this time I had seen a transcript of Naming and Necessity, and I tried to relate some of my
FIGURE
37.2 Direct reference picture
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ideas to Kripke’s.5 I also had written out the forma1 semantics for my Logic of Demonstratives. That summer at the Irvine Philosophy of Language Institute I lectured again on the semantics of direct reference and repeated some of these lectures at various institutions in fall 1971. And there the matter has stood except for a bit of updating of the 1971 Logic of Demonstratives notes in 1973. I now think that demonstratives can be treated correctly only on a direct reference model, but that my earlier lectures at Princeton and Irvine on direct reference semantics were too broad in scope, and that the most important and certainly the most convincing part of my theory is just the logic of demonstratives itself. It is based on just a few quite simple ideas, but the conceptual apparatus turns out to be surprisingly rich and interesting. At least I hope that you will find it so. In this work I have concentrated on pedagogy. Philosophically, there is little here that goes beyond the Summer Institute Lectures, but I have tried, by limiting the scope, to present the ideas in a more compelling way. Some new material appears in the two speculative sections: XVII (Epistemological Remarks) and XX (Adding ‘Says’). It is my hope that a theory of demonstratives will give us the tools to go on in a more sure-footed way to explore the de re propositional attitudes, as well as other semantical issues.
I Introduction I believe my theory of demonstratives to be uncontrovertable and largely uncontroversial. This is not a tribute to the power of my theory but a concession of its obviousness. In the past, no one seems to have followed these obvious facts out to their obvious consequences. I do that. What is original with me is some terminology to help fix ideas when things get complicated. It has been fascinating to see how interesting the obvious consequences of obvious principles can be.6
II Demonstratives, indexicals, and pure indexicals I tend to describe my theory as “a theory of demonstratives,” but that is poor usage. It stems from the fact that I began my investigations by asking what is said when a speaker points at someone and says, “He is suspicious.”7 The word ‘he’, so used, is a demonstrative, and the accompanying pointing is the requisite associated demonstration. I hypothesized a certain semantical theory for such demonstratives, and then I invented a new demonstrative, ‘dthat’, and stipulated that its semantics be in accord with my theory. I was so delighted with this methodological sleight of hand for my demonstrative ‘dthat’, that when I generalized the theory to apply to words like ‘I’, ‘now’, ‘here’, et cetera—words which do not require an associated demonstration—I continued to call my theory a “theory of demonstratives” and I referred to these words as “demonstratives.” That terminological practice conflicts with what I preach, and I will try to correct it. (But I tend to backslide.) The group of words for which I propose a semantical theory includes the pronouns ‘I’, ‘my’, ‘you’, ‘he’, ‘his’, ‘she’, ‘it’; the demonstrative pronouns ‘that’, ‘this’; the adverbs ‘here’, ‘now’, ‘tomorrow’, ‘yesterday’; the adjectives ‘actual’, ‘present’; and others. These words have uses other than those in which I am interested (or, perhaps, depending on how you individuate words, we should say that they have homonyms in which I am not interested). For example, the pronouns ‘he’ and ‘his’ are used not as demonstratives but as bound variables in For what is a man profited, if he shall gain the whole world, and lose his own soul?
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What is common to the words or usages in which I am interested is that the referent is dependent on the context of use and that the meaning of the word provides a rule which determines the referent in terms of certain aspects of the context. The term I now favor for these words is “indexical.” Other authors have used other terms; Russell used “egocentric particular,” and Reichenbach used “token reflexive.” I prefer “indexical” (which, I believe, is due to Peirce) because it seems less theory laden than the others, and because I regard Russell’s and Reichenbach’s theories as defective. Some of the indexicals require, in order to determine their referents, an associated demonstration: typically, though not invariably, a (visual) presentation of a local object discriminated by a pointing.8 These indexicals are the true demonstratives, and ‘that’ is their paradigm. The demonstrative (an expression) refers to that which the demonstration demonstrates. I call that which is demonstrated the “demonstratum.” A demonstrative without an associated demonstration is incomplete. The linguistic rules which govern the use of the true demonstratives ‘that’, ‘he’, etc., are not sufficient to determine their referent in all contexts of use. Something else—an associated demonstration—must be provided. The linguistic rules assume that such a demonstration accompanies each (demonstrative) use of a demonstrative. An incomplete demonstrative is not vacuous like an improper definite description. A demonstrative can be vacuous in various cases. For example, when its associated demonstration has no demonstratum (a hallucination)—or the wrong kind of demonstratum (pointing to a flower and saying ‘he’ in the belief that one is pointing to a man disguised as a flower9— or too many demonstrata (pointing to two intertwined vines and saying ‘that vine’). But it is clear that one can distinguish a demonstrative with a vacuous demonstration: no referent; from a demonstrative with no associated demonstration: incomplete. All this is by way of contrasting true demonstratives with pure indexicals. For the latter, no associated demonstration is required, and any demonstration supplied is either for emphasis or is irrelevant.10 Among the pure indexicals are ‘I’, ‘now’, ‘here’ (in one sense), ‘tomorrow’, and others. The linguistic rules which govern their use fully determine the referent for each context.11 No supplementary actions or intentions are needed. The speaker refers to himself when he uses ‘I’, and no pointing to another or believing that he is another or intending to refer to another can defeat this reference.12 Michael Bennett has noted that some indexicals have both a pure and a demonstrative use. ‘Here’ is a pure indexical in I am in here and is a demonstrative in In two weeks, I will be here [pointing at a city on a map].
III Two obvious principles So much for preliminaries. My theory is based on two obvious principles. The first has been noted in every discussion of the subject: PRINCIPLE 1
The referent of a pure indexical depends on the context, and the referent of a demonstrative depends on the associated demonstration.
If you and I both say ‘I’ we refer to different persons. The demonstratives ‘that’ and ‘he’ can be correctly used to refer to any one of a wide variety of objects simply by adjusting the accompanying demonstration. The second obvious principle has less often been formulated explicitly: PRINCIPLE 2
Indexicals, pure and demonstrative alike, are directly referential.
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IV Remarks on rigid designators In an earlier draft I adopted the terminology of Kripke, called indexicals “rigid designators,” and tried to explain that my usage differed from his. I am now shying away from that terminology. But because it is so well known, I will make some comments on the notion or notions involved. The term “rigid designator” was coined by Saul Kripke to characterize those expressions which designate the same thing in every possible world in which that thing exists and which designate nothing elsewhere. He uses it in connection with his controversial, though, I believe, correct claim that proper names, as well as many common nouns, are rigid designators. There is an unfortunate confusion in the idea that a proper name would designate nothing if the bearer of the name were not to exist.13 Kripke himself adopts positions which seem inconsistent with this feature of rigid designators. In arguing that the object designated by a rigid designator need not exist in every possible world, he seems to assert that under certain circumstances what is expressed by ‘Hitler does not exist’ would have been true, and not because ‘Hitler’ would have designated nothing (in that case we might have given the sentence no truth-value) but because what ‘Hitler’ would have designated—namely, Hitler—would not have existed.14 Furthermore, it is a striking and important feature of the possible world semantics for quantified intensional logics, which Kripke did so much to create and popularize, that variables, those paradigms of rigid designation, designate the same individual in all possible worlds whether the individual “exists” or not.15 Whatever Kripke’s intentions (did he, as I suspect, misdescribe his own concept?) and whatever associations or even meaning the phrase “rigid designator” may have, I intend to use “directly referential” for an expression whose referent, once determined, is taken as fixed for all possible circumstances—that is, is taken as being the propositional component. For me, the intuitive idea is not that of an expression which turns out to designate the same object in all possible circumstances, but an expression whose semantical rules provide directly that the referent in all possible circumstances is fixed to be the actual referent. In typical cases the semantical rules will do this only implicitly, by providing a way of determining the actual referent and no way of determining any other propositional component.16 We should beware of a certain confusion in interpreting the phrase ‘designates the same object in all circumstances’. We do not mean that the expression could not have been used to designate a different object. We mean, rather, that given a use of the expression, we may ask of what has been said whether it would have been true or false in various counterfactual circumstances, and in such counterfactual circumstances, which are the individuals relevant to determining truth-value. Thus we must distinguish possible occasions of use—which I call contexts—from possible circumstances of evaluation of what was said on a given occasion of use. Possible circumstances of evaluation I call circumstances or, sometimes, just counterfactual situations. A directly referential term may designate different objects when used in different contexts. But when evaluating what was said in a given context, only a single object will be relevant to the evaluation in all circumstances. This sharp distinction between contexts of use and circumstances of evaluation must be kept in mind if we are to avoid a seeming conflict between Principles 1 and 2.17 To look at the matter from another point of view, once we recognize the obviousness of both principles (I have not yet argued for Principle 2), the distinction between contexts of use and circumstances of evaluation is forced upon us. If I may wax metaphysical in order to fix an image, let us think of the vehicles of evaluation—the what-is-said in a given context—as propositions. Don’t think of propositions as sets of possible worlds but, rather, as structured entities looking something like the sentences which express them. For each occurrence of a singular term in a sentence there will be a corresponding constituent in the proposition expressed. The constituent of the proposition determines, for each circumstance of evaluation, the object relevant to evaluating the proposition in that circumstance.
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In general, the constituent of the proposition will be some sort of complex, constructed from various attributes by logical composition. But in the case of a singular term which is directly referential, the constituent of the proposition is just the object itself. Thus it is that it does not just turn out that the constituent determines the same object in every circumstance, the constituent (corresponding to a rigid designator) just is the object. There is no determining to do at all. On this picture—and this is really a picture and not a theory—the definite description (1)
The n[(Snow is slight ∧ n2 = 9) ∨ (~Snow is slight ∧ 22 = n + 1)]18
would yield a constituent which is complex although it would determine the same object in all circumstances. Thus, (1), though a rigid designator, is not directly referential from this (metaphysical) point of view. Note, however, that every proposition which contains the complex expressed by (1) is equivalent to some singular proposition which contains just the number three itself as constituent.19 The semantical feature that I wish to highlight in calling an expression directly referential is not the fact that it designates the same object in every circumstance, but the way in which it designates an object in any circumstance. Such an expression is a device of direct reference. This does not imply that it has no conventionally fixed semantical rules which determine its referent in each context of use; quite the opposite. There are semantical rules which determine the referent in each context of use—but that is all. The rules do not provide a complex which together with a circumstance of evaluation yields an object. They just provide an object. If we keep in mind our sharp distinction between contexts of use and circumstances of evaluation, we will not be tempted to confuse a rule which assigns an object to each context with a “complex” which assigns an object to each circumstance. For example, each context has an agent (loosely, a speaker). Thus an appropriate designation rule for a directly referential term would be: (2)
In each possible context of use the given term refers to the agent of the context.
But this rule could not be used to assign a relevant object to each circumstance of evaluation. Circumstances of evaluation do not, in general, have agents. Suppose I say, (3)
I do not exist.
Under what circumstances would what I said be true? It would be true in circumstances in which I did not exist. Among such circumstances are those in which no one, and thus, no speakers, no agents exist. To search a circumstance of evaluation for a speaker in order to (mis)apply rule (2) would be to go off on an irrelevant chase. Three paragraphs ago I sketched a metaphysical picture of the structure of a proposition. The picture is taken from the semantical parts of Russell’s Principles of Mathematics.20 Two years later, in “On Denoting,”21 even Russell rejected that picture. But I still like it. It is not a part of my theory, but it well conveys my conception of a directly referential expression and of the semantics of direct reference. (The picture needs some modification in order to avoid difficulties which Russell later noted—though he attributed them to Frege’s theory rather than his own earlier theory.)22 If we adopt a possible worlds semantics, all directly referential terms will be regarded as rigid designators in the modified sense of an expression which designates the same thing in all possible worlds (irrespective of whether the thing exists in the possible world or not).23 However, as already noted, I do not regard all rigid designators—not even all strongly rigid designators (those that designate something that exists in all possible worlds) or all rigid designators in the modified sense— as directly referential. I believe that proper names, like variables, are directly referential. They are
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not, in general, strongly rigid designators, nor are they rigid designators in the original sense.24 What is characteristic of directly referential terms is that the designatum (referent) determines the propositional component, rather than the propositional component, along with a circumstance, determining the designatum. It is for this reason that a directly referential term that designates a contingently existing object will still be a rigid designator in the modified sense. The propositional component need not choose its designatum from those offered by a passing circumstance; it has already secured its designatum before the encounter with the circumstance. When we think in terms of possible world semantics, this fundamental distinction becomes subliminal. This is because the style of the semantical rules obscures the distinction and makes it appear that directly referential terms differ from ordinary definite descriptions only in that the propositional component in the former case must be a constant function of circumstances. In actual fact, the referent, in a circumstance, of a directly referential term is simply independent of the circumstance and is no more a function (constant or otherwise) of circumstance, than my action is a function of your desires when I decide to do it whether you like it or not. The distinction that is obscured by the style of possible world semantics is dramatized by the structured propositions picture. That is part of the reason why I like it. Some directly referential terms, like proper names, may have no semantically relevant descriptive meaning, or at least none that is specific; that distinguishes one such term from another. Others, like the indexicals, may have a limited kind of specific descriptive meaning relevant to the features of a context of use. Still others, like ‘dthat’ terms (see below), may be associated with full-blown Fregean senses used to fix the referent. But in any case, the descriptive meaning of a directly referential term is no part of the propositional content.
V Argument for principle 2: Pure indexicals As stated earlier, I believe this principle is uncontroversial. But I had best distinguish it from similar principles which are false. I am not claiming, as has been claimed for proper names, that indexicals lack anything that might be called “descriptive meaning.” Indexicals, in general, have a rather easily statable descriptive meaning. But it is clear that this meaning is relevant only to determining a referent in a context of use and not to determining a relevant individual in a circumstance of evaluation. Let us return to the example in connection with the sentence (3) and the indexical ‘I’. The bizarre result of taking the descriptive meaning of the indexical to be the propositional constituent is that what I said in uttering (3) would be true in a circumstance of evaluation if and only if the speaker (assuming there is one) of the circumstance does not exist in the circumstance. Nonsense! If that were the correct analysis, what I said could not be true. From which it follows that It is impossible that I do not exist. Here is another example to show that the descriptive meaning of an indexical may be entirely inapplicable in the circumstance of evaluation. When I say, I wish I were not speaking now, the circumstances desired do not involve contexts of use and agents who are not speaking. The actual context of use is used to determine the relevant individual: me—and time: now—and then we query the various circumstances of evaluation with respect to that individual and that time. Here is another example, not of the inapplicability of the descriptive meaning to circumstances but of its irrelevance. Suppose I say at t0, “It will soon be the case that all that is now beautiful is faded.” Consider what was said in the subsentence, All that is now beautiful is faded. I wish to evaluate that content at some near future time t1. What is the relevant time associated with the indexical ‘now’? Is it the future time t1? No, it is t0, of course: the time of the context of use. See how rigidly the indexicals cling to the referent determined in the context of use: (4)
It is possible that in Pakistan, in five years, only those who are actually here now are envied.
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The point of (4) is that the circumstance, place, and time referred to by the indexicals ‘actually’, ‘here’, and ‘now’ are the circumstance, place, and time of the context, not a circumstance, place, and time determined by the modal, locational, and temporal operators within whose scope the indexicals lie. It may be objected that this only shows that indexicals always take primary scope (in the sense of Russell’s scope of a definite description). This objection attempts to relegate all direct reference to implicit use of the paradigm of the semantics of direct reference, the variable. Thus (4) is transformed into The actual circumstances, here, and now are such that it is possible that in Pakistan in five years only those who, in the first, are located at the second, during the third, are envied.
Although this may not be the most felicitous form of expression, its meaning and, in particular, its symbolization should be clear to those familiar with quantified intensional logics. The pronouns, ‘the first’, ‘the second’, and ‘the third’ are to be represented by distinct variables bound to existential quantifiers at the beginning and identified with ‘the actual circumstance’, ‘here’, and ‘now’, respectively: (5)
(∃w)(∃p)(∃t)[w=the actual circumstance ∧ p=here ∧ t=now ∧ ◊ In Pakistan In five years ∀x(x is envied → x is located at p during t in w)]
But such transformations, when thought of as representing the claim that indexicals take primary scope, do not provide an alternative to Principle 2, since we may still ask of an utterance of (5) in a context c, when evaluating it with respect to an arbitrary circumstance, to what do the indexicals ‘actual’, ‘here’, and ‘now’ refer? The answer, as always, is: the relevant features of the context c. [In fact, although (4) is equivalent to (5), neither indexicals nor quantification across intensional operators is dispensable in favor of the other.] Perhaps enough has been said to establish the following: (T1) The descriptive meaning of a pure indexical determines the referent of the indexical with respect to a context of use but is either inapplicable or irrelevant to determining a referent with respect to a circumstance of evaluation.
I hope that your intuition will agree with mine that it is for this reason that: (T2) When what was said in using a pure indexical in a context c is to be evaluated with respect to an arbitrary circumstance, the relevant object is always the referent of the indexical with respect to the context c.
This is just a slightly elaborated version of Principle 2. Before turning to true demonstratives, we will adopt some terminology.
VI Terminological remarks Principle 1 and Principle 2 taken together imply that sentences containing pure indexicals have two kinds of meaning. VI.1 Content and circumstance What is said in using a given indexical in different contexts may be different. Thus if I say, today, I was insulted yesterday, and you utter the same words tomorrow, what is said is different. If
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what we say differs in truth-value, that is enough to show that we say different things. But even if the truth-values were the same, it is clear that there are possible circumstances in which what I said would be true but what you said would be false. Thus we say different things. Let us call this first kind of meaning—what is said—content. The content of a sentence in a given context is what has traditionally been called a proposition. Strawson, in noting that the sentence The present king of France is bald could be used on different occasions to make different statements, used “statement” in a way similar to our use of content of a sentence. If we wish to express the same content in different contexts, we may have to change indexicals. Frege, here using ‘thought’ for content of a sentence, expresses the point well: If someone wants to say the same today as he expressed yesterday using the word ‘today’, he must replace this word with ‘yesterday’. Although the thought is the same its verbal expression must be different so that the sense, which would otherwise be affected by the differing times of utterance, is readjusted.25
I take content as a notion applying not only to sentences taken in a context but to any meaningful part of speech taken in a context. Thus we can speak of the content of a definite description, an indexical, a predicate, et cetera. It is contents that are evaluated in circumstances of evaluation. If the content is a proposition (i.e., the content of a sentence taken in some context), the result of the evaluation will be a truth-value. The result of evaluating the content of a singular term at a circumstance will be an object (what I earlier called “the relevant object”). In general, the result of evaluating the content of a well-formed expression a at a circumstance will be an appropriate extension for a (i.e., for a sentence, a truth-value; for a term, an individual; for an n-place predicate, a set of n-tuples of individuals, etc.). This suggests that we can represent a content by a function from circumstances of evaluation to an appropriate extension. Carnap called such functions intensions. The representation is a handy one, and I will often speak of contents in terms of it, but one should note that contents which are distinct but equivalent (i.e., share a value in all circumstances) are represented by the same intension. Among other things, this results in the loss of my distinction between terms which are devices of direct reference and descriptions which turn out to be rigid designators. (Recall the metaphysical paragraph of section IV.) I wanted the content of an indexical to be just the referent itself, but the intension of such a content will be a constant function. Use of representing intensions does not mean I am abandoning that idea—just ignoring it temporarily. A fixed content is one represented by a constant function. All directly referential expressions (as well as all rigid designators) have a fixed content. [What I elsewhere call a stable content.] Let us settle on circumstances for possible circumstances of evaluation. By this I mean both actual and counterfactual situations with respect to which it is appropriate to ask for the extensions of a given well-formed expression. A circumstance will usually include a possible state or history of the world, a time, and perhaps other features as well. The amount of information we require from a circumstance is linked to the degree of specificity of contents, and thus to the kinds of operators in the language. Operators of the familiar kind treated in intensional logic (modal, temporal, etc.) operate on contents. (Since we represent contents by intensions, it is not surprising that intensional operators operate on contents.) Thus an appropriate extension for an intensional operator is a function from intensions to extensions.26 A modal operator when applied to an intension will look at the behavior of the intension with respect to the possible state of the world feature of the circumstances of evaluation. A temporal operator will, similarly, be concerned with the time of the circumstance. If we built the time of evaluation into the contents (thus removing time from the circumstances leaving only, say, a possible world history, and making contents specific as to time),
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it would make no sense to have temporal operators. To put the point another way, if what is said is thought of as incorporating reference to a specific time, or state of the world, or whatever, it is otiose to ask whether what is said would have been true at another time, in another state of the world, or whatever. Temporal operators applied to eternal sentences (those whose contents incorporate a specific time of evaluation) are redundant. Any intensional operators applied to perfect sentences (those whose contents incorporate specific values for all features of circumstances) are redundant.27 What sorts of intensional operators to admit seems to me largely a matter of language engineering. It is a question of which features of what we intuitively think of as possible circumstances can be sufficiently well defined and isolated. If we wish to isolate location and regard it as a feature of possible circumstances, we can introduce locational operators: ‘Two miles north it is the case that’, et cetera. Such operators can be iterated and can be mixed with modal and temporal operators. However, to make such operators interesting, we must have contents which are locationally neutral. That is, it must be appropriate to ask if what is said would be true in Pakistan. (For example, ‘It is raining’ seems to be locationally as well as temporally and modally neutral.) This functional notion of the content of a sentence in a context may not, because of the neutrality of content with respect to time and place, say, exactly correspond to the classical conception of a proposition. But the classical conception can be introduced by adding the demonstratives ‘now’ and ‘here’ to the sentence and taking the content of the result. I will continue to refer to the content of a sentence as a proposition, ignoring the classical use. Before leaving the subject of circumstances of evaluation I should, perhaps, note that the mere attempt to show that an expression is directly referential requires that it be meaningful to ask of an individual in one circumstance whether and with what properties it exists in another circumstance. If such questions cannot be raised because they are regarded as metaphysically meaningless, the question of whether a particular expression is directly referential (or even, a rigid designator) cannot be raised. I have elsewhere referred to the view that such questions are meaningful as haecceitism, and I have described other metaphysical manifestations of this view.28 I advocate this position, although I am uncomfortable with some of its seeming consequences (for example, that the world might be in a state qualitatively exactly as it is, but with a permutation of individuals). It is hard to see how one could think about the semantics of indexicals and modality without adopting such a view. VI.2
Character
The second kind of meaning, most prominent in the case of indexicals, is that which determines the content in varying contexts. The rule, ‘I’ refers to the speaker or writer, is a meaning rule of the second kind. The phrase ‘the speaker or writer’ is not supposed to be a complete description, nor is it supposed to refer to the speaker or writer of the word ‘I’. (There are many such.) It refers to the speaker or writer of the relevant occurrence of the word ‘I’—that is, the agent of the context. Unfortunately, as usually stated, these meaning rules are incomplete in that they do not explicitly specify that the indexical is directly referential, and thus do not completely determine the content in each context. I will return to this later. Let us call the second kind of meaning, character. The character of an expression is set by linguistic conventions and, in turn, determines the content of the expression in every context.29 Because character is what is set by linguistic conventions, it is natural to think of it as meaning in the sense of what is known by the competent language user. Just as it was convenient to represent contents by functions from possible circumstances to extensions (Carnap’s intentions), so it is convenient to represent characters by functions from
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possible contexts to contents. (As before we have the drawback that equivalent characters are identified.30) This gives us the following picture: Character: Contexts ⇒ Contents Content: Circumstances ⇒ Extensions
or, in more familiar language, Meaning + Context ⇒ Intension Intension + Possible World ⇒ Extension
Indexicals have a context-sensitive character. It is characteristic of an indexical that its content varies with context. Nonindexicals have a fixed character. The same content is invoked in all contexts. This content will typically be sensitive to circumstances—that is, the nonindexicals are typically not rigid designators but will vary in extension from circumstance to circumstance. Eternal sentences are generally good examples of expressions with a fixed character: All persons alive in 1977 will have died by 2077 expresses the same proposition no matter when said, by whom, or under what circumstances. The truth-value of that proposition may, of course, vary with possible circumstances, but the character is fixed. Sentences with fixed character are very useful to those wishing to leave historical records. Now that we have two kinds of meaning in addition to extension, Frege’s principle of intensional interchange31 becomes two principles: (F1) The character of the whole is a function of the character of the parts. That is, if two compound well-formed expressions differ only with respect to components which have the same Character, then the Character of the compounds is the same. (F2) The Content of the whole is a function of the Content of the parts. That is, if two compound well-formed expressions, each set in (possibly different) contexts differ only with respect to components which when taken in their respective contexts have the same content, then the content of the two compounds each taken in its own context is the same.
It is the second principle that accounts for the often noted fact that speakers in different contexts can say the same thing by switching indexicals. (And, indeed, they often must switch indexicals to do so.) Frege illustrated this point with respect to ‘today’ and ‘yesterday’ in “The Thought.” (But note that his treatment of ‘I’ suggests that he does not believe that utterances of ‘I’ and ‘you’ could be similarly related!) Earlier, in my metaphysical phase, I suggested that we should think of the content of an indexical as being just the referent itself, and I resented the fact that the representation of contents as intensions forced us to regard such contents as constant functions. A similar remark applies here. If we are not overly concerned with standardized representations (which certainly have their value for model-theoretic investigations), we might be inclined to say that the character of an indexical-free word or phrase just is its (constant) content.
VII Earlier attempts: Index theory The following picture seems to emerge. The meaning (character) of an indexical is a function from contexts to extensions (substituting for fixed contents). The meaning (content, substituting for fixed characters) of a nonindexical is a function from circumstances to extensions. From this point of view it may appear that the addition of indexicals requires no new logic, no sharp distinction between contexts and circumstances, just the addition of some special new features (“con-
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textual” features) to the circumstances of evaluation. (For example, an agent to provide an interpretation for ‘I’.) Thus an enlarged view of intension is derived. The intension of an expression is a function from certain factors to the extension of the expression (with respect to those factors). Originally such factors were simply possible states of the world, but as it was noticed that the so-called tense operators exhibited a structure highly analogous to that of the modal operators the factors with respect to which an extension was to be determined were enlarged to include moments of time. When it was noticed that contextual factors were required to determine the extension of sentences containing indexicals, a still more general notion was developed and called an “index.” The extension of an expression was to be determined with respect to an index. The intension of an expression was that function which assigned to every index, the extension at that index: The above example supplies us with a statement whose truth-value is not constant but varies as a function of i ∈ I. This situation is easily appreciated in the context of time-dependent statements; that is, in the case where I represents the instant of time. Obviously the same statement can be true at one moment and false at another. For more general situations one must not think of the i ∈ I as anything as simple as instants of time or even possible worlds. In general we will have i = (w, t, p, a, . . .) where the index i has many coordinates: for example, w is a world, t is a time, p = (x, y, z) is a (3–dimensional) position in the world, a is an agent, etc. All these coordinates can be varied, possibly independently, and thus affect the truth-values of statements which have indirect references to these coordinates. [From the Advice of a prominent logician.]
A sentence f was taken to be logically true if true at every index (in every ‘structure’), and
f was taken to be true at a given index (in a given structure) just in case f was true at every index (in that structure). Thus the familiar principle of modal generalization: if f, then f, is validated. This view, in its treatment of indexicals, was technically wrong and, more importantly, conceptually misguided. Consider the sentence (6)
I am here now.
It is obvious that for many choices of index—that is, for many quadruples 〈w, x, p, t〉 where w is a possible world history, x is a person, p is a place, and t is a time—(6) will be false. In fact, (6) is true only with respect to those indices 〈w, x, p, t〉 which are such that in the world history w, x is located at p at the time t. Thus (6) fares about on a par with (7)
David Kaplan is in Portland on 26 March 1977.
[Example] (7) is empirical, and so is (6). But here we have missed something essential to our understanding of indexicals. Intuitively, (6) is deeply, and in some sense, which we will shortly make precise, universally, true. One need only understand the meaning of (6) to know that it cannot be uttered falsely. No such guarantees apply to (7). A Logic of lndexicals which does not reflect this intuitive difference between (6) and (7) has bypassed something essential to the logic of indexicals. What has gone wrong? We have ignored the special relationship between ‘I’, ‘here’, and ‘now’. Here is a proposed correction. Let the class of indices be narrowed to include only the proper ones—namely, those 〈w, x, p, t〉 such that in the world w, x is located at p at the time t.
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Such a move may have been intended originally since improper indices are like impossible worlds; no such contexts could exist, and thus there is no interest in evaluating the extensions of expressions with respect to them. Our reform has the consequence that (6) comes out, correctly, to be logically true. Now consider (8)
I am here now.
Since the contained sentence (namely (6)) is true at every proper index, (8) also is true at every proper index and thus also is logically true. (As would be expected by the aforementioned principle of modal generalization.) But (8) should not be logically true, since it is false. It is certainly not necessary that I be here now. But for several contingencies, I would be working in my garden now, or even delivering this paper in a location outside of Portland. The difficulty here is the attempt to assimilate the role of a context to that of a circumstance. The indices 〈w, x, p, t〉 that represent contexts must be proper in order that (6) be a truth of the logic of indexicals, but the indices that represent circumstances must include improper ones in order that (8) not be a logical truth. If one wishes to stay with this sort of index theory and blur the conceptual difference between context and circumstance, the minimal requirement is a system of double indexing—one index for context and another for circumstance. It is surprising, looking back, that we (for I was among the early index theorists) did not immediately see that double indexing was required, for in 1967, at UCLA, Hans Kamp had reported his work on ‘now’32 in which he had shown that double indexing was required to properly accommodate temporal indexicals along with the usual temporal operators. But it was four years before it was realized that this was a general requirement for (and, in a sense, the key to) a logic of indexicals. However, mere double indexing, without a clear conceptual understanding of what each index stands for, is still not enough to avoid all pitfalls.
VIII Monsters begat by elegance My liberality with respect to operators on content—that is, intensional operators (any feature of the circumstances of evaluation that can be well defined and isolated) does not extend to operators which attempt to operate on character. Are there such operators as ‘In some contexts it is true that’, which when prefixed to a sentence yields a truth if and only if in some context the contained sentence (not the content expressed by it) expresses a content that is true in the circumstances of that context? Let us try it: (9)
In some contexts it is true that I am not tired now.
For (9) to be true in the present context, it suffices that some agent of some context not be tired at the time of that context. [Example] (9), so interpreted, has nothing to do with me or the present moment. But this violates Principle 2! Principle 2 can also be expressed in a more theory-laden way by saying that indexicals always take primary scope. If this is true—and it is—then no operator can control the character of the indexicals within its scope, because they will simply leap out of its scope to the front of the operator. I am not saying we could not construct a language with such operators, just that English is not one.33 And such operators could not be added to it. There is a way to control an indexical, to keep it from taking primary scope, and even to refer it to another context (this amounts to changing its character): Use quotation marks. If we
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mention the indexical rather than use it, we can, of course, operate directly on it. Carnap once pointed out to me how important the difference between direct and indirect quotation is in Otto said “I am a fool.” Otto said that I am a fool.
Operators like ‘In some contexts it is true that’, which attempt to meddle with character, I call monsters. I claim that none can be expressed in English (without sneaking in a quotation device). If they stay in the metalanguage and confine their attention to sentences as in In some contexts “I am not tired now” is true, they are rendered harmless and can even do socially useful work (as does, ‘is valid’ [see below]). I have gone on at perhaps excessive length about monsters because they have recently been begat by elegance. In a specific application of the theory of indexicals there will be just certain salient features of a circumstance of evaluation. So we may represent circumstances by indexed sets of features. This is typical of the model-theoretic way, As already indicated, all the features of a circumstance will generally be required as aspects of a context, and the aspects of a context may all be features of a circumstance. If not, a little ingenuity may make it so.34 We could then represent contexts by the same indexed sets we use to represent circumstances, and instead of having a logic of contexts and circumstances we have simply a two-dimensional logic of indexed sets. This is algebraically very neat, and it permits a very simple and elegant description of certain important classes of characters (for example, those which are true at every pair 〈i, i〉, though the special significance of the set is somehow diminished in the abstract formulation).35 But it also permits a simple and elegant introduction of many operators which are monsters. In abstracting from the distinct conceptual roles played by contexts of use and circumstances of evaluation, the special logic of indexicals has been obscured. Of course restrictions can be put on the two-dimensional logic to exorcise the monsters, but to do so would be to give up the mathematical advantages of that formulation.36
IX Argument for principle 2: True demonstratives I return now to the argument that all indexicals are directly referential. Suppose I point at Paul and say, He now lives in Princeton, New Jersey. Call what I said—that is, the content of my utterance, the proposition expressed—‘Pat’. Is Pat true or false? True! Suppose that unbeknownst to me, Paul had moved to Santa Monica last week. Would Pat have then been true or false? False! Now, the tricky case: suppose that Paul and Charles had each disguised themselves as the other and had switched places. If that had happened, and I had uttered as I did, then the proposition I would have expressed would have been false. But in that possible context the proposition I would have expressed is not Pat. That is easy to see because the proposition I would have expressed, had I pointed to Charles instead of Paul—call this proposition ‘Mike’—not only would have been false but actually is false. Pat, I would claim, would still be true in the circumstances of the envisaged possible context provided that Paul—in whatever costume he appeared—were still residing in Princeton. IX.1
The arguments
I am arguing that in order to determine what the truth-value of a proposition expressed by a sentence containing a demonstrative would be under other possible circumstances, the relevant individual is not the individual that would have been demonstrated had those circumstances obtained and the demonstration been set in a context of those circumstances, but rather the individual
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demonstrated in the context which did generate the proposition being evaluated. As I have already noted, it is characteristic of sentences containing demonstratives—or, for that matter, any indexical—that they may express different propositions in different contexts. We must be wary of confusing the proposition that would have been expressed by a similar utterance in a slightly different context—say, one in which the demonstratum is changed—with the proposition that was actually expressed. If we keep this distinction in mind—that is, we distinguish Pat and Mike— we are less likely to confuse what the truth-value of the proposition actually expressed would have been under some possible circumstances with what the truth-value of the proposition that would have been expressed would have been under those circumstances. When we consider the vast array of possible circumstances with respect to which we might inquire into the truth of a proposition expressed in some context c by an utterance u, it quickly becomes apparent that only a small fraction of these circumstances will involve an utterance of the same sentence in a similar context, and that there must be a way of evaluating the truth-value of propositions expressed using demonstratives in counterfactual circumstances in which no demonstrations are taking place and no individual has the exact characteristics exploited in the demonstration. Surely, it is irrelevant to determining whether what I said would be true or not in some counterfactual circumstance, whether Paul, or anyone for that matter, looked as he does now. All that would be relevant is where he lives. Therefore, (T3) the relevant features of the demonstratum qua demonstratum (compare, the relevant features of the x Fx qua the x Fx)—namely, that the speaker is pointing at it, that it has a certain appearance, is presented in a certain way—cannot be the essential characteristics used to identify the relevant individual in counterfactual situations.
These two arguments—the distinction between Pat and Mike, and consideration of counterfactual situations in which no demonstration occurs—are offered to support the view that demonstratives are devices of direct reference (rigid designators, if you will) and, by contrast, to reject a Fregean theory of demonstratives. IX.2 The Fregean theory of demonstrations In order to develop the latter theory, in contrast to my own, we turn first to a portion of the Fregean theory which I accept: the Fregean theory of demonstrations. As you know, for a Fregean the paradigm of a meaningful expression is the definite description, which picks out or denotes an individual, a unique individual, satisfying a condition s. The individual is called the denotation of the definite description, and the condition s we may identify with the sense of the definite description. Since a given individual may uniquely satisfy several distinct conditions, definite descriptions with distinct senses may have the same denotation. And since some conditions may be uniquely satisfied by no individual, a definite description may have a sense but no denotation. The condition by means of which a definite description picks out its denotation is the manner of presentation of the denotation by the definite description. The Fregean theory of demonstratives claims, correctly I believe, that the analogy between descriptions (short for “definite descriptions”) and demonstrations is close enough to provide a sense and denotation analysis of the “meaning” of a demonstration. The denotation is the demonstratum (that which is demonstrated), and it seems quite natural to regard each demonstration as presenting its demonstratum in a particular manner, which we may regard as the sense of the demonstration. The same individual could be demonstrated by demonstrations so different in manner of presentation that it would be informative to a competent auditor-observer to be told that the demonstrata were one. For example, it might be informative to you for me to tell you that
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That [pointing to Venus in the morning sky] is identical with that [pointing to Venus in the evening sky]
(I would, of course, have to speak very slowly.) The two demonstrations—call the first one ‘Phos’ and the second one ‘Hes’—which accompanied the two occurrences of the demonstrative expression ‘that’ have the same demonstratum but distinct manners of presentation. It is this difference between the sense of Hes and the sense of Phos that accounts, the Fregean claims, for the informativeness of the assertion. It is possible, to pursue the analogy, for a demonstration to have no demonstratum. This can arise in several ways: through hallucination, through carelessness (not noticing, in the darkened room, that the subject had jumped off the demonstration platform a few moments before the lecture began), through a sortal conflict (using the demonstrative phrase that F , where F is a common noun phrase, while demonstrating something which is not an F), and in other ways. Even Donnellans’s important distinction between referential and attributive uses of definite descriptions seems to fit, equally comfortably, the case of demonstrations.37 The Fregean hypostatizes demonstrations in such a way that it is appropriate to ask of a given demonstration, say Phos, what would it have demonstrated under various counterfactual circumstances? Phos and Hes might have demonstrated distinct individuals.38 We should not allow our enthusiasm for analogy to overwhelm judgment in this case. There are some relevant respects in which descriptions and demonstrations are disanalogous. First, as David Lewis has pointed out, demonstrations do not have a syntax, a fixed formal structure in terms of whose elements we might try to define, either directly or recursively, the notion of sense.39 Second, to different audiences (for example, the speaker, those sitting in front of the demonstration platform, and those sitting behind the demonstration platform) the same demonstration may have different senses. Or perhaps we should say that a single performance may involve distinct demonstrations from the perspective of distinct audiences. (“Exactly like proper names!” says the Fregean, “as long as the demonstratum remains the same, these fluctuations in sense are tolerable. But they should be avoided in the system of a demonstrative science and should not appear in a perfect vehicle of communication.”) IX.3 The Fregean theory of demonstratives Let us accept, tentatively and cautiously, the Fregean theory of demonstrations, and turn now to the Fregean theory of demonstratives.40 According to the Fregean theory of demonstratives, an occurrence of a demonstrative expression functions rather like a place-holder for the associated demonstration. The sense of a sentence containing demonstratives is to be the result of replacing each demonstrative by a constant whose sense is given as the sense of the associated demonstration. An important aim of the Fregean theory is, of course, to solve Frege’s problem. And it does that quite neatly. You recall that the Fregean accounted for the informativeness of That [Hes] = that [Phos] in terms of the distinct senses of Hes and Phos. Now we see that the senses of the two occurrences of ‘that’ are identified with these two distinct senses so that the ultimate solution is exactly like that given by Frege originally. The sense of the left ‘that’ differs from the sense of the right ‘that’. IX.4 Argument against the Fregean theory of demonstratives Let us return now to our original example: He [Delta] now lives in Princeton, New Jersey where ‘Delta’ is the name of the relevant demonstration. I assume that in the possible circumstances described earlier, Paul and Charles having disguised themselves as each other, Delta would have demonstrated Charles. Therefore, according to the Fregean theory, the proposition I just expressed,
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Pat, would have been false under the counterfactual circumstances of the switch. But this, as argued earlier, is wrong. Therefore, the Fregean theory of demonstratives—though it nicely solves Frege’s problem—is simply incorrect in associating propositions with utterances. Let me recapitulate. We compared two theories as to the proposition expressed by a sentence containing a demonstrative along with an associated demonstration. Both theories allow that the demonstration can be regarded as having both a sense and a demonstratum. My theory, the direct reference theory, claims that in assessing the proposition in counterfactual circumstances it is the actual demonstratum—in the example, Paul—that is the relevant individual. The Fregean theory claims that the proposition is to be construed as if the sense of the demonstration were the sense of the demonstrative. Thus, in counterfactual situations it is the individual that would have been demonstrated that is the relevant individual. According to the direct reference theory, demonstratives are rigid designators. According to the Fregean theory, their denotation varies in different counterfactual circumstances as the demonstrata of the associated demonstration would vary in those circumstances. The earlier distinction between Pat and Mike, and the discussion of counterfactual circumstances in which, as we would now put it, the demonstration would have demonstrated nothing, argue that with respect to the problem of associating propositions with utterances the direct reference theory is correct and the Fregean theory is wrong. I have carefully avoided arguing for the direct reference theory by using modal or subjunctive sentences for fear the Fregean would claim that the peculiarity of demonstratives is not that they are rigid designators but that they always take primary scope. If I had argued only on the basis of our intuitions as to the truth-value of If Charles and Paul had changed chairs, then he (Delta) would not now be living in Princeton, such a scope interpretation could be claimed. But I didn’t. The perceptive Fregeans among you will have noted that I have said nothing about how Frege’s problem fares under a direct reference theory of demonstratives. And indeed, if ‘that’ accompanied by a demonstration is a rigid designator for the demonstratum, then that (Hes) = that (Phos) looks like two rigid designators designating the same thing. Uh oh! I will return to this in my Epistemological Remarks (section XVII).
X Fixing the reference vs. supplying a synonym41 The Fregean is to be forgiven. He has made a most natural mistake. Perhaps he thought as follows: If I point at someone and say ‘he’, that occurrence of ‘he’ must refer to the male at whom I am now pointing. It does! So far, so good. Therefore, the Fregean reasons, since ‘he’ (in its demonstrative sense) means the same as ‘the male at whom I am now pointing’ and since the denotation of the latter varies with circumstances, the denotation of the former must also. But this is wrong. Simply because it is a rule of the language that ‘he’ refers to the male at whom I am now pointing (or, whom I am now demonstrating, to be more general), it does not follow that any synonymy is thereby established. In fact, this is one of those cases in which—to use Kripke’s excellent idiom—the rule simply tells us how to fix the reference but does not supply a synonym. Consider the proposition I express with the utterance He [Delta] is the male at whom I am now pointing. Call that proposition ‘Sean’. Now Sean is certainly true. We know from the rules of the language that any utterance of that form must express a true proposition. In fact, we would be justified in calling the sentence, He is the male at whom I am now pointing, almost analytic. (“Almost” because of the hypothesis that the demonstrative is proper—that I am pointing at a unique male—is needed.) But is Sean necessary? Certainly not: I might have pointed at someone else. This kind of mistake—to confuse a semantical rule which tells how to fix the reference to a directly referential term with a rule which supplies a synonym—is easy to make. Since seman-
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tics must supply a meaning in the sense of content (as I call it), for expressions, one thinks naturally that whatever way the referent of an expression is given by the semantical rules, that way must stand for the content of the expression. (Church [or was it Carnap?] says as much, explicitly.) This hypothesis seems especially plausible, when, as is typical of indexicals, the semantical rule which fixes the reference seems to exhaust our knowledge of the meaning of the expression. X.1
Reichenbach on Token Reflexives
It was from such a perspective, I believe, that Reichenbach built his ingenious theory of indexicals. Reichenbach called such expressions “token-reflexive words” in accordance with his theory. He writes as follows: We saw that most individual-descriptions are constructed by reference to other individuals. Among these there is a class of descriptions in which the individual referred to is the act of speaking. We have special words to indicate this reference; such words are ‘I’, ‘you’, ‘here’, ‘now’, ‘this’. Of the same sort are the tenses of verbs, since they determine time by reference to the time when the words are uttered. To understand the function of these words we have to make use of the distinction between token and symbol, ‘token’ meaning the individual sign, and ‘symbol’ meaning the class of similar tokens (cf. §2). Words and sentences are symbols. The words under consideration are words which refer to the corresponding token used in an individual act of speech, or writing; they may therefore be called token-reflexive words. It is easily seen that all these words can be defined in terms of the phrase ‘this token’. The word ‘I’, for instance, means the same as ‘the person who utters this token’; ‘now’ means the same as ‘the time at which this token was uttered’; ‘this table’ means the same as ‘the table pointed to by a gesture accompanying this token’. We therefore need inquire only into the meaning of the phrase ‘this token’.42
But is it true, for example, that (10) ‘I’ means the same as ‘the person who utters this token’?
It is certainly true that I am the person who utters this token. But if (10) correctly asserted a synonymy, then it would be true that (11) If no one were to utter this token, I would not exist.
Beliefs such as (11) could make one a compulsive talker.
XI The meaning of indexicals In order to correctly and more explicitly state the semantical rule which the dictionary attempts to capture by the entry I:
the person who is speaking or writing
we would have to develop our semantical theory—the semantics of direct reference—and then state that (D1)
‘I’ is an indexical, different utterances of which may have different contents.
(D3)
‘I’ is, in each of its utterances, directly referential.
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(D2) In each of its utterances, ‘I’ refers to the person who utters it.
We have seen errors in the Fregean analysis of demonstratives and in Reichenbach’s analysis of indexicals, all of which stemmed from failure to realize that these words are directly referential. When we say that a word is directly referential, are we saying that its meaning is its reference (its only meaning is its reference, its meaning is nothing more than its reference)? Certainly not.43 Insofar as meaning is given by the rules of a language and is what is known by competent speakers, I would be more inclined to say in the case of directly referential words and phrases that their reference is no part of their meaning. The meaning of the word ‘I’ does not change when different persons use it. The meaning of ‘I’ is given by the rules (D1), (D2), and (D3) above. Meanings tell us how the content of a word or phrase is determined by the context of use. Thus the meaning of a word or phrase is what I have called its character. (Words and phrases with no indexical element express the same content in every context; they have a fixed character.) To supply a synonym for a word or phrase is to find another with the same character; finding another with the same content in a particular context certainly won’t do. The content of ‘I’ used by me may be identical with the content of ‘you’ used by you. This doesn’t make ‘I’ and ‘you’ synonyms. Frege noticed that if one wishes to say again what one said yesterday using ‘today’, today one must use ‘yesterday’. (Incidentally the relevant passage, quoted on 758 (this volume), propounds what I take to be a direct reference theory of the indexicals ‘today’ and ‘yesterday’.) But ‘today’ and ‘yesterday’ are not synonyms. For two words or phrases to be synonyms, they must have the same content in every context. In general, for indexicals, it is not possible to find synonyms. This is because indexicals are directly referential, and the compound phrases which can be used to give their reference (‘the person who is speaking’, ‘the individual being demonstrated’, etc.) are not.
XII Dthat It would be useful to have a way of converting an arbitrary singular term into one which is directly referential. Recall that we earlier regarded demonstrations, which are required to “complete” demonstratives, as a kind of description. The demonstrative was then treated as a directly referential term whose referent was the demonstratum of the associated demonstration. Now why not regard descriptions as a kind of demonstration, and introduce a special demonstrative which requires completion by a description and which is treated as a directly referential term whose referent is the denotation of the associated description? Why not? Why not, indeed! I have done so, and I write it thus: dthat[a]
where a is any description, or, more generally, any singular term. ‘Dthat’44 is simply the demonstrative ‘that’ with the following singular term functioning as its demonstration. (Unless you hold a Fregean theory of demonstratives, in which case its meaning is as stipulated above.) Now we can come much closer to providing genuine synonyms: ‘I’ means the same as ‘dthat [the person who utters this token]’.
(The fact that this alleged synonymy is cast in the theory of utterances rather than occurrences introduces some subtle complications, which have been discussed by Reichenbach.)
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XIII Contexts, truth, and logical truth I wish, in this section, to contrast an occurrence of a well-formed expression (my technical term for the combination of an expression and a context) with an utterance of an expression. There are several arguments for my notion, but the main one is from Remark 1 on the Logic of Demonstratives (section XIX below): I have sometimes said that the content of a sentence in a context is, roughly, the proposition the sentence would express if uttered in that context. This description is not quite accurate on two counts. First, it is important to distinguish an utterance from a sentence-in-a-context. The former notion is from the theory of speech acts; the latter from semantics. Utterances take time, and utterances of distinct sentences cannot be simultaneous (i.e., in the same context). But in order to develop a logic of demonstratives, we must be able to evaluate several premises and a conclusion all in the same context. We do not want arguments involving indexicals to become valid simply because there is no possible context in which all the premises are uttered, and thus no possible context in which all are uttered truthfully. Since the content of an occurrence of a sentence containing indexicals depends on the context, the notion of truth must be relativized to a context: If c is a context, then an occurrence of f in c is true iff the content expressed by f in this context is true when evaluated with respect to the circumstance of the context.
We see from the notion of truth that among other aspects of a context must be a possible circumstance. Every context occurs in a particular circumstance, and there are demonstratives such as ‘actual’ which refer to that circumstance. If you try out the notion of truth on a few examples, you will see that it is correct. If I now utter a sentence, I will have uttered a truth just in case what I said, the content, is true in these circumstances. As is now common for intensional logics, we provide for the notion of a structure, comprising a family of circumstances. Each such structure will determine a set of possible contexts. Truth in a structure, is truth in every possible context of the structure. Logical truth is truth in every structure.
XIV Summary of findings (so far): Pure indexicals Let me try now to summarize my findings regarding the semantics of demonstratives and other indexicals. First, let us consider the nondemonstrative indexicals such as ‘I’, ‘here’ (in its nondemonstrative sense), ‘now’, ‘today’, ‘yesterday’, and so on. In the case of these words, the linguistic conventions which constitute meaning consist of rules specifying the referent of a given occurrence of the word (we might say, a given token, or even utterance, of the word, if we are willing to be somewhat less abstract) in terms of various features of the context of the occurrence. Although these rules fix the referent and, in a very special sense, might be said to define the indexical, the way in which the rules are given does not provide a synonym for the indexical. The rules tell us for any possible occurrence of the indexical what the referent would be, but they do not constitute the content of such an occurrence. Indexicals are directly referential. The rules tell us what it is that is referred to. Thus, they determine the content (the propositional constituent) for a particular occurrence of an indexical. But they are not a part of the content (they constitute no part of the propositional constituent). In order to keep clear on a topic where ambiguities constantly threaten, I have introduced two technical terms—content and character—for the two kinds of meaning (in addition to extension) I associate with indexicals. Distinct occurrences of
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an indexical (in distinct contexts) may not only have distinct referents, they may have distinct meanings in the sense of content. If I say “I am tired today” today, and Montgomery Furth says “I am tired today” tomorrow, our utterances have different contents in that the factors which are relevant to determining the truth-value of what Furth said in both actual and counterfactual circumstances are quite different from the factors which are relevant to determining the truth-value of what I said. Our two utterances are as different in content as are the sentences “David Kaplan is tired on 26 March 1977” and “Montgomery Furth is tired on 27 March 1977.” But there is another sense of meaning in which, absent lexical or syntactical ambiguities, two occurrences of the same word or phrase must mean the same. (Otherwise how could we learn and communicate with language?) This sense of meaning—which I call character—is what determines the content of an occurrence of a word or phrase in a given context. For indexicals, the rules of language constitute the meaning in the sense of character. As normally expressed, in dictionaries and the like, these rules are incomplete in that, by omitting to mention that indexicals are directly referential, they fail to specify the full content of an occurrence of an indexical. Three important features to keep in mind about these two kinds of meaning are the following: 1. Character applies only to words and phrases as types, content to occurrences of words and phrases in contexts. 2. Occurrences of two phrases can agree in content, although the phrases differ in character, and two phrases can agree in character but differ in content in distinct contexts. 3. The relationship of character to content is something like that traditionally regarded as the relationship of sense to denotation: character is a way of presenting content.
XV Further details: Demonstratives and demonstrations Let me turn now to the demonstratives proper, those expressions which must be associated with a demonstration in order to determine a referent. In addition to the pure demonstratives ‘that’ and ‘this’, there are a variety of demonstratives which contain built-in sortals—‘he’ for ‘that male’, ‘she’ for ‘that female’,45 etc.—and there are demonstrative phrases built from a pure demonstrative and a common noun phrase: ‘that man drinking a martini’, et cetera. Words and phrases which have demonstrative use may have other uses as well—for example, as bound variable or pronouns of laziness (anaphoric use). I accept, tentatively and cautiously, the Fregean theory of demonstrations according to which: 1. A demonstration is a way of presenting an individual. 2. A given demonstration in certain counterfactual circumstances would have demonstrated (i.e., presented) an individual other than the individual actually demonstrated. 3. A demonstration which fails to demonstrate any individual might have demonstrated one, and a demonstration which demonstrates an individual might have demonstrated no individual at all. So far we have asserted that it is not an essential property of a given demonstration (according to the Fregean theory) that it demonstrate a given individual, or, indeed, that it demonstrate any individual at all. It is this feature of demonstration—that demonstrations which in fact demonstrate the same individual might have demonstrated distinct individuals—which provides a solution to the demonstrative version of Frege’s problem (why is an utterance of ‘that [Hes] =
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that [Phos]’ informative?) analogous to Frege’s own solution to the definite description version. There is some theoretical latitude as to how we should regard such other features of a demonstration as its place, time, and agent. Just to fix ideas, let us regard all these features as accidental. (It may be helpful to think of demonstrations as types and particular performances of them as their tokens). Then, 4. A given demonstration might have been mounted by someone other than its actual agent, and might be repeated in the same or a different place. Although we are not now regarding the actual place and time of a demonstration as essential to it, it does seem to me to be essential to a demonstration that it present its demonstrata from some perspective—that is, as the individual that looks thusly from here now. On the other hand, it does not seem to me to be essential to a demonstration that it be mounted by any agent at all.46 We now have a kind of standard form for demonstrations: The individual that has appearance A from here now
where an appearance is something like a picture with a little arrow pointing to the relevant subject. Trying to put it into words, a particular demonstration might come out like: The brightest heavenly body now visible from here.
In this example we see the importance of perspective. The same demonstration, differently located, may present a different demonstratum (a twin, for example). If we set a demonstration, d, in a context, c, we determine the relevant perspective (i.e., the values of ‘here’ and ‘now’). We also determine the demonstratum, if there is one—if, that is, in the circumstances of the context there is an individual that appears that way from the place and time of the context.47 In setting d and c we determine more than just the demonstratum in the possible world of the context. By fixing the perspective, we determine for each possible circumstance what, if anything, would appear like that from that perspective. This is to say, we determine a content. This content will not, in general, be fixed (like that determined by a rigid designator). Although it was Venus that appeared a certain way from a certain location in ancient Greece, it might have been Mars. Under certain counterfactual conditions, it would have been Mars that appeared just that way from just that location. Set in a different context, d may determine a quite different content or no content at all. When I look at myself in the mirror each morning I know that I didn’t look like that ten years ago—and I suspect that nobody did. The preceding excursion into a more detailed Fregean theory of demonstrations was simply in order to establish the following structural features of demonstrations: 1. A demonstration, when set in a context (i.e., an occurrence of a demonstration), determines a content. 2. It is not required that an occurrence of a demonstration have a fixed content. In view of these features, we can associate with each demonstration a character which represents the “meaning” or manner of presentation of the demonstration. We have now brought the semantics of demonstrations and descriptions into isomorphism.48 Thus, I regard my ‘dthat’ operator as representing the general case of a demonstrative. Demonstratives are incomplete expressions which must be completed by a demonstration (type). A complete sentence (type) will include an associated demonstration (type) for each of its demonstratives. Thus each demonstrative, d, will be accompanied by a demonstration, d, thus: d[d]. The character of a complete demonstrative is given by the semantical rule:
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In any context c, d[d] is a directly referential term that designates the demonstratum, if any, of d in c, and that otherwise designates nothing.
Obvious adjustments are to be made to take into account any common noun phrase which accompanies or is built in to the demonstrative. Since no immediately relevant structural differences have appeared between demonstrations and descriptions, I regard the treatment of the ‘dthat’ operator in the formal logic LD as accounting for the general case. It would be a simple matter to add to the syntax a category of “nonlogical demonstration constants.” (Note that the indexicals of LD are all logical signs in the sense that their meaning [character] is not given by the structure but by the evaluation rules.)
XVI Alternative treatments of demonstrations The foregoing development of the Fregean theory of demonstrations is not inevitable. Michael Bennett has proposed that only places be demonstrata and that we require an explicit or implicit common noun phrase to accompany the demonstrative, so that that [pointing at a person] becomes dthat [the person who is there [pointing at a place]]. My findings do not include the claim that the—or better, a—Fregean theory of demonstrations is correct. I can provide an alternative account for those who regard demonstrations as nonrepeatable nonseparable features of contexts. The conception now under consideration is that in certain contexts the agent is demonstrating something, or more than one thing, and in others not. Thus just as we can speak of agent, time, place, and possible world history as features of a context, we may also speak of first demonstratum, second demonstratum, . . . (some of which may be null) as features of a context. We then attach subscripts to our demonstratives and regard the n-th demonstrative, when set in a context, as rigid designator of the n-th demonstratum of the context. Such a rule associates a character with each demonstrative. In providing no role for demonstrations as separable “manners of presentation,” this theory eliminates the interesting distinction between demonstratives and other indexicals. We might call it the Indexical theory of demonstratives. (Of course, every reasonable theory of demonstratives treats them as indexicals of some kind. I regard my own theory of indexicals in general, and the nondemonstrative indexicals in particular, as essentially uncontroversial. Therefore I reserve Indexical theory of demonstratives for the controversial alternative to the Fregean theory of demonstrations—the Fregean theory of demonstratives having been refuted.) Let us call my theory as based on the Fregean theory of demonstrations the Corrected Fregean theory of demonstratives. The Fregean theory of demonstrations may be extravagant, but compared with its riches, the indexical theory is a mean thing. From a logical point of view, the riches of the Corrected Fregean theory of demonstratives are already available in connection with the demonstrative ‘dthat’ and its descriptive pseudodemonstrations, so a decision to enlarge the language of LD with additional demonstratives whose semantics are in accord with the Indexical theory need not be too greatly lamented. If we consider Frege’s problem, we have the two formulations: that [Hes] = that [Phos] that1 = that2
Both provide their sentence with an informative character. But the Fregean idea that that very demonstration might have picked out a different demonstratum seems to me to capture more of the epistemological situation than the Indexicalist’s idea that in some contexts the first and second demonstrata differ.
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The Corrected Fregean theory, by incorporating demonstration types in its sentence types, accounts for more differences in informativeness as differences in meaning (character). It thereby provides a nice Frege-type solution to many Frege-type problems. But it can only forestall the resort to directly epistemological issues; it cannot hold them in abeyance indefinitely. Therefore I turn to epistemological remarks.
XVII Epistemological remarks How do content and character serve as objects of thought?49 Let us state, once again, Frege’s problem (FP) How can (an occurrence of) a = b (in a given context), if true, differ in cognitive significance from (an occurrence of) a = a (in the same context)?
In (FP) a, b are arbitrary singular terms. (In future formulations, I will omit the parentheticals as understood.) When a and b are demonstrative free, Frege explained the difference in terms of his notion of sense—a notion which, his writings generally suggest, should be identified with our content. But it is clear that Frege’s problem can be reinstituted in a form in which resort to contents will not explain differences in “cognitive significance.” We need only ask, (FPD) How can dthat[a] = dthat[b] if true, differ in cognitive significance from dthat[a] = dthat[a] ?
Since, as we shall show, for any term g, g = dthat[g] is analytic, the sentence pair in (FP) will differ in cognitive significance if and only if the sentence pair in (FPD) differ similarly. [There are a few assumptions built in here, but they are O.K.] Note, however, that the content of dthat[a] and the content of dthat[b] are the same whenever a = b is true. Thus the difference in cognitive significance between the sentence pair in (FPD) cannot be accounted for in terms of content. If Frege’s solution to (FP) was correct, then a and b have different contents. From this it follows that dthat[a] and dthat[b] have different characters. [It doesn’t really, because of the identification of contents with intensions, but let it pass.] Is character, then, the object of thought? If you and I both say to ourselves, (B) “I am getting bored”
have we thought the same thing? We could not have, because what you thought was true, while what I thought was false. What we must do is disentangle two epistemological notions: the objects of thought (what Frege called “Thoughts”) and the cognitive significance of an object of thought. As has been noted above, a character may be likened to a manner of presentation of a content. This suggests that we identify objects of thought with contents and the cognitive significance of such objects with characters. E PRINCIPLE 1
Objects of thought (Thoughts) = Contents E PRINCIPLE 2
Cognitive significance of a Thought = Character
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According to this view, the thoughts associated with dthat[a] = dthat[b] and dthat[a] = dthat[a] are the same, but the thought (not the denotation, mind you, but the thought) is presented differently. It is important to see that we have not simply generalized Frege’s theory, providing a higher order Fregean sense for each name of a regular Fregean sense.50 In Frege’s theory, a given manner of presentation presents the same object to all mankind.51 But for us, a given manner of presentation—a character; what we both said to ourselves when we both said (B)—will, in general, present different objects (of thought) to different persons (and even different Thoughts to the same person at different times). How then can we claim that we have captured the idea of cognitive significance? To break the link between cognitive significance and universal Fregean senses and at the same time forge the link between cognitive significance and character, we must come to see the context-sensitivity (dare I call it ego-orientation?) of cognitive states. Let us try a Putnam-like experiment. We raise two identical twins, Castor and Pollux, under qualitatively identical conditions, qualitatively identical stimuli, et cetera. If necessary, we may monitor their brain states and make small corrections in their brain structures if they begin drifting apart. They respond to all cognitive stimuli in identical fashion.52 Have we not been successful in achieving the same cognitive (i.e., psychological) state? Of course we have, what more could one ask! But wait, they believe different things. Each sincerely says, My brother was born before I was, and the beliefs they thereby express conflict. In this, Castor speaks the truth, while Pollux speaks falsely. This does not reflect on the identity of their cognitive states, for, as Putnam has emphasized, circumstances alone do not determine extension (here, the truth-value) from cognitive state. Insofar as distinct persons can be in the same cognitive state, Castor and Pollux are. COROLLARY 1
It is an almost inevitable consequence of the fact that two persons are in the same cognitive state, that they will disagree in their attitudes toward some object of thought.
The corollary applies equally well to the same person at different times, and to the same person at the same time in different circumstances.53 In general, the corollary applies to any individuals x, y in different contexts. My aim was to argue that the cognitive significance of a word or phrase was to be identified with its character, the way the content is presented to us. In discussing the twins, I tried to show that persons could be in the same total cognitive state and still, as we would say, believe different things. This doesn’t prove that the cognitive content of, say, a single sentence or even a word is to be identified with its character, but it strongly suggests it. Let me try a different line of argument. We agree that a given content may be presented under various characters and that, consequently, we may hold a propositional attitude toward a given content under one character but not under another. (For example, on March 27 of this year, having lost track of the date, I may continue to hope to be finished by this March 26, without hoping to be finished by yesterday.) Now instead of arguing that character is what we would ordinarily call cognitive significance, let me just ask why we should be interested in the character under which we hold our various attitudes. Why should we be interested in that special kind of significance that is sensitive to the use of indexicals—‘I’, ‘here’, ‘now’, ‘that’, and the like? John Perry, in his stimulating and insightful paper “Frege on Demonstratives” asks and answers this question. [Perry uses ‘thought’ where I would use ‘object of thought’ or ‘content’ and he uses ‘apprehend’ for ‘believe’, but note that other psychological verbs would yield analogous cases. I have taken a few liberties in substituting my own terminology for Perry’s and have added the emphasis.]
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Why should we care under what character someone apprehends a thought, so long as he does? I can only sketch the barest suggestion of an answer here. We use the manner of presentation, the character, to individuate psychological states, in explaining and predicting action. It is the manner of presentation, the character and not the thought apprehended, that is tied to human action. When you and I have beliefs under the common character of ‘A bear is about to attack me’, we behave similarly. We both roll up in a ball and try to be as still as possible. Different thoughts apprehended, same character, same behavior. When you and I both apprehend that I am about to be attacked by a bear, we behave differently. I roll up in a ball, you run to get help. Same thought apprehended, different characters, different behaviors.54
Perry’s examples can be easily multiplied. My hope to be finished by a certain time is sensitive to how the content corresponding to the time is presented, as ‘yesterday’ or as ‘this March 26’. If I see, reflected in a window, the image of a man whose pants appear to be on fire, my behavior is sensitive to whether I think, ‘His pants are on fire’ or ‘My pants are on fire’, though the object of thought may be the same. So long as Frege confined his attention to indexical free expressions, and given his theory of proper names, it is not surprising that he did not distinguish objects of thought (content) from cognitive significance (character), for that is the realm of fixed character and thus, as already remarked, there is a natural identification of character with content. Frege does, however, discuss indexicals in two places. The first passage, in which he discusses ‘yesterday’ and ‘today’, I have already discussed. Everything he says there is essentially correct. (He does not go far enough.) The second passage has provoked few endorsements and much skepticism. It too, I believe, is susceptible of an interpretation which makes it essentially correct. I quote it in full: Now everyone is presented to himself in a particular and primitive way, in which he is presented to no one else. So, when Dr. Lauben thinks that he has been wounded, he will probably take as a basis this primitive way in which he is presented to himself. And only Dr. Lauben himself can grasp thoughts determined in this way. But now he may want to communicate with others. He cannot communicate a thought which he alone can grasp. Therefore, if he now says ‘I have been wounded’, he must use the ‘I’ in a sense that can be grasped by others, perhaps in the sense of ‘he who is speaking to you at this moment’, by doing which he makes the associated conditions of his utterance serve for the expression of his thought.55
What is the particular and primitive way in which Dr. Lauben is presented to himself? What cognitive content presents Dr. Lauben to himself, but presents him to nobody else? Thoughts determined this way can be grasped by Dr. Lauben, but no one else can grasp that thought determined in that way. The answer, I believe, is, simply, that Dr. Lauben is presented to himself under the character of ‘I’. A sloppy thinker might succumb to the temptation to slide from an acknowledgement of the privileged perspective we each have on ourselves—only I can refer to me as ‘I’—to the conclusions: first, that this perspective necessarily yields a privileged picture of what is seen (referred to), and second, that this picture is what is intended when one makes use of the privileged perspective (by saying ‘I’). These conclusions, even if correct, are not forced upon us. The character of ‘I’ provides the acknowledged privileged perspective, whereas the analysis of the content of particular occurrences of ‘I’ provides for (and needs) no privileged pictures. There may be metaphysical, epistemological, or ethical reasons why I (so conceived) am especially important to myself. (Compare: why now is an especially important time to me. It too is presented in a particular and primitive way, and this moment cannot be presented at any other time in the same way.)56 But the phenomenon noted by Frege—that everyone is presented to himself in a particular and primitive way—can be fully accounted for using only our semantical theory.
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Furthermore, regarding the first conclusion, I sincerely doubt that there is, for each of us on each occasion of the use of ‘I’, a particular, primitive, and incommunicable Fregean self-concept which we tacitly express to ourselves. And regarding the second conclusion: even if Castor were sufficiently narcissistic to associate such self-concepts with his every use of ‘I’, his twin, Pollux, whose mental life is qualitatively identical with Castor’s, would associate the same self-concept with his every (matching) use of ‘I’.57 The second conclusion would lead to the absurd result that when Castor and Pollux each say ‘I’, they do not thereby distinguish themselves from one another. (An even more astonishing result is possible. Suppose that due to a bit of self-deception the self-concept held in common by Castor and Pollux fits neither of them. The second conclusion then leads irresistibly to the possibility that when Castor and Pollux each say ‘I’ they each refer to a third party!) The perceptive reader will have noticed that the conclusions of the sloppy thinker regarding the pure indexical ‘I’ are not unlike those of the Fregean regarding true demonstratives. The sloppy thinker has adopted a demonstrative theory of indexicals: ‘I’ is synonymous with ‘this person’ [along with an appropriate subjective demonstration], ‘now’ with ‘this time’, ‘here’ with ‘this place’ [each associated with some demonstration], and so on. Like the Fregean, the sloppy thinker errs in believing that the sense of the demonstration is the sense of the indexical, but the sloppy thinker commits an additional error in believing that such senses are in any way necessarily associated with uses of pure indexicals. The slide from privileged perspective to privileged picture is the sloppy thinker’s original sin. Only one who is located in the exact center of the Sahara Desert is entitled to refer to that place as ‘here’, but aside from that, the place may present no distinguishing features.58 The sloppy thinker’s conclusions may have another source. Failure to distinguish between the cognitive significance of a thought and the thought itself seems to have led some to believe that the elements of an object of thought must each be directly accessible to the mind. From this it follows that if a singular proposition is an object of thought, the thinker must somehow be immediately acquainted with each of the individuals involved. But, as we have seen, the situation is rather different from this. Singular propositions may be presented to us under characters which neither imply nor presuppose any special form of acquaintance with the individuals of the singular propositions. The psychological states, perhaps even the epistemological situations, of Castor and Pollux are alike, yet they assert distinct singular propositions when they each say “My brother was born before me.” Had they lived at different times, they might still have been situated alike epistemologically while asserting distinct singular propositions in saying “It is quiet here now.” A kidnapped heiress, locked in the trunk of a car, knowing neither the time nor where she is, may think “It is quiet here now,” and the indexicals will remain directly referential.59 COROLLARY 2
Ignorance of the referent does not defeat the directly referential character of indexicals.
From this it follows that a special form of knowledge of an object is neither required nor presupposed in order that a person may entertain as object of thought a singular proposition involving that object. There is nothing inaccessible to the mind about the semantics of direct reference, even when the reference is to that which we know only by description. What allows us to take various propositional attitudes towards singular propositions is not the form of our acquaintance with the objects but is, rather, our ability to manipulate the conceptual apparatus of direct reference.60 The foregoing remarks are aimed at refuting Direct Acquaintance Theories of direct reference. According to such theories, the question whether an utterance expresses a singular proposition turns, in the first instance, on the speaker’s knowledge of the referent rather than on the form of the reference. If the speaker lacks the appropriate form of acquaintance with the referent,
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the utterance cannot express a singular proposition, and any apparently directly referring expressions used must be abbreviations or disguises for something like Fregean descriptions. Perhaps the Direct Acquaintance theorist thought that only a theory like his could permit singular propositions while still providing a solution for Frege’s problem. If we could directly refer to a given object in nonequivalent ways (e.g., as ‘dthat[Hes]’ and ‘dthat[Phos]’), we could not—so he thought—explain the difference in cognitive significance between the appropriate instances of
a = a and a = b . Hence, the objects susceptible to direct reference must not permit such reference in inequivalent ways. These objects must, in a certain sense, be wholly local and completely given so that for any two directly coreferential terms a and b, a = b will be uniformative to anyone appropriately situated, epistemologically, to be able to use these terms.61 I hope that my discussion of the two kinds of meaning—content and character—will have shown the Direct Acquaintance Theorist that his views are not the inevitable consequence of the admission of directly referential terms. From the point of view of a lover of direct reference this is good, since the Direct Acquaintance theorist admits direct reference in a portion of language so narrow that it is used only by philosophers.62 I have said nothing to dispute the epistemology of the Direct Acquaintance theorist, nothing to deny that there exists his special kind of object with which one can have his special kind of acquaintance. I have only denied the relevance of these epistemological claims to the semantics of direct reference. If we sweep aside metaphysical and epistemological pseudo-explanations of what are essentially semantical phenomena, the result can only be healthy for all three disciplines. Before going on to further examples of the tendency to confuse metaphysical and epistemological matters with phenomena of the semantics of direct reference, I want to briefly raise the problem of cognitive dynamics. Suppose that yesterday you said, and believed it, “It is a nice day today.” What does it mean to say, today, that you have retained that belief? It seems unsatisfactory to just believe the same content under any old character—where is the retention?63 You can’t believe that content under the same character. Is there some obvious standard adjustment to make to the character, for example, replacing today with yesterday? If so, then a person like Rip van Winkle, who loses track of time, can’t retain any such beliefs. This seems strange. Can we only retain beliefs presented under a fixed character? This issue has obvious and important connections with Lauben’s problem in trying to communicate the thought he expresses with “I have been wounded.” Under what character must his auditor believe Lauben’s thought in order for Lauben’s communication to have been successful? It is important to note that if Lauben said “I am wounded” in the usual meaning of ‘I’, there is no one else who can report what he said, using indirect discourse, and convey the cognitive significance (to Lauben) of what he said. This is connected with points made in section VIII, and has interesting consequences for the inevitability of so-called de re constructions in indirect discourse languages which contain indexicals. (I use “indirect discourse” as a general term for the analogous form of all psychological verbs.) A prime example of the confusion of direct reference phenomena with metaphysical and epistemological ideas was first vigorously called to our attention by Saul Kripke in Naming and Necessity. I wish to parallel his remarks disconnecting the a priori and the necessary. The form of a prioricity that I will discuss is that of logical truth (in the logic of demonstratives). We saw very early that a truth of the logic of demonstratives, like “I am here now” need not be necessary. There are many such cases of logical truths which are not necessary. If a is any singular term, then a = dthat[a] is a logical truth. But (a = dthat[a]) is generally false. We can, of course, also easily produce the opposite effect: (dthat[a] = dthat[b]) may be true, although dthat[a] = dthat[b] is not logically true, and is even logically equivalent to the contingency, a = b. (I call f and y logically equivalent when f ↔ y is logically true.) These cases are reminiscent of Kripke’s case of the terms, ‘one meter’ and ‘the length of bar x’. But where Kripke focuses on the special epistemological situation of one who is present at the dubbing, the descriptive meaning associated with our directly referential term dthat[a] is carried in the semantics of the language.64
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How can something be both logically true, and thus certain, and contingent at the same time? In the case of indexicals the answer is easy to see: COROLLARY 3
The bearers of logical truth and of contingency are different entities. It is the character (or, the sentence, if you prefer) that is logically true, producing a true content in every context. But it is the content (the proposition, if you will) that is contingent or necessary.
As can readily be seen, the modal logic of demonstratives is a rich and interesting thing. It is easy to be taken in by the effortless (but fallacious) move from certainty (logical truth) to necessity. In his important article “Three Grades of Modal Involvement,”65 Quine expresses his skepticism of the first grade of modal involvement: the sentence predicate and all it stands for, and his distaste for the second grade of modal involvement: disguising the predicate as an operator ‘It is necessary that’. But he suggests that no new metaphysical undesirables are admitted until the third grade of modal involvement: quantification across the necessity operator into an open sentence. I must protest. That first step let in some metaphysical undesirables, falsehoods. All logical truths are analytic, but they can go false when you back them up to ‘ ’. One other notorious example of a logical truth which is not necessary, I exist. One can quickly verify that in every context, this character yields a true proposition—but rarely a necessary one. It seems likely to me that it was a conflict between the feelings of contingency and of certainty associated with this sentence that has led to such painstaking examination of its “proofs.” It is just a truth of logic! Dana Scott has remedied one lacuna in this analysis. What of the premise I think and the connective therefore? His discovery was that the premise is incomplete, and that the last five words up the logic of demonstratives had been lost in an early manuscript version.66
XVIII The formal system Just to be sure we have not overlooked anything, here is a machine against which we can test our intuitions. The Language
LD
The Language LD is based on first-order predicate logic with identity and descriptions. We deviate slightly from standard formulations in using two sorts of variables, one sort for positions and a second for individuals other than positions (hereafter called simply “individuals”). Primitive symbols PRIMITIVE SYMBOLS FOR TWO-SORTED PREDICATE LOGIC
0. Punctuation: (,), [,] 1. Variables: (i) An infinite set of individual variables: Vi (ii) An infinite set of position variables: Vp 2. Predicates: (i) An infinite number of m-n-place predicates, for all natural numbers m, n (ii) The 1-0-place predicate: Exist (iii) The 1-1-place predicate: Located
DEMONSTRATIVES
779
3. Functors: (i) An infinite number of m-n-place i-functors (functors which form terms denoting individuals) (ii) An infinite number of m-n-place p-functors (functors which form terms denoting positions) 4. Sentential Connectives: ∧, ∨, ¬, →, ↔ 5. Quantifiers: ∀, ∃ 6. Definite Description Operator: the 7. Identity: = PRIMITIVE SYMBOLS FOR MODAL AND TENSE LOGIC
8. Modal Operators: , ◊ 9. Tense Operators: (i) F (it will be the case that) (ii) P (it has been the case that) (iii) G (one day ago, it was the case that) PRIMITIVE SYMBOLS FOR THE LOGIC OF DEMONSTRATIVES
10. Three 1-place sentential operators: (i) N (it is now the case that) (ii) A (it is actually the case that) (iii) Y (yesterday, it was the case that) 11. A 1-place functor: dthat 12. An individual constant (0-0-place i-functor): I 13. A position constant (0-0-place p-functor): Here Well-formed expressions The well-formed expressions are of three kinds: formulas, position terms (p-terms), and individual terms (i-terms). 1. (i) If a ∈ Vi, then a is an i-term (ii) If a ∈ Vp, then a is a p-term 2. If p is an m-n-place predicate, a1 , . . . , am are i-terms, and b1 , . . . , bn are p-terms, then pa1 . . . amb1 . . . bn is a formula 3. (i) If h is an m-n-place i-functor, a1 , . . . , am, b1 , . . . , bn are as in 2, then ha1 . . . amb1 . . . bn is an i-term (ii) If h is an m-n-place p-functor, a1 , . . . , am, b1 , . . . , bn are as in 2, then ha1 . . . amb1 . . . bn is a p-term 4. If f, y are formulas, then (f ∧ y), (f ∨ y), ¬f, (f → y), (f ↔ y) are formulas 5. If f is a formula and a ∈ Vi ∪ Vp, then ∀af and ∃af are formulas 6. If f is a formula, then (i) if a ∈ Vi, then ‘the a f’ is an i-term (ii) if a ∈ Vp, then ‘the a f’ is a p-term 7. If a, b are either both i-terms or both p-terms, then a = b is a formula 8. If f is a formula, then f and ◊f are formulas 9. If f is a formula, then F f, P f, and G f are formulas 10. If f is a formula, then N f, A f, and Y f are formulas 11. (i) If a is an i-term, then dthat[a] is an i-term (ii) If a is a p-term, then dthat[a] is a p-term
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Semantics for LD LD structures DEFINITION:
U is an LD structure iff there are C, W, U, P, T, and I such that:
1. U = 〈C, W, U, P, T, I〉 2. C is a nonempty set (the set of contexts; see 10 below) 3. If c ∈ C, then (i) cA ∈ U (the agent of c) (ii) cT ∈ T (the time of c) (iii) cP ∈ P (the position of c) (iv) cW ∈ W (the world of c) 4. W is a nonempty set (the set of worlds) 5. U is a nonempty set (the set of all individuals; see 9 below) 6. P is a nonempty set (the set of positions, common to all worlds) 7. T is the set of integers (thought of as the times, common to all worlds) 8. I is a function which assigns to each predicate and functor an appropriate intension as follows: (i) If p is an m-n-predicate, Iπ is a function such that for each t ∈ T and w ∈ W, Iπ(t,w) ⊆ (Um × Pn) (ii) If h is an m-n-place i-functor, Iη is a function such that for each t ∈ T and w ∈ W, Iη(t,w) ∈ (U ∪ {†})(Um × Pn) (Note: † is a completely alien entity, in neither U nor P, which represents an ‘undefined’ value of the function. In a normal set theory we can take † to be {U,P}.) (iii) If h is an m-n-place p-functor, Iη is a function such that for each t ∈ T and m n w ∈ W, Iη(t,w) ∈ (P ∪ {†})(U × P ) 9. i ∈ U iff (∃t ∈ T)(∃w ∈ W)(〈i〉 ∈ IExist(t,w)) 10. If c ∈ C, then 〈cA, cP〉 ∈ ILocated(cT, cW) 11. If 〈i, p〉 ∈ ILocated(t,w), then 〈i〉 ∈ IExist(t,w) Truth and denotation in a context U We write cƒt w f for f, when taken in the context c (under the assignment ƒ and in the structure U), is true with respect to the time t and the world w. U We write |a|cƒt w for The denotation of a, when taken in the context c (under the assignment ƒ and in the structure U), with respect to the time t and the world w.
In general we will omit the superscript ‘U’, and we will assume that the structure U is 〈C, W, U, P, T, I〉. ƒ is an assignment (with respect to 〈C, W, U, P, T, I〉) iff: ∃ƒ1ƒ2(ƒ1∈UVi & ƒ2 ∈ & ƒ = ƒ1 ∪ ƒ2).
DEFINITION:
PVp
ƒ xa = (ƒ ~ {〈a, ƒ(a)〉}) ∪ {〈a, x〉} (i.e., the assignment which is just like ƒ except that it assigns x to a). DEFINITION:
For the following recursive definition, assume that c ∈ C, ƒ is an assignment, t ∈ T, and w ∈ W:
DEFINITION:
DEMONSTRATIVES
1. 2. 3.
If a is a variable, |a|cƒt w = ƒ(a) cƒt wpa1 . . . amb1 . . . bn iff 〈|a1|cƒt w . . . |bn|cƒt w〉 ∈ Ip(t,w) If h is neither ‘I’ nor ‘Here’ (see 12, 13 below), then ηα1 . . . α mβ1 . . . βn
4.
5.
6.
cftw
(
Ι (t,w) α η 1 cftw . . . βn = †, otherwise
cftw
), if noneof α
j cftw
. . . βk
cftw
are †;
(i) cƒt w(f ∧ y) iff cƒt wf & cƒt wy (ii) cƒt w¬f iff ~ cƒt wf etc. (i) If a ∈ Vi, then cƒt w∀af iff ∀i∈Ui cƒ ai twf (ii) If a ∈ Vp, then cƒt w∀af iff ∀p∈P, cƒ aptwf (iii) Similarly for ∃af (i) If a ∈ Vi, then: the unique i ∈U such that α φ, if there is such; cft tw the αφ cftw = †, otherwise
7. 8. 9.
10.
11. 12. 13.
(ii) Similarly for a ∈ Vp cƒt wa = b iff |acƒt w = |b|cƒt w (i) cƒt w f iff ∀w' ∈ W, cƒt w'f (ii) cƒt w◊f iff ∃w' ∈ W, cƒt w'f (i) cƒt wFf iff ∃t' ∈ T such that t' > t and cƒt 'wf (ii) cƒt wPf iff ∃t' ∈ T such that t' < t and cƒt 'wf (iii) cƒt wGf iff cƒ(t – 1)wf (i) cƒt wNf iff cƒcTwf (ii) cƒt wAf iff cƒtcWf (iii) cƒt wYf iff cƒ(cT – 1)wf |dthat[a]|cƒt w = |a| cƒcTcW |I| cƒt w = cA |Here| cƒt w = cP
XIX Remarks on the formal system Expressions containing demonstratives will, in general, express different concepts in different contexts. We call the concept expressed in a given context the Content of the expression in that context. The Content of a sentence in a context is, roughly, the proposition the sentence would express if uttered in that context. This description is not quite accurate on two counts. First, it is important to distinguish an utterance from a sentence-in-a-context. The former notion is from the theory of speech acts; the latter is from semantics. Utterances take time, and utterances of distinct sentences cannot be simultaneous (i.e., in the same context). But to develop a logic of demonstratives it seems most natural to be able to evaluate several premises and a conclusion all in the same context. Thus the notion of f being true in c and U does not require an utterance of f. In particular, cA need not be uttering f in cW at cT. Second, the truth of a proposition is not usually thought of as dependent on a time as well as a possible world. The time is thought of as fixed by the context. If f is a sentence, the more usual notion of the proposition expressed by f-in-c is what is here called the Content of Nf in c. REMARK 1:
U Where G is either a term or formula, we write: {G}cƒ for The Content of G in the context c (under the assignment ƒ and in the structure U).
781
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DAVID KAPLAN DEFINITION:
U = that function which assigns to each t ∈ T and w ∈ W, (i) If f is a formula, {f}cƒ U Truth, if cƒt wf, and Falsehood otherwise. U = that function which assigns to each t ∈ T and w ∈ W, |a| (ii) If a is a term, {a}cƒ cƒt w.
Ucƒt wf iff {f}Ucƒ(t,w) = Truth. Roughly speaking, the sentence f taken in context c is true with respect to t and w iff the proposition expressed by f-in-the-context-c would be true at the time t if w were the actual world. In the formal development of pages 780 and 781 it was smoother to ignore the conceptual break marked by the notion of Content in a context and to directly define truth in a context with respect to a possible time and world. The important conceptual role of the notion of Content is partially indicated by the following two definitions:
REMARK 2:
f is true in the context c (in the structure U) iff for every assignment ƒ, {f}Ucƒ (cT, cW) = Truth.
DEFINITION:
DEFINITION:
c (in U).
f is valid in LD () iff for every LD structure U, and every context c of U, f is true in
REMARK 3: (a = dthat[a]); (f ↔ ANf); N(Located I, Here); Exist I. But, ~ (a = dthat[a); ~ (f ↔ ANf); ~ N(Located I, Here); ~ (Exist I). Also, ~ F(f ↔ ANf). In the converse direction (where the original validity has the form f, we have the usual results in view of the fact that ( f → f). DEFINITION:
If a1 , . . . , an are all the free variables of f in alphabetical order then the closure of f = AN∀a1 . . . ∀anf.
DEFINITION:
f is closed iff f is equivalent (in the sense of Remark 12) to its closure.
If f is closed, then f is true in c (and U) iff for every assignment ƒ, time t, and world w, Ucƒt wf.
REMARK 4:
DEFINITION:
Where G is either a term or a formula, the Content of G in the context c (in the structure U) is Stable iff for every assignment ƒ, {G}Ucƒ is a constant function (i.e., {G}Ucƒ(t,w) = {G}Ucƒ(t',w'), for all t, t', w, and w' in U).
REMARK 5: Where f is a formula, a is a term, and b is a variable, each of the following has a Stable Content in every context (in every structure): ANf, dthat[a], b, I, Here. If we were to extend the notion of Content to apply to operators, we would see that all indexicals (including N, A, Y, and dthat) have a Stable Content in every context. The same is true of the familiar logical constants although it does not hold for the modal and tense operators (not, at least, according to the foregoing development).
That aspect of the meaning of an expression which determines what its Content will be in each context, we call the Character of the expression. Although a lack of knowledge about the context (or perhaps about the structure) may cause one to mistake the Content of a given utterance, the Character of each well-formed expression is determined by rules of the language (such as rules 1–13 in the section “Truth and Denotation in a Context”), which are presumably known to all competent speakers. Our notation ‘{f}Ucƒ’ for the Content of an expression gives a natural notation for the Character of an expression, namely ‘{f}’.
REMARK 6:
DEFINITION:
Where G is either a term or a formula, the Character of G is that function which assigns to each structure U, assignment ƒ, and context c of U, {G}Ucƒ.
DEMONSTRATIVES DEFINITION:
Where G is either a term or a formula, the Character of G is Stable iff for every structure U, and assignment ƒ, the Character of G (under ƒ in U) is a constant function (i.e., U = {G}U , for all c, c' in U). {G}c'ƒ c'ƒ A formula or term has a Stable Character iff it has the same Content in every context (for each U, ƒ).
REMARK 7:
A formula or term has a Stable Character iff it contains no essential occurrence of a demonstrative.
REMARK 8:
REMARK 9: The logic of demonstratives determines a sublogic of those formulas of LD which contain no demonstratives. These formulas (and their equivalents which contain inessential occurrences of demonstratives) are exactly the formulas with a Stable Character. The logic of demonstratives brings a new perspective even to formulas such as these. The sublogic of LD which concerns only formulas of Stable Character is not identical with traditional logic. Even for such formulas, the familiar Principle of Necessitation (if f, then f) fails. And so does its tense logic counterpart: if f, then (¬P¬f ∧ ¬F¬f ∧ f). From the perspective of LD, validity is truth in every possible context. For traditional logic, validity is truth in every possible circumstance. Each possible context determines a possible circumstance, but it is not the case that each possible circumstance is part of a possible context. In particular, the fact that each possible context has an agent implies that any possible circumstance in which no individuals exist will not form a part of any possible context. Within LD, a possible context is represented by 〈U,c〉 and a possible circumstance by 〈U,t,w〉. To any 〈U,c〉, there corresponds 〈U,cT, cW〉. But it is not the case that to every 〈U,t, w〉 there exists a context c of U such that t = cT and w = cW. The result is that in LD such sentences as ‘∃x Exist x’ and ‘∃x∃p Located x, p’ are valid, although they would not be so regarded in traditional logic. At least not in the neotraditional logic that countenances empty worlds. Using the semantical developments of pages 780–781 we can define this traditional sense of validity (for formulas which do not contain demonstratives) as follows. First note that by Remark 7, if f has a Stable Character,
Ucƒt wf iff Uc'ƒt wf Thus for such formulas we can define, f is true at t, w (in U) iff for every assignment ƒ and every context c, Ucƒt wf The neotraditional sense of validity is now definable as follows, Tf iff for all structures U, times t, and worlds w, f is true at t, w (in U) (Properly speaking, what I have called the neo-traditional sense of validity is the notion of validity now common for a quantified S5 modal tense logic with individual variables ranging over possible individuals and a predicate of existence.) Adding the subscript ‘LD’ for explicitness, we can now state some results: 1. If f contains no demonstratives, if Tf, then LDf 2. LD∃x Exist x, but ~ T∃x Exist x Of course, ‘ ∃x Exist x’ is not valid even in LD. Nor are its counterparts, ‘¬F¬∃x Exist x’, and ‘¬P¬∃x Exist x’. This suggests that we can transcend the context-oriented perspective of LD by generalizing over times and worlds so as to capture those possible circumstances 〈U, t, w〉 which do not correspond to any possible contexts 〈U, c〉. We have the following result: 3. If f contains no demonstratives, Tf iff LD (¬F¬f ∧ ¬P¬f ∧ f).
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Although our definition of the neotraditional sense of validity was motivated by consideration of demonstrative-free formulas, we could apply it also to formulas containing essential occurrences of demonstratives. To do so would nullify the most interesting features of the logic of demonstratives. But it raises the question, can we express our new sense of validity in terms of the neotraditional sense? This can be done: 4. LDf iff TANf REMARK 10: Rigid designators (in the sense of Kripke) are terms with a Stable Content. Since Kripke does not discuss demonstratives, his examples all have, in addition, a Stable Character (by Remark 8). Kripke claims that for proper names a, b it may happen that a = b, though not a priori, is nevertheless necessary. This, in spite of the fact that the names a, b may be introduced by means of descriptions a', b' for which a' = b' is not necessary. An analogous situation holds in LD. Let a', b' be definite descriptions (without free variables) such that a' =b' is not a priori, and consider the (rigid) terms dthat[a'] and dthat[b'] which are formed from them. We know that: (dthat[a'] = dthat[b'] ↔ a' = b'). Thus, if a' = b' is not a priori, neither is dthat[a'] = dthat[b']. But, (dthat[a’] = dthat[b'] ↔ (dthat[a'] = dthat[b'])), it may happen that dthat[a'] = dthat[b'] is necessary. The converse situation can be illustrated in LD. Since (a = dthat[a]) is valid (see Remark 3), it is surely capable of being known a priori. But if a lacks a Stable Content (in some context c), (a = dthat[a]) will be false. REMARK 11: Our 0-0-place i-functors are not proper names, in the sense of Kripke, since they do not have a Stable Content. But they can easily be converted by means of stabilizing influence of ‘dthat’. Even dthat[a] lacks a Stable Character. The process by which such expressions are converted into expressions with a Stable Character is “dubbing”—a form of definition in which context may play an essential role. The means to deal with such contextindexed definitions is not available in our object language. There would, of course, be no difficulty in supplementing our language with a syntactically distinctive set of 0-0-place i-functors whose semantics requires them to have both a Stable Character and a Stable Content in every context. Variables already behave this way; what is wanted is a class of constants that behave, in these respects, like variables. The difficulty comes in expressing the definition. My thought is that when a name, like ‘Bozo’, is introduced by someone saying, in some context c., “Let’s call the governor, ‘Bozo’”, we have a context-indexed definition of the form: A = c. a, where A is a new constant (here, ‘Bozo’) and a is some term whose denotation depends on context (here, ‘the governor’). The intention of such a dubbing is, presumably, to induce the semantical clause: for all c, {A}Ucƒ = {a}c.ƒ. Such a clause gives A a Stable Character. The context-indexing is required by the fact that the Content of a (the “definiens”) may vary from context to context. Thus the same semantical clause is not induced by taking either A = a or even A = dthat[a] as an axiom. I think it is likely that such definitions play a practically (and perhaps theoretically) indispensable role in the growth of language, allowing us to introduce a vast stock of names on the basis of a meager stock of demonstratives and some ingenuity in the staging of demonstrations. Perhaps such introductions should not be called “definitions” at all, since they essentially enrich the expressive power of the language. What a nameless man may express by “I am hungry” may be inexpressible in remote contexts. But once he says ‘Let’s call me ‘Bozo’,” his Content is accessible to us all. REMARK 12: The strongest form of logical equivalence between two formulas f and f' is sameness of Character, {f} = {f'}. This form of synonymy is expressible in terms of validity:
{f} = {f'} iff [¬F¬(f ↔ f') ∧ ¬P¬(f ↔ f') ∧ (f ↔ f')]
DEMONSTRATIVES
785
[Using Remark 9 (iii) and dropping the condition, which was stated only to express the intended range of applicability of T, we have: {f} = {f'} iff T(f ↔ f').] Since definitions of the usual kind (as opposed to dubbings) are intended to introduce a short expression as a mere abbreviation of a longer one, the Character of the defined sign should be the same as the Character of the definiens. Thus, within LD, definitional axioms must take the unusual form indicated above. REMARK 13: If b is a variable of the same sort as the term a but is not free in a, then {dthat[a]} = {the b AN(b = a)}. Thus for every formula f, there can be constructed a formula f' such that f' contains no occurrence of ‘dthat’ and {f} = {f'}. REMARK 14: Y (yesterday) and G (one day ago) superficially resemble one another in view of the fact that (Yf ↔ Gf). But the former is a demonstrative, whereas the latter is an iterative temporal operator. “One day ago it was the case that one day ago it was the case that John yawned” means that John yawned the day before yesterday. But “Yesterday it was the case that yesterday it was the case that John yawned” is only a stutter.
Notes on possible refinements 1. The primitive predicates and functors of first-order predicate logic are all taken to be extensional. Alternatives are possible. 2. Many conditions might be added on P; many alternatives might be chosen for T. If the elements of T do not have a natural relation to play the role of
