Term Limits

Term Limits Stephen Neale Philosophical Perspectives, Vol. 7, Language and Logic. (1993), pp. 89-123. Stable URL: http://links.jstor.org/sici?sici=1520-8583%281993%297%3C89%3ATL%3E2.0.CO%3B2-H Philosophical Perspectives is currently published by Blackwell Publishing.

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Philosophical Perspectives, 7, Language and Logic, 1993

TERM LIMITS*

Stephen Neale

University of California, Berkeley

1. Introduction A distinction between reference and predication is central to much philosophy, and it has been demonstrated, more than a few times, that insensitivity to such a distinction can lead to definite philosophical error. This is one reason many recent philosophers-Frege, Russell, Quine, Geach, and Strawson, to name some of the most distinguished-have attempted to elucidate the distinction (or a closely related distinction between subject and predicate). In the last thirty years or so, philosophers have tended to work less on the distinction itself than they have on characterizing the differences between the various types of noun phrases standardly taken to be devices of reference, with the result that definite progress has been made in understanding the semantics of proper names, demonstratives, descriptions, and pronouns. Equally importantly, tremendous progress has been made in understanding the semantics of quantificational noun phrases. As a result of this work, I think the philosopher's toolbox now contains just about everything necessary (i) to get to the heart of the notion of singular reference, (ii) to elucidate the distinction between reference and predication, and (iii) to get much clearer about the logic of a number of locutions frequently used by philosophers in discussions of time, events, causation, necessity, possibility, and probability. My aim here is to spell out this statement and at the same time motivate and defend a number of rich theses about the logic and semantics of natural language. The theses in question strike me as perfectly sensible and possibly even correct (in the sense that they do not make false predictions); but to judge by some of the comments I have received, I am going to have an uphill battle convincing many others. I shall mention just three of the theses in question here. In my view, an especially interesting and fruitful picture of the semantics

90 / Stephen Neale and logic of natural language can be delimited by the following: (TI) Every meaningful noun phrase (NP) in natural language is either a semantically unstructured, rigid referring expression (singular term) or else a semantically structured, restricted quantifier. (T2) The linguistic contexts governed by modal and causal sentential operators/connectivesare nonextensional but referentially transparent. (73) The "scope" of an expression in natural language is formally (treegeometrically) identical to the scope of an expression in a simple formal language (e.g. the language of first-order logic).

On the face of it, (T1)-(T3) may look implausible and invite the following sorts of responses: "Isn't it just obvious that English contains both nonrigid singular terms and semantically structured singular terms?" "Isn't it well known that modal contexts are referentially opaque?" "Isn't it clear that in sentences of English containing two or more quantified noun phrases, very definite ambiguities are attributable to the fact that quantifiers can be assigned different scopes?" I have two initial comments on remarks like these. First, (T1)-(T3) are worth attacking only to the extent that expressions such as 'semantically unstructured', 'referring expression', 'nonextensional', and so on are given precise and coherent conditions of application. Second, there is not much point in sniping at even a coherent and precisely stated semantical thesis before examining how it interacts with other coherent and precisely stated semantical theses (whether somewhat novel or part of the background culture). Semantical theorizing is both modular and holistic. It is modular in the sense that a semantical theory for any interesting fragment of a language will be composed of various interacting subtheories such as theories of names, demonstratives, quantification, mass terms, indexicality, anaphora, conditionals, nominals, adjectives, adverbs, and tense. From a methodological standpoint we have no choice but to proceed in a modular fashion, attempting to isolate phenomena that are to some suitable extent open to investigation in abstraction from too many other phenomena. We can then construct theories of the phenomena that interest us. But at the same time, we need to investigate the predictive power of such theories as they interact with theories of other relatively isolable phenomena. That is, semantical theorizing is holistic in the sense that individual semantical theses gain respectability in the context of other semantical theses with which they interact to provide or shape semantical theories for significant fragments of languages. It is my hope that when certain confusions about the nature of singular terms, substitution, logical form, and nonextensional contexts are cleared away, (T1)-(T3) will begin to look very attractive to both philosophers and linguists. It should be clear from the foregoing that I shall not be arguing directly for the truth of any of (T1)-(T3). Direct argumentation seems to me as out of place

Term Limits / 91 in semantics as it is elsewhere in philosophy. To a large extent, philosophy consists in the articulation, development, testing, defense, and refining of theories designed to make sense of our surroundings, our experiences, and conceptual puzzles of one form or another. Support for a philosophical position comes not in the form of proof or demonstration; rather it resides in the capacity of the theory to help us make sense of things in a systematic or otherwise pleasing way. Methodologically, my own preference is for the articulation, development, testing, defense, and refining of suonger rather than weaker theses as one proceeds, hence the strength of (T1)-(T3), each of which seems to me to have considerable empirical and aesthetic merit, especially when taken in conjunction with the other two and with other theses that I will not discuss here (but some of which will be understood as part of a widely accepted background or else smuggled in harmlessly). My main efforts here will be directed toward explaining some of the merits of (Tl) and countering a notorious argument against the possibility of referentially transparent contexts that are nonextensional, an argument that, if sound, would defeat not only (T2), but also (Tl). I have discussed (T3) at length elsewhere and I will simply assume its correctness here (nothing very important will turn on this).' In my view, (T2) is certainly correct (in the sense that once certain confusions are cleared away (a) it has a strong intuitive appeal and (b) there is no good evidence for its falsity).2 I am less confident about (Tl); but even if it should ultimately turn out to be false, I am sure that it is very much closer to being correct than many people think, and pushing it hard may reveal a great deal about the workings of natural language. 2. Terms and Predicates With a view to minimizing misunderstanding later, I want to begin by rehearsing some familiar points. One useful way of sharpening the traditional distinction between subject and predicate is to see it as corresponding to (or even underwriting) a term-predicate distinction in the simplest formal (artificial) languages. Consider a formal language that approximates a fragment of English in that it contains a number of names and one- and two-place predicates. After specifying the sets of terms and predicates precisely, a syntactical distinction emerges between these categories in the formation rules (syntax): if a is a term and ll is a one-place predicate, then ran1 is a sentence (e.g. 'Achilles snored'); if a and j3 are terms and I1 is a two-place predicate, then raI'Ipl is a sentence (e.g. 'Achilles killed Hector'). A semantical distinction between term and predicate typically emerges in the truth definition for the sort of language we are considering. We can think of a (recursively structured) truth definition for a language L as a set of axioms that (together with an underlying logic) recursively generates a true theorem of the form

92 1Stephen Neale (4) C is true (in L) iff p

for every sentence C of L, where "p" is a translation of C in the metalanguage M that we are using to talk about L, and 'iff' is understood as the material biconditional '='.3 (By saying that a truth definition highlights a semantical distinction between term and predicate, I do not mean to be explicitly claiming that a Tarskian truth definition for L (or a suitably constrained Davidsonian truth theory for L) is the same thing as a semantical theory for L. For present purposes, I can afford to be agnostic about such matters; I am simply operating within the logical tradition that construes .a (recursively structured) truth definition for L as providing or displaying important semantical information about L.) Appropriate axioms for a truth definition in which each primitive expression (word) of our simple language gets its own private axiom might take the following form: (5) The referent of 'Achilles' = Achilles (6) ra snoredl is true iff the referent of a snored (7) ra killed j31 is true iff the referent of a killed the referent of P. The axiom in (5) captures the intuition that terms are used to refer to things. By contrast, the axioms in (6) and (7) do not appear to involve reference: they do not attribute referential properties to the predicates they concern. The intuitive idea embodied in (6) and (7) is that predicates are "true of' ordered collections ("tuples") of objects. For example, (7) says that for arbitrary terms a and j3, the sentence [a killed j31 is true just in case the referent of the term a killed the referent of the term p; so we might think of (7) as capturing the idea that the two-place predicate 'killed' is "true of' (or "satisfied by") pairs of objects. 3. Extensions

From the point of view of providing a rudimentary truth definition, then, it is not necessary to talk about the references of predicates or sentences. Many logicians, philosophers, linguists, and cognitive scientists interested in formal and natural languages do in fact talk of expressions other than terms having certain entities as their references (for example, functions, properties, types, sets, algorithms, truth-values, facts, propositions, situations, psychological schemata, mental models, ...). There is no need for us to enter the various debates surrounding such entities here. Let us accept that terms are meant to refer to individuals and remain agnostic on the matter of whether (and, if so, to what) expressions other than terms are meant to refer. What we can do completely uncontroversially, I think, is adopt some theoretical vocabulary and stipulate that terms, predicates, and sentences all have extensions. Following standard practice, we can say that (i) the extension of a term is its referent; (ii) the extension of an n-place predicate is the set of ordered n-tuples of which it holds; (iii) the

Term Limits 1 93 extension of a sentence is its truth value. (Once we add the extensional sentential connectives '7', '&', 'v', '3',and '=' (see below) we can say that (iv) the extension of an n-place sentential connective is a function from n-tuples of truth values to truth values. These connectives are extensional operators because they take us from extensions to extensions.) The notion of an extension, so characterized, enables us to specify precisely a semantical distinction between reference and predication within a traditional extensional semantics. Although terms, predicates, and sentences are alike in having extensions (by stipulation), there are still fundamental mechanical differences between these categories. An extensional language (or language fragment) is one in which the extension of every expression is completely determined either by a single axiom or by extensional composition from the extensions of its constituents. A traditional extensional semantics for a language (or fragment) L assigns an extension to every well-formed expression of L either by a single axiom or by extensional composition. Whereas the extensions of the primitive (atomic) expressions terms and predicates are given by axioms, the extensions of sentences are functions of the extensions of their parts, viz. the terms and predicates that are their syntactical constituents. Terms and predicates play their own distinctive rBles in determining the extensions of sentences: the extension of a sentence C.depends upon whether the ordered n-tuple consisting of the extensions of the term(s) in C is a member of the extension of the predicate of C.. 1.e. for predicates n and terms a and j3,

(8) ~ x t a o n I) = Truth iff Ext(a) E Ext(n) (9) ~xt(faIlj3)= Truth iff cExt(a), Ext(P)> E Extm).

In a moment I want to say something about the behavior of NPs occurring in nonextensional contexts. In order to do this, I need to make some clarificatory remarks about two different types of nonextensional contexts found in natural and formal languages. I shall be concerned here only with the linguistic contexts governed by what I shall call S-operators: expressions that combine with some number of sentences to form a sentence (e.g., 'not' ('7'), 'and ('&'), 'or' ('v'), 'necessarily' ('n'), 'possibly' ('O'), 'moreover', 'because', and 'despite the fact that').4 The "scope" of an S-operator is simply the sentence or sentences with which it combines to form another sentence.5 An extensional operator operates on the extensions of its operands. Consider a phrase r0(a)1 composed of an operator 0 and an operand a . 0 is an extensional operator if and only if the extension of r0(a)1 depends only upon the extension of a. The extension of an n-place extensional S-operator is just a function from n-tuples of truth values to truth values. The truth-functional

94 / Stephen Neale

operators 'T','&', and so on, are of course extensional S-operators. Notice that an S-operator 0 is extensional if and only if any sentence Pi with the same extension (i.e. truth value) as sentence ai can be substituted for ai in rO(al, ..., a,)l to produce a sentence with the same extension (i.e. truth value) as rO(al, ..., a,). As we might put it, for an extensional n-place S-operator 0 , the extension (i.e. truth value) of rO(al, ..., a,)l depends only upon the extensions (i.e. truth values) of a l , ..., a,. If they are S-operators at all, the modal operators 'necessarily' and 'possibly', and the causal operators 'because' and 'the fact that...caused it to be the case that' are nonextensional S-operators. (That this is so is plain from the fact that coextensional sentences cannot always be substituted for a in (e.g.) rnecessarily a 1 or because a 1 salva veritate.) Notoriously, Quine and Davidson have raised serious doubts about nonextensional S-operators.6 In particular, Quine has presented arguments designed to discredit 'necessarily' and 'possibly', and Davidson has presented arguments designed to show that 'because' (on one of its readings), and 'the fact that ...caused it to be the case that' cannot be understood as nonextensional S-operators. In addition, Quine has presented a very general argument designed to show that we cannot have nonextensional S-operators at all. If Quine's general argument succeeds, a lot of what passes for intelligible talk about possibility, time, and causation must be regarded as nonsense or else logically reparsed in a way that eliminates reference to nonextensional operators. The argument will be examined in detail in section 11; right now, on the assumption there are nonextensional S-operators,I need to say more about them. In order to forestall possible confusion, two different types of nonextensional S-operators-and hence two types of nonextensional contexts-need to be distinguished. I shall use the labels intensional and epistemic. An n-place S-operator 0 is intensional if and only if the extension (i.e. truth value) of rO(al, ..., a,)l depends not upon the extensions (i.e. truth values) of a l , ..., a, but upon their intensions (i.e. truth conditions, in the standard coarse-grained sense).7 Thus 0 is intensional if and only if any sentence Pi with the same intension (i.e. truth conditions) as ai can be substituted for ai in rO(al, ..., a,)l to produce a sentence with the same extension (i.e. truth value) as [ ~ ( a l ..., , a,)! Thus the modal operators 'necessarily' and 'possibly' are one-place intensional S-operators. And to the extent that it is possible to treat causal expressions such as 'the fact that ...caused it to be the case that', as nonextensional S-operators, they are also intensional in the strict sense. I shall say that an S-operator 0 is epistemic-just a label-if and only if it is neither extensional nor intensional. For an n-place epistemic S-operator 0 , the truth value of r O ( a l , ..., a,)] is determined by neither the truth values (extensions) nor the truth conditions (intensions) of a l , ..., a,. Nothing I shall say here depends upon the existence of epistemic S-operators.8 For present purposes, I bring up epistemic S-operators, if there are any, only to get them out

r/3

,

Term Limits / 95

,

of the way and to prepare the ground for talking about substitutions within the scopes of extensional and intensional S-operators. The possibility of drawing metaphysical or epistemological conclusions from logical maneuvers within the scopes of S-operators depends upon whether or not the operator is intensional or epistemic.9 We are now able to provide clean definitions of intensional and extensional positions. Where X is a particular occurrence of an expression we can say that: (i) X occupies an epistemic position (X occupies in an epistemic context) if and only if it is within the scope of an epistemic operator (not necessarily an epistemic S-operator); (ii) X occupies an intensional position (X occurs in an intensional context) if and only if it is within the scope of an intensional operator and not within the scope of any epistemic operator; and (iii) X occupies an extensional position (X occurs in an extensional context) if and only if it is not within the scope of any nonextensional (i.e. intensional or epistemic) operator.

5. Proper Names and Rigidity I want now to discuss a feature of names (and other terms) impressed upon us by Kripke [1971, 19721. Consider the following sentence:

(10) Aristotle was fond of dogs. According to Kripke, understanding the statement expressed by an utterance of (10) involves not only a grasp of "the (extensionally correct) conditions under which it is in fact true" but also of "the conditions under which a counterfactual course of history, resembling the actual course in some respects but not in others, would be correctly (partially) described by [(lo)]" [1980, p. 61. The generalized version of this claim is Kripke's thesis of rigid designation. A proper name like 'Aristotle' is a rigid designator: Presumably everyone agrees that there is a certain man-the philosopher we call 'Aristot1e'-such that, as a matter of fact, [ ( l o ) ]is true if and only if he was fond of dogs. [Footnote omitted.] The thesis of rigid designation is simply-subtle points aside [footnote:In particular, we ignore the question of what to say about counterfactual situations in which Aristotle would not have existed]-that the same paradigm applies to the truth conditions of [ ( l o ) ]as it describes counferfactual situations. That is, [ ( l o ) ]truly describes a counterfactual situation if and only if the same aforementioned man would have been fond of dogs, had that situation obtained (ibid.).

The quick way of putting all this is to say, along with Kripke, that a rigid designator refers to the same individual in every "possible world" in which that individual exists-summarizing in this way involves no commitment to "possible worlds" in any objectionable sense. (To say that an expression R is a rigid designator is not to make any claim about languages spoken in other

%/ Stephen Neale

possible worlds (counterfactual situations); it is to make a claim about R as used in our actual language (does R exist in any other language?). If R is a rigid designator of x, then whether or not the proposition expressed by an utterance of the sentence r...~...l-a sentence of our actual language-is true at a counterfactual situation depends only upon how things are with x.)10 Naturally enough, the rigidity of proper names comes through very clearly in sentences containing modal operators. Consider the following: (11) (Plato met Aristotle) & O(lPlato met Aristotle)).

,

Sentence (11) is supposed to do duty for the English sentence 'Plato met Aristotle but he might not have done'. In the parlance of "possible worlds" semantics, the possibility operator '0' might be read as an existential quantifier over worlds and (11) paraphrased as 'Plato met Aristotle but there is some possible world in which Plato did not meet Aristotle'. The important semantical point here is that even though there is a sense in which, to speak loosely, the subject matter of the second conjunct of (11) is a counterfactual situation, the occurrences of the names 'Plato' and 'Aristotle' in that conjunct still refer to Plato and Aristotle (the actual men).ll In short, the references (i.e. extensions) of names are "preserved across possible worlds." Indeed, if this were not the case, what sense could we make of (1 1) or its English counterpart? In my view, Kripke has uncovered an important property of proper names (and has thereby made a very forceful case against certain popular approaches to their semantics inspired by the work of Frege and Russell 12); but I think we can view his notion of rigidity as deriving from more general facts about reference. Consider (12): (12) (In 368 B.C. Plato met Aristotle) & (in 369 B.C. ( ~ P l a t omet Aristotle)). Even though there is a sense in which, to speak loosely, the subject matter of the two conjuncts of (12) are different years, the two occurrences of 'Plato' refer to the same individual (viz. Plato), and the two occurrences of 'Aristotle' refer to the same individual (viz. Aristotle).l3 In short, the references (i.e. extensions) of names are preserved over times. Indeed, if this were not the case, what sense would we be able to make of (12) or its English counterpart? Without too much abuse of Kripke's original terminology, we might say, then, that names are both "modally rigid" and "temporally rigid."l4 If this is correct, then corefemng names can be substituted salva veritate within the scopes of modal operators and temporal expressions (as long as they are not also within the scopes of epistemic operators, of course). I return to this matter in section 10.15

Term Limits / 97 6. Quantifiers and Variables

In surface syntax, phrases such as 'every man' and 'some poets' appear to occupy term positions, i.e. the sorts of positions that terms typically occupy. However, for various reasons it is customary to view such phrases as semantically very different from terms: rather than devices of reference they are devices of quantification; and, in effect, this means they are much more like predicates than terms. In order to connect the discussion of quantifiers and variables with the discussion of proper names, it will pay to review certain facts about the semantics of quantification. To the vocabulary of the extensional language introduced earlier and augmented with the usual extensional S-connectives,let us add the quantifiers 'V' and ' 3 ' , and a stock of variables rxkl (for all k2l)-quantifiers that do a better job of capturing the semantics of quantified noun phrases in natural language will be introduced in section 7. Since the variables we have added are terms, we have given ourselves the means of generating formulae such as 'xl defeated Achilles' and '(xl defeated xz) & (Achilles defeated xs)'. To generate quantified formulae, we add to our formation rules the following: If C is a wellformed formula ("wff') then so are r(3xk)CI and r(Vxk)C1(for all k2l). We now have the means to generate wffs such as '(3x1)(x1snored)' and '(Vx3)(x3 defeated Achilles 3 x3 snored)'. For simplicity, we can use a variation of Tarski's method of defining truth for a quantified language. We define a new primitive semantical notion, satisfaction and then define truth in terms of satisfaction (where formulae are satisfied by sequences of individuals). Before we define satisfaction, we define a new semantical notion "Ref' or "reference with respect to a sequence." For each proper name we will have an axiom similar to the following: (13) Ref('Achilles7,s) = Achilles. This just says that the referent of 'Achilles' relative to an arbitrary sequence s is Achilles. (For ease of exposition, I shall ignore many innocuous details of the truth definition; for example, in the statements of axioms and axiom schemata, universal quantification over sequences, terms, and formulae will be suppressed). For individual variables rxk'l,we will have the following axiom schema:

which says that the referent of rxklrelative to a sequence s is the k-th element of S.

Both the similarities and differences between names and variables are clear. The reference of a name (with respect to a sequence) is indifferent to the choice of sequence (names are constants). By contrast, the reference of a variable rxkl (with respect to a sequence) depends upon the sequence in question. If s = cPriam,

98 / Stephen Neale Achilles, Hector, Helen, ...>, then Ref('x2', s) = Achilles. Axioms for other expressions are straightforward, for example: (15) s satisfies Fa killed j31 iff Ref(a, s) killed Ref@, s) (16) s satisfies rC & TI iff s satisfies C and s satisfies T (where a and p are terms (i.e., names or variables) and C and T are wffs). The axiom for '3' can be stated thus: (17) r(3xk)Cl is satisfied by s iff C is satisfied by at least one sequence that differs from s at most in the k-th position mutatis mutandis for 'V'. The scope of an operator 0 is the wff(s) with which it combines to form a wff;16 a sentence is a wff that contains no free occurrence of any variable; and an occurrence of a variable rxkl is free if and only if it is not within the scope of an occurrence of a quantifier expression r(3xk)l or r(yxk)l. Finally, a sentence is true if and only if it is satisfied by every sequence. We.should now pause to let the theory of extensions catch up. Henceforth, we can, where necessary, use "extension" as shorthand for "extension relative to a sequence." This allows us to view the extension of a variable as an individual. As Kripke and Kaplan have stressed, the extension of a variable (relative to a sequence) is just as rigid as the extension of a name. Rigidity of extension does not consist in having the same extension relative to every sequence. Certainly names have this property, but it is crucial to see that it is not constitutive of rigidity. Rigidity consists in the fact that extension (relative to a sequence) does not vary over time or across possible circumstances. In a word, rigidity is not the same thing as constancy: constancy implies rigidity but not vice versa. The point can be made very clear once again by looking at sentences containing intensional S-operators. First, let's informally add the modal Soperators to our quantified language and then consider the following sentence, which differs from (1 1) only in that it contains occurrences of the variable 'xs' in place of 'Plato', and an initially placed quantifier that binds them: (18) (3x5)((x5met Aristotle) & O(l(xs met Aristotle))). Intuitively, (18) is true if and only if there is at least one person who both met Aristotle and might not have done; and as Kaplan [I9891 has stressed, this makes sense only on the assumption that 'x5' is modally rigid (relative to a sequence). (18) is true if and only if there is someone in the actual world who (a) met Aristotle and (b) is such that there is some alternative way the world could have been in which he or she-the very same person -did not meet Aristotle. That is, (18) is true if and only if there is at least one person who satisfies both '(xs met Aristotle)' and 'Ol(xs met Aristotle)'. (It is not enough for the truth of (18) that at least one person satisfy '(xs met Aristotle)' and at least one person satisfy 'Ol(xs met Aristotle)'). It is a condition of the intelligibility of (18), then, that

Term Limits 199 the variable preserve its extension (relative to a sequence) across alternative circumstances.l7 As before, a more or less analogous point can be made where temporal expressions are concerned. Adding '368 B.C.' and '369 B.C.' to our quantified language we can formulate (19): (19) (3x~)((in368 B.C. x5 met Aristotle) & 7(in 369 B.C. xs met Aristotle)). This is true if and only if there is at least one person who both met Aristotle in 368 B.C. and did not meet Aristotle in 369 B.C.. And this makes sense only on the assumption that 'x5' is temporally rigid. That is, (19) is true if and only if there is at least one person who satisfies both '(in 368 B.C. x5 met Aristotle)' and 'l(in 369 B.C x5 met Aristotle)'. (It is not enough for the truth of (19) that at least one person satisfy '(in 368 B.C. xs met Aristotle)' and at least one person satisfy 'l(in 369 B.C x.j met Aristotle)'). It is a condition of the intelligibility of (19), then, that the variable preserve its extension (relative to a sequence) across times. The semantically important difference and the equally important similarity between names and variables should now be clear. Names and variables are terms and hence they have (modally and temporally) rigid extensions. But names are constants and variables are, well, variables. The extension of a constant is constant across sequences but the extension of a variable varies with the sequence. 7. Restricted Quantification In order to depict the logical forms of quantified sentences, often we resort to formulae of first-order logic. When we are concerned with formal inference, this is a productive exercise; but when we want to construct a systematic semantics for a fragment of natural language, it has limited value because of well-known semantical and syntactical problems.18 We can accomplish much more if we construe noun phrases of the forms revery ~ 1rno , ~ 1etc. , as restricted quantifiers. A truth definition for a language containing restricted quantifiers can be obtained by replacing the axioms for the unrestricted quantifiers 'V' and "3' by axioms such as the following for certain quantificational determiners ('every', 'most', 'no', etc.): (20) s satisfies [[every xk: alp1 iff every sequence satisfying a and differing from s at most in the k-th place also satisfies p. (21) s satisfies [[no xk: alp1 iff no sequence satisfying a and differing from s at most in the k-th place also satisfies j3. On this account, the English sentence (22) can be represented as (23):

100/ Stephen Neale (22) every poet snores (23) [every x3: poet x31 (x3 snores). Following Davidson, let us say that the logical form of a sentence S belonging to-a language L is the structure imposed upon S in the course of providing a principled truth definition for L.19 (In other work, I have attempted to set out, defend, and develop the view that the level of syntactical representation called "LF" in Chomskyan grammatical theory should be seen as representing the logical form of a sentence in this sense.20 Since something very like (23) is the "LF representation" for (22)-in effect, an independently motivated and mathematically precise syntactical operation maps the structural description for (22) onto something like (23)21-we might say that (23) gives the logical form of (22).) Following Russell, it is clear that phrases of the form [the F1 are best viewed as belonging to the same syntactical and semantical category as phrases of the forms revery ~ 1[no , ~ 1[some ~ 1and , so on. In short, descriptions are , quantificational rather than referential. There is no need to rehearse the rationale for this here; suffice to say that Russell's insight can be captured perfectly if 'the' is treated as just another quantificational determiner on a par with 'every', 'no', 'most', etc.: (24) s satisfies [[the xk: alp1 iff the sequence satisfying a and differing from s at most in the k-th position also satisfies P. The right-hand side of (24) is to be understood as equivalent to "there is exactly one sequence satisfying a and differing from s at most in the k-th position and every such sequence also satisfies P."22 I want to stress an important terminological point. Once descriptions are treated as quantificational, we must think carefully about what we are saying when we succumb to the temptation to use the phrase "rigid description" in application to phrases such as 'the positive square root of sixty-four', 'the set of even numbers', 'the actual number of apostles', 'the atomic number of gold', and 'Hector's father'. Take 'the positive square root of sixty-four'. This description is satisfied by the same entity in every possible world; but if one classifies this description as 'rigid' one runs the risk of being understood as claiming that it is a referential device (i.e. a term) rather than a device of quantification. Since a description [the F1 consists of a quantificational determiner 'the' and a predicate expression F, the interesting feature of a "rigid description" [the F1 is not that it refers (rigidly), but that the same single individual satisfies the predicate F in every possible world: to use terminology introduced in the next section, the contained predicate has a rigid extension. And as far as the semantics of descriptions is concerned, this fact is utterly irrelevant (a great number of predicates have rigid extensions, whether or not they are combined with 'the', 'no', 'every', or any other determiner). I should add that Kripke himself is not guilty of assuming that "rigid" descriptions are referential rather than quanti-

Term Limits / 101 ficational; indeed his leanings are explicitly Russellian for descriptions, whether or not they happen to contain predicates with rigid extensions (see Kripke [1971, 19771). Consequently, there is less than meets the eye to criticisms of Kripke that see "rigid" descriptions as undermining the connections between naming and necessity that he unearths. 8. Rigidity and the Term-Predicate Distinction

I think we now have much of what is needed if we are to provide a precise semantical specification of the term-predicate distinction in natural language. Borrowing and extending Kripke's terminology again, I would like to suggest that it is a characteristic feature of terms that they have "rigid extensions" (modally and temporally) and that this is not a characteristic feature of predicates. (To say this is not to say that there are no predicates whose extensions are rigid; the extensions of (e.g.) 'is odd' 'is even', and 'is prime' do not vary with respect to times or worlds.) Rigidity is an essential property not just of proper names but of terms quite generally. (Some philosophers are likely to object to this claim on the grounds that many definite descriptions are nonrigid terms (e.g. 'the Emperor', 'the man who lives upstairs', 'Napoleon's horse', 'Fred's new car'). But this objection is at most as strong as the highly dubious claim that these definite descriptions are terms. By treating descriptions as devices of quantification (see (24) above) we have, of course, rejected the view that descriptions are terms.) There is, I think, a natural explanation of why the principal phrasal division in natural language corresponds to a distinction between a class of expressions in whose nature it is to have rigid extensions and a class of expressions not so disposed. The sort of story I have in mind emerges from reflection on our ordinary conception of reality and on the nature of the information about it that we seek to represent and communicate. The central ideas here derive from the work of Strawson [1959, 19741, Peacocke [1975], and Fgllesdal [1986]. It is a commonplace of much philosophy that ordinarily we conceive of the world as containing individuals (e.g., material objects, persons, and other living things). Individuals have several interesting features that seem to be important from the perspective of our attempts to cope with and represent aspects of the world. Borrowing heavily from Fgllesdal's discussion, we might focus on the following. First, individuals typically possess a large number of properties (including relational properties); in normal circumstances, we know only a small number of the properties that a particular individual has; however the individual in question is still understood to possess many further properties of which we are unaware, but some of which we could become aware of. Second, we may have false beliefs about individuals. We often seek to correct these beliefs, but typically the beliefs in question, whether true or false, are still beliefs about the

102/ Stephen Neale individuals in question. A belief is not about whichever individual just happens best to be tailored by it. (To say all of this is not, of course, to say that we may never be confused about which individual we are thinking about.) Third, with the exception of mathematical objects and some others, individuals change over time. That is, the same individual can have a property at one time and lack it at another. In such a case, the individual remains identical through changes. (To say all of this is not to say that there are no properties that an individual must possess throughout its history.) Fourth, with the exception of mathematical objects and some others, individuals might have had some different properties from the ones they actually have. That is, not all of the properties an individual has are essential properties (though some may be). On the reasonable assumption that objects and other individuals play important r6les in our attempts to understand and organize our experiences and deal with our surroundings, Follesdal is surely correct when he says it would be odd if the features of individuals just mentioned were not reflected somehow in the languages we use to talk about the world. To speak loosely, it would be strange 'if natural languages did not contain expressions that stayed with individuals throughout the actual and possible changes that these individuals (and our beliefs about them) might undergo. It is tempting to go further: it would be strange if natural languages failed to contain a category of expressions (a) whose extensions were meant to be individuals (rather than, say, n-tuples of individuals) and (b) whose extensions were modally and temporally rigid. This is, I maintain, the category of singular terms in natural language. We are now at the heart of the concepts of rigidity and singular reference. The sorts of considerations just adduced suggest that we view rigidity as an intrinsic feature of terms in natural language. We need to keep track of objects as we take them to have different properties at different times and as we take them to have the potential to have (or to have had) properties different from those they actually have. And to the extent that the natural languages we use contain devices that hang onto objects through these changes or projections, those languages contain singular terms.23 This is what terms are for. Nonrigid terms simply would not serve any useful and lasting purpose for creatures with our interests. To say this is not to say that the idea of a nonrigid term is incoherent. It may be possible to construct an artificial language containing nonrigid terms. The claim I am concerned with here is more of an empirical one: a language containing nonrigid terms would not be a natural language. Even if such expressions could be introduced, given our interests they would not survive, they would disappear through lack of use. At the very least, then, functional considerations virtually dictate that terms are going to have rigid extensions. Here I part company with F~llesdal,who sees the rigidity of singular terms as "an ideal, something like a Kantian regulative ideal, that prescribes the way we use language to speak about the world" (p. 111).24 "There is in our use of names and other genuine singular terms" says Follesdal, "a normative pull

Term Limits / 103 towards always doing our best to keep track of the reference and keep on refemng to it" (ibid.). By viewing rigidity as an "ideal," F~llesdalbelieves he can reconcile the possibility of a name changing its referent over time with the temporal rigidity of proper names. A purported example of reference shift involves 'Madagascar', apparently first used to name a part of mainland Africa rather than the adjacent island (see Evans [1973]). There are a number of issues one could take up here. First, although one might hold that a single name 'Madagascar' changed its referent over time, one might instead opt for the view that one name died out and another homophonic name replaced it.25 Second, even if this move is resisted, the possibility of reference shift does not bear on the matter of temporal rigidity quite as directly as Fprllesdal seems to suggest. As mentioned earlier, to say that an expression R is modally rigid is not to make any claim about languages spoken at other possible worlds; it is to make a claim about the expression R as used in our actual language. Without making too many tendentious assumptions about the persistence criteria for languages (or their fragments), a parallel point can be made concerning temporal rigidity: to say that R is temporally rigid is not to say anything'about languages spoken at other times; rather it is to say something about R as used at the present time (in our actual language). And this should not encourage the thought that the temporal rigidity of R conflicts with the possibility of R changing its reference over a period of time. To say that R is temporally rigid is not to say anything about past or future uses of R (or its descendants) in our actual language (or its descendants). Of course the connection between the temporal rigidity of R and its use at different times is quite different from the connection between the modal rigidity of R and its uses at different worlds: although R-users do not move across worlds, they do move through time (potentially) producing and encountering different tokens of R at different moments.26 And certainly a massive degree of consistency in the use of linguistic devices is beneficial to continued successful communication. Whether we understand this in terms of functional considerations, normative pulls, or regulative ideals is not going to impinge upon a functional explanation of the rigidity of terms. I think we have here more than just the outline of an account of how terms function: we also have a great deal of what is needed if we are to provide a plausible account of the nature of the distinction between term and predicate. The possibility of using terms (as I have characterized them) in their normal way in substantial exchanges of information about the world and our experiences presupposes a second class of expressions with rather different properties. When we represent the world to ourselves or communicate information about it, we represent individuals as having certain properties, as changing their properties over time, as having the potential to have (or have had) different properties if the world had been different in various ways. Focusing on language and returning to our theoretical vocabulary, we represent individuals (or n-tuples of individuals) as falling under the extensions of certain predicates, and as falling under the

104 / Stephen Neale extensions of different predicates at different times or in different possible circumstances. It would seem, then, that if a linguistic system is to allow for the possibility of substantial exchanges of information about a dynamic and contingent world, it must contain not only a category of expressions that by their nature are meant to be used in such a way that they are understood to have extensions that do not vary across time and across possible circumstances, but also a category of expressions lacking this property. 9. Structure

Hitherto, in my discussion of referring expressions I have mentioned only names and variables. Names and variables are certainly rigid, but they share another important feature: they are semantically unstructured, in the sense that their references are not determined compositionally. Following Russell and Wittgenstein (as I read them), I see an important connection between reference and structure: only a semantically unstructured expression can be viewed as a device of reference. Certainly many philosophers treat certain expressions as referring to things in virtue of the meanings or references of their parts, but I find myself very sceptical about this business. As I entertain the semantical notion of reference -in contrast to the important but quite different notion of speaker'sreferencen-it is an arbitrary relation that holds between a symbol and an individual, and as soon as one invokes a constructive or compositional procedure for determining the semantical value of an expression, one is no longer engaged in trying to establish reference. If an NP has any internal semantical structure it is to be accorded a nonreferential treatment (though, of course, some of its parts may be referential). And if, as I have suggested, the class of meaningful NPs comprises just referring expressions and restricted quantifiers, any meaningful NP with semantical structure is a quantifier. It should be clear just how liberating the Theory of Descriptions is for anyone sceptical about semantically complex referring expressions. The sceptic rejects the view adopted by Frege, Tarski, avids son, and others according to which expressions such as 'the King of Troy', 'Hector's father', 'the referent of "Achilles"', "'Achilles killed Hector"", 'the successor of zero', 'S(S(S(O)))', xu)', '449', '2 + 2', might be treated as complex referring expressions (as well as the view that so-called 'that'-clauses refer to propositions or similar entities). Following the lead of Russell, such expressions are viewed as definite descriptions, and hence as quantifiers.28 In short, the Theory of Descriptions provides an independently motivated way of avoiding the view that the semantically complex expressions just mentioned are referring expressions. (It is difficult to see how the projects of The Philosophy of Logical Atomism and the Tractatus could have been attempted without the Theory of Descriptions, or some similar method for contextually defining descriptive phrases.)

Term Limits / 105 As far as constructing one part of a truth definition for a fragment of English is concerned, the existence of only semantically unstructured referring expressions appears to simplify life. On the assumption that the semantical value (truth-theoretic contribution) of an expression is determined by and only by the semantical values of its constituents and their syntactical organization, in effect a referential NP @ will be an NP whose semantical value is exhausted by a simple axiom of the form And on the reasonable assumption that only a referential NP may occupy an argument position in logical form, the semantical value of anything in an argument position will be completely determined by such an axiom, just as in the simplest first-order languages (i.e. those that do not contain complex terms of the form Tf(x)l where f is a functional expression). In a nutshell: a noun phrase can occupy an argument position in logical form only if it has its own private axiom, i.e. only if it is semantically atomic.29 But can this position be maintained? Certainly names and pronouns anaphoric on names are referential. So in (26) the names 'Bill' and 'Henry' and also the pronoun 'he', when understood as anaphoric on (e.g.) 'Henry', are referential: (26) Bill told Henry that he was a fool. There are many ways of thinking about how a pronoun P anaphoric on a refemng expression R functions as far as a truth definition is concerned. Perhaps the simplest view is that P is subject to the same axiom as R. There is no need to explore this matter here; for present concerns the important point is that the pronoun has no internal semantical structure.30 But what about indexical pronouns ('1', 'you'), demonstrative occurrences of pronouns ('she', 'her'), simple demonstratives ('this' 'that'), complex demonstratives ('this pen', 'that man drinking ouzo'), mass noun phrases ('water', 'most marble'), abstract noun phrases ('wisdom', 'courage'), derived nominals ('George's departure'), gerundive nominals ('George's departing') and so on? There is not the space for anything close to an extensive discussion of all of these here; but I can at least illustrate why I think the problems they raise for the complexity sceptic are much less severe than one might initially suppose. In his pioneering work on demonstratives, Kaplan [1977, 19891 argues convincingly that demonstrative occurrences of pronouns, indexical pronouns, and simple demonstratives are rigid referring expressions. Exactly how the reference of a demonstrative is fixed is a matter for debate. Originally, Kaplan was inclined to see the demonstration as playing the key role;31 more recently he is more favorably inclined toward the directing intention.32 But as in the case of anaphoric pronouns, for immediate concerns we can ignore this matter; the important point is that a demonstrative has a particular semantical value that is

106/ Stephen Neale not determined compositionally. So far, so good; but what about complex demonstratives, phrases of the forms [this ~ 1 and rthat ~ 1 used demonstratively?33 Notoriously, such expressions raise a number of serious difficulties for theories of reference and attempts to provide rigorous truth definitions for fragments of natural language. On the face of it, complex demonstratives possess two features that cannot go together if the complexity sceptic is on the right track: they seem to be both semantically structured and referential. The semantical values (truth-conditional contributions) of 'this man' and 'that man drinking ouzo' would appear to be functions of the semantical values of their syntactical constituents (i.e. the determiner 'this' and the common noun 'man', in the case of 'this man'). But in view of Kaplan's work on simple demonstratives, there is certainly some temptation to view their complex counterparts as rigid referring expressions. So if the sceptic's position is to be maintained, either the purported structure in complex demonstratives is illusory or else such NPs are really quantificational. Let us look briefly at two candidate accounts of complex demonstratives that the complexity sceptic might explore. (1) Although there is no solid evidence for the view that some descriptions are referential (even when there is accompanying "speaker's reference"34)-surely 'The Morning Star' and 'The Holy Roman Empire' are now names whose references are not determined compositionally-it might be suggested that phrases of the form rthat F l are rigid referring expressions and as such have no semantical structure. Borrowing from Kaplan's account of 'dthat', it might be suggested that the descriptive material internal to a complex demonstrative functions as an aside that makes no contribution to truth conditions. For example, rthat man is ~ 1might be viewed as truth-conditionally equivalent to , 'he' is used demonstratively), the descriptive rthat is ~ 1(or [he is ~ 1where material functioning only as a device for steering the hearer toward the right individual. On this proposal, an NP will be a referring expression if and only if its semantical value (truth-theoretic contribution) is exhausted by the semantical value of exactly one of its syntactical constituents. There are a number of things to be said about such a proposal and I shall just mention those that seem to me to be the most important. First, a seemingly negative feature is that although the descriptive material 'man' certainly is a genuine syntactical constituent of 'that man', it can no longer be regarded as a genuine semantical constituent even though it is elsewhere a meaningful expression. Second, cases involving misdescription may have a bearing on the viability of the proposal. Cases involving misdescription were once used by philosophers advocating a semantically distinct referential reading of definite descriptions.35 But in the light of work (due mostly to Grice36) on an important distinction between what a speaker says by uttering a sentence on a given occasion and what the speaker means by uttering that sentence on that occasion, it has gradually become clear that cases involving misdescription bolster the case

Term Limits / 107 for a unitary Russellian analysis of descriptions.37 When it comes to demonstratives, it is not at all clear what to say. If I point to someone and say 'that man drinking water introduced me to modal logic', then if the person I am demonstrating is Dagfinn Follesdal and he is drinking water, what I have said is true. If the person I am demonstrating is Saul Kripke, then what I have said is false. But what if it is Follesdal and he is drinking a martini? The proposal under consideration rules that what I have said is true. But while it seems perfectly reasonable for the sceptic to maintain that what I meant (in Grice's sense) is true, it is not clear one way or the other what to say about what I said. Interestingly, bringing up counterfactual situations doesn't seem to help here. There may well be more elaborate cases of misdescription that either support or undermine this account of complex demonstratives; certainly the case at hand does neither. Third, this general approach to complex demonstratives might receive support from the fact that, unlike quantification into definite descriptions and (other quantified NPs), quantification into complex demonstratives seems to be highly unnatural, if not downright ungrammatical:38 (27) Every driver knows the mechanic working for him [every xl: driver xl] ([the x2: mechanic x2 & x2 is working for xll (xl knows x2)) (28) ??Every driver knows that mechanic working for him. If the function of the descriptive material in a complex demonstrative is to direct the hearer to a particular individual who is (or is being made) salient in some way or other, and if the material does not contribute to the semantical value of the NP, then the relativization of a unique mechanic per driver in (27) cannot be mirrored in (28).39 (2) Complex demonstratives are "actualized" definite descriptions, and hence quantificational and semantically structured. Before looking at this proposal, we can note a disanalogy between Kripke's discussion of proper names and Kaplan's discussion of demonstratives. Kripke's arguments show that the name 'Aristotle' is not equivalent to any ordinary definite description rthe ~1 (even if Aristotle is uniquely F). Furthermore, they show that 'Aristotle' is not equivalent to the "rigid description" rthe actual ~1 (even if Aristotle is actually uniquely F), and also that the name does not have its referent fixed rigidly by description.40 One ingredient in some of Kripke's argumentation is that in order to be a competent user of 'Aristotle', it is not necessary to see a connection between being Aristotle and being F, or a connection between 'Aristotle' and 'F'. Coritrast this with the case of demonstratives. Here, Kaplan's arguments show that the demonstrative 'that' is not equivalent to the definite description 'the thing I am demonstrating' (following Kaplan, assume that the indexical 'I' is a rigid referring expression). However, Kaplan points out that the competent user of a demonstrative must grasp its "character," which can be thought of as a rule for

108/ Stephen Neale determining its reference on a particular occasion of use. So it looks as though there may be some privileged description or other that is associated with a demonstrative (on the assumption that its character can be described). So although there are counterfactual considerations that preclude treating 'that' as equivalent to the ordinary definite description 'the thing I am demonstrating', it is not wholly unreasonable to suppose that something like this description captures its character. So it may yet be possible to view demonstratives as equivalent to actualized descriptions, and hence as quantifiers. For example, on the assumption that 'I' is a rigid referring expression, we might consider analysing a complex demonstrative 'that F' in terms of, or at least as equivalent to, a description such as [the actual F I am demon~tratin~l.41 On this account, a better narne.for complex demonstratives might be demonstrative descriptions. One way of implementing this proposal would be to view 'this' and 'that' as quantificational determiners on a par with 'the', 'every', 'no', etc. (if simple demonstratives are to be included, then perhaps they will be treated as demonstrative descriptions composed of the determiner and a phonetically empty complement). One special stipulation seems to be required however: although the actualization of a description effectively eliminates a certain type of scope ambiguity in modal contexts, it has no analogous impact on other nonextensional contexts. For example, (29) is ambiguous between de re and de dicto readings, naturally captured by allowing the description to have either large or small scope as in (291) and (292) respectively: (29) John thinks the actual man I am demonstrating is a fool (291) [the xl: actually (man xl & I am demonstrating XI)](John thinks xl is a fool) (292) John thinks [the xl: actually (man xl & I am demonstrating xl)l (xl is a fool) But (30) is not ambigious in the same way: (30) John thinks that man is a fool. It would seem, then, that demonstrative descriptions must have large scope with respect to attitude frames, and from the point of view of implementation it is simplest (perhaps even mandatory) to view them as taking large scope quite generally. This might in turn be used to explain the fact that 'every driver' cannot bind a variable inside 'that mechanic working for him' in example (28).42 Let me conclude this section with a few brief remarks on other types of NP. Following Russell, NPs of the form ~ N P ' S~ ' ('George's 1 mother', 'my apartment', 'that man's cough', 'George's departure', 'George's departing', etc.) are most plausibly viewed as (or as semantically equivalent to) definite descriptions (of persons, objects, events, facts, or whatever) and hence semantically structured quantificational NPs.43 Many promising accounts of

Term Limits 1 109 mass NPs such as 'most marble', 'the water', and 'some sand' treat such phrases as quantificational.44 Bare occurrences of mass nouns such as 'water' and 'marble' and count nouns such as 'lemons' and 'beavers' in N P positions might be treated either as semantically structured restricted quantifiers with phonetically null determiners' whose values are fixed contextually-'whales are mammals' seems to be understood as 'all whales are mammals' whereas 'Frenchmen are good cooks' seems to be understood as ' a lot of Frenchmen are good cooks' -or as unstructured rigid referring expressions in the manner suggested by Kripke [I9721 and Pumam [1975]). NPs of the form ~ N Pand N P ~seem to present more of a difficulty. Notoriously, not all sentences containing NPs of this form can be analysed as sentential conjunctions. While 'Russell and Whitehead lived in Cambridge' can be understood as 'Russell lived in Cambridge and Whitehead lived in Cambridge', the sentence 'Russell and Whitehead wrote Principia Mathematics' resists an analogous treatment because the sentence is most naturally understood collectively rather than distributively. Matters appear to be further complicated by the fact that blends of referential and quantificational NPs are perfectly acceptable in NPs of the form rNP and NP1: (31) Janet and more than twenty federal marshals are tailing Hamilton (32) Fred, Janet, and a few of their students are compiling a bibliography. At the very least, the complex N P 'Janet and more than twenty federal marshals' has a quantificational component; this suggests that it may be fruitful to explore the idea that all NPs of this general form are inherently quantificational. Much more work needs to be done on complex NPs-certainly names and descriptions of numbers ('ten', 'lo', '5 + 5', 'five plus five', 'the sum of five and five') will bring up interesting questions. Even if there turn out to be some, perhaps special, cases that create insurmountable difficulties for the complexity sceptic, it ought to be clear from this brief discussion that (Tl) is much closer to being correct that one might otherwise have thought; and to this extent something very close to (TI) may well be correct.

10. The Terms of Substitution I want now to turn to (T2), the thesis that modal and causal S-connectives are referentially transparent but nonextensional. In view of the care taken in section 4-recall that we defined "X occurs in an extensional context" not "X is an extensional context9'-the thesis needs to be clarified if it is to admit of serious examination. (T2) can be restated thus: (i) coextensional terms may be substituted salva veritate within the scopes of modal and causal S-operators (as long as they are not also within the scopes of any psychological operators, of

110/ Stephen Neale course), but (ii) coextensional sentences may not be so substituted. In work in progress, I attempt to explain the virtues of (T2) in the context of a detailed discussion of the logic of modal, temporal and causal connectives, itself located within a more general discussion of events and causation. For present purposes, I seek only to ward off a notorious argument, which, if sound, would demonstrate the futility of my larger project. Since there has been (and continues to be) a considerable amount of very loose talk about substitution, referential transparency, and extensionality, it will pay to proceed with caution. The real concern here is the status of two useful substitution rules often used in systems of extensional logic and in the derivation of T-sentences, analogs of which are used in general philosophical argumentation. The first rule is for coextensional terms; the second is for coextensional sentences. (1) The Principle of Substitutivity of (Singular) Terms, (PSST) might be stated thus: PSST

Z(a)

a=P

%PI This just says that if r ~ ( a ) is l a true (false) sentence containing at least one occurrence of the term a , and ra = is a true identity statement, then rZ(j3)l is also a true (false) sentence, where c ( P ) ~is the result of replacing at least one l an occurrence of the term P. Thus PSST says that occurrence of a in r ~ ( a )by if two sentences differ only in that one contains the term a where the other contains the coextensional term j3, the sentences in question have the same extension. Clearly PSST is valid when a occurs in an extensional context (i.e. when a occupies an extensional position) as defined in section 4. As shorthand for this, let us say that extensional contexts are +PSST (as opposed to -PSST). And by obvious extension of this terminology, let us say that extensional Soperators are +PSST. (2) For coextensional sentences, we can state an analogous rule, the Principle of Substitutivity of Material Equivalents (or PSME) for short:

P1

PS ME

SeT

VT) This just says that if r Z ( ~ ) 1is a true (false) sentence containing at least one occurrence of the sentence S, and S and T have the same extension, then r~(T)1 is also a true (false) sentence, where rZ(T)1 is the result of replacing at least one occurrence of S in TC(S)~by an occurrence of T. Thus PSME says that if two sentences differ only in that one contains the sentence S where the other contains

Term Limits / 111 the coextensional sentence T, the sentences in question have the same extension. Clearly PSME is valid when S occurs in an extensional context (i.e. when S occupies an extensional position). As shorthand for this, let us say that extensional contexts are +PSME (as opposed to -PSME). And by obvious extension of this terminology, let us say that extensional S-operators are +PSME. We can now address the matter of the relationship between extensionality and referential transparency head on. Let X be a particular occurrence of an expression in a sentence S. X occurs in a referentially transparent context if and only if X does not occur within the scope of any operator that is -PSST. To say that X occurs in an extensional context is to say substantially more: X occurs in an extensional context if and only if X does not occur within the scope of any operator that is -PSST and does not occur within the scope of any operator that is -PSME. So if X occurs in an extensional context it also occurs in a referentially transparent context. Notice that it does not follow from anything on the table that if X occurs in a referentially transparent context it also occurs in an extensional context. What would be needed to show this? A proof that every S-operator that is +PSST is also +PSME. Every extensional S-operator is both +PSME and +PSST. And every S-operator that is +PSME is also +PSST. So if every S-operator that is +PSST is also +PSME, referentially transparent contexts and extensional contexts amount to the same thing. This would be a startling and extremely important conclusion. By the definition of intensional operator given in section 4, all intensional S-operators are +PSST and -PSME. That they are -PSME is self-evident; that they are +PSST is easily demonstrated: If a and P are terms that both refer to z, then r@aland rap1 have the same truth conditions (where @ is a one-place predicate): r@al and are both true if and on1 if z is @. If 0 is an intensional operator, then by definition the truth value of 0 (@a)ldepends only upon the truth conditions of r@al; and the truth value of rO(@j3)1depends have the same truth only upon the truth conditions of r@pl. But r@aland conditions (they are both true if and only if z is a).Hence ro(@a)l is true if and only if r0(@~)1is true. Hence 0 is +PSST. The upshot of all this is that if it can be demonstrated that every S-operator that is +PSST is also +PSME, it will have been demonstrated that there can be no intensional S-operators! So much the worse for intensional logic; in particular, so much the worse for systems in which the modal adverbs 'necessarily' and 'possibly' are treated as +PSST/-PSME S-operators, and so much the worse for systems in which causal expressions such as 'because', and 'the fact that...caused it to be the case that' are treated as +PSST/-PSME S-operators. In effect, Quine has argued that every S-operator that is +PSST is also +PSME; to be precise, he has presented an argument designed to show that no S-operator can have the combination of features +PSST and -PSME. And Davidson has provided a more specific version of the same argument designed to

r'

112/ Stephen Neale show that certain expressions (e.g. 'before' and 'the fact that...caused it to be the case that') cannot be treated as S-operators with the combination of features +PSST and -PSME. I shall focus on Quine's general argument here (though more or less everything that is relevant to disarming it carries over mutatis mutandis to Davidson's argument). I think we have nearly enough on the table to show that the argument does not succeed. Notice that if (Tl) is true-the thesis that the class of meaningful NPs in natural language consists of just rigid referring expressions and restricted quantifiers-no general argument of the sort Quine aims to provide can succeed. For it is a consequence of (Tl) that the modal operators 'necessarily' and 'possibly' are +PSST, and we know these operators are -PSME from the fact that coextensional sentences cannot be substituted salva veritate within the scope of 'necessarily' in (e.g.) 'necessarily nine is greater than seven'. One final point needs to be made before we examine the details of Quine's argument, an important (but frequently overlooked) point concerning substitutions involving definite descriptions. If definite descriptions are quantified NPs, purported substitutions involving them are not licensed directly by PSST.45 This is not to say that rules for substituting descriptions cannot be provided; with enough ingenuity substitution rules for all sorts of expressions can be concocted. This matter merits some attention. In order for PSST to be applied correctly we need an identity statement of the form 'a = 6'. One of Russell's greatest contributions to philosophy was to point out that what might look like an identity statement involving descriptive phrases is really no such thing. In first-order logic with identity, the logical forms of sentences of the superficial grammatical forms rthe F = a1 and [the F = the GI are given by the following:

Neither (31) nor (32) is an identity statement. An identity statement contains the identity sign with a term on either side. (31) and (32) are quantificational statements that contains important identity statements as proper parts. The force of this point becomes clear if we reflect on the nature of formal derivations. From the premises [l] Lewis Carroll = Charles Dodgson, and [21 Lewis Carroll snored, we can draw the conclusion that [3] Charles Dodgson snored. In order to provide a formal derivation of the conclusion from the premises in a standard logic with identity, we can use PSST, which sanctions a direct move from [I] and [2] to [3]: (1) [l] c = d [21 SC (2) (1,2) [31 Sd

Premise Premise 1, 2, PSST

From the premises [l] Lewis Carroll = the author of Alice in Wonderland, and [2] Lewis Carroll snored, we can draw the conclusion that [3] the author of

Term Limits / 113

Alice in Wonderland snored. But, and this is the important point, we cannot use PSST to move directly from lines [I] and [2] to line [3] in the formal analog of this argument in first-order logic with identity augmented with Russell's abbreviatory notation for descriptions-('G(uc)(Ax)' is shorthand for '(3x)((Vy)(Ay= y = x) & Gx)'; 'Ax' is read as 'x authored Alice in Wonderland': (11 (21 (l,2)

Dl c = (a)(&) P I SC [31 S(uc)(Ax)

Premise Premise 1 , 2, PSST

This derivation is illegitimate because PSST can be invoked only where we have a genuine identity statement, and a genuine identity statement has terms on either side of the identity sign. Premise [I] is not an identity statement; it is merely shorthand for a complex quantificational statement. However, to say that PSST does not sanction a direct move from line [2] to line [3] on the basis of the truth of the entry on line [I] is not to say that one cannot derive the entry on line [3] from the entries on lines [I] and [2] using our normal rules of inference (including, of course, PSST). Indeed, it is a straightforward exercise to provide such a derivation: Premise Premise 1, def of ' ( u ) ' Temporary Premise 4, &-elim 2, 5, PSST 4, &-elim 6, 7, &-intr 8, EG 3, 4, 9, EI 10, def of ' ( u ) ' . Realizing just how difficult and how tedious the project of Principia Mathematica would be if they had to proceed in this way every time they wanted to set out a proof involving a definite description-though of course they would be appealing to axioms rather than inference rules -Whitehead and Russell reduced their workload by showing that although descriptions are not terms, if a predicate F has exactly one thing in its extension, in extensional contexts the description '(uc)(Fx)' can be treated a s if it were a term for certain logical purposes. On p. 179 of PM the following theorem is proved for extensional contexts: *14.15 ( ( u ) ( F x )= b ) 3 (G(u)(Fx)= G b ) . What this really says is that if the individual referred to by 'b' exhausts the extension of a predicate F , then one can "verbally substitute" b for a definite

114 / Stephen Neale description '(uc)(Fx)'. It is a mistake to think that when one performs a "verbal substitution" of this sort, one is simply making a direct application of PSST. *14.15 is not PSST; it is a derived rule of inference that can be used in extensional contexts. Indeed, the fact that *14.15 holds in extensional contexts trades on the fact that such contexts are +PSST and +PSME, for it is essentially a rule that licenses certain substitutions when the extension of a t e n coincides with the membership of the extension of a predicate. Following our earlier conventions, we can say that extensional contexts and extensional operators are +14.15. Adding *14.15 to our system, the following derivation is now available: (1) (2) (l,2)

[ll [21 131

c = (w)(Ax) SC S(uc)(Ax)

Premise Premise 1, 2, *14.15.

Not surprisingly, the following is also valid in extensional contexts

This says that if the predicate F has just one thing in its extension and is coextensional with the predicate G, then one can "verbally substitute" the description '(uc)(Gx)' for the definite description '(uc)(Fx)', or vice versa. It is surely only because extensional contexts are +14.15 and +14.16 that Whitehead and Russell introduce descriptive terms into the formal language of PM: they drastically simplify formulas and proofs. 11. Quine's Argument Against Intensional S-Operators We are now ready to examine Quine's argument to the conclusion that we cannot have S-operators that are +PSST and -PSME.47 To prevent one possible misunderstanding of the argument, let's assume that there are no psychological operators in play. The conclusion of the argument is as follows: for any Soperator O that is +PSST, then as long as O permits the substitution of logically equivalent sentences within its scope salva veritate, 0 is also +PSME, and so extensional. (If 0 permits the substitution of logically equivalent sentences withii; its scope salva veritate let's say that it is +PSLE.) I am going to spell out the argument in rather more detail than Quine does.48 Quine proposes the following abbreviatory convention: Where 'p' represents a sentence, let us write 'Sp' (following Kronecker) as short for the description: the number x such that ((x = 1) and p) or ((x = 0) and not p).49

The central part of Quine's argument can be set out as the following derivation, where 0 is an arbitrary S-operator that is +PSST (and +PSLE of course):

Term Limits / 115 [l] 121 [3] [4] [5] [61

p =q 00) O(6p = 1) 6p = 69 0(6q= 1) o(9)

Premise Premise 2, log. equiv. of '6p = 1' and 'p' (by def. of '6') 1, def. of '6' 3, 4, PSST

5, log. equiv. of '6q = 1' and '9'.

Gloss: (1) Let 'p' and 'q' be any two extensional sentences that agree in truth value. (2) Embed 'p' under '0' to form the sentence 'O(p)'. (3) By the definition of '6', 'p' is logically equivalent to '6p = 1'; by hypothesis, '0' is +PSLE so we can establish 'O(6p = 1)'. (4) Since 'p' and ' 9' have the same truth value (premise), '6p = 69' is true by definition of '6'. (5) By hypothesis, '0' is +PSST, so substituting '69' for '6p' in 'O(6p = 1)' we get 'O(6q = 1)'. (6) By definition of '6', '69 = 1' is logically equivalent to '9'; by hypothesis, '0 ' is +PSLE so we can establish 'O(q)'. Moral: '0' is actually an extensional Soperator since it has been shown to be +PSME ('O(p)' differs from 'O(q)' only in the substitution of the mere material equivalents 'p' and '9'). Upon careful examination, it is clear that the main flaw in this argument is of almost the same general form as the one that Smullyan [I9481 spotted in Quine's argument for the referential opacity of modal contexts.50 Fortunately, there is no need to examine that argument or understand where it breaks down in order to see where Quine's intensional S-operator argument breaks down. The error in the latter is the appeal to PSST in moving from lines [3] and [4] to line [5]. By Quine's own lights, '6p' and '6q' are definite descriptions, hence PSST itself does not license a move from lines [3] and [4] to line [5]. The entry on line [4] is not a genuine identity statement at all; it is an abbreviation for the following monstrosity:

To make the point completely clear, let us pluck lines [3], [4], and [5] out of the original derivation and treat them as constituting the following derivation: [3] O(6p = 1) 141 6~= 69 [5] O(6q = 1)

Premise Premise 3, 4, PSST

On the reading that interests Quine, this derivation has the following logical form92 [3] 0((3x)((Vy)((y = 1 & p) v (y = 0 & ~ p I)y = x) & x = 1)) [41 (3x)((Vy)((y = 1 & p) v 0,= 0 & 1 p ) = y = x) & (~)((VW)((W = 1 & q) v (w = 0 & 7q) = w = Z) & x = z)) [5] 0((3z)((Vw)((w = 1 & q) v (w = 0 & l q ) = w = z) & z = 1))

Premise Premise 3, 4 PSST

1161Stephen Neale And PSST simply does not license the move from lines [3] and [4] to line [5]. Let us consider some possible reactions to this. (1) It might be thought that Quine could still reach his desired conclusion by appealing to PM * 14.16 (rather than PSST):

But such an appeal would involve substituting one error for another: *14.16 is a derived rule of inference for +PSME contexts (if a context is +14.16 it is +PSME). The upshot of all this is that no appeal can be made to *14.16 without presupposing that 0 is +PSME; and that would be begging the question as far as Quine's argument is concerned, for the whole point of the argument is to demonstrate that 0 is +PSME. (2) It might be thought that Quine could rescue his argument by insisting that definite descriptions are referential rather than quantificational NPs. But such a move runs into problems. First, when it comes to the construction of a plausible compositional semantics there are many syntactical and semantical reasons for thinking that descriptions are structured, quantificational NPs and no compelling reasons for thinking of them as terms. Second, Quine himself insists on treating definite descriptions in accordance with Russell's theory (i.e. as quantificational NPs) in his own logical and philosophical works. So it might be suggested that Quine treat ordinary descriptions as Russellian but stipulate that Kronecker descriptions are terms. However, this will not work because the claim that '6p' and '69' are not genuine terms is crucial to Quine's claim that 'p' and ' 6 p = 1' are logically equivalent.53 I would have thought that, if pressed, Quine would justify the claim that these sentences are logically equivalent by pointing to the fact that ' 6 p = 1' is simply an abbreviation for the following sentence of first-order logic

which is logically equivalent to ' p ' . I see no other way in which he could justify the equivalence (certainly if '6p' is provided with a treatment upon which the sentence 'p' is not a semantically significant and proper constituent of ' 6 p ' , then the claim that ' p ' and ' 6 p = 1' are logically equivalent will not stand up). Without this logical equivalence, the original derivation breaks down in the move from line [2] to line [3]:

=q

Premise Premise [3] 0 ( 6 p = 1) 2, ?? [l] p

P I O@)

It must be concluded, then, that Quine has presented no case against the existence and coherence of +PSLE S-operators that are also both +PSST and -PSME.s4 Furthermore, I would maintain that modal and causal S-operators are

Term Limits / 117 +PSLE, +PSST and -PSME. N o doubt many philosophers are already operating under this assumption; in my view, those who are not may well be led into serious philosophical error. N o doubt there are awkward problems with much that I have been saying about terms, but I do not think that any of these problems will impinge upon what I have said about substitution inferences. Certainly, a clear account of substitution and the functioning of terms is going to be a prerequisite to clear-headed philosophical inquiries that make use of locutions that appear to say things about possibility, time, events, and causation. Notes

*

A shortened version of this paper was presented at the Moral Sciences Club, Cambridge University, in May 1992, and subseauentlv at Oxford University, the ~ n i v e r s i of i ~ Oslo, ihe university of stockholm, ~ i & ' s College, univer$ty of London, and the Ecole Polytechnique, Paris. I thank Kent Bach, Jeremy Butterfield, Herman Cappelen, Charles Chihara, Donald Davidson, Michael Dummett, Olav Gjelsvik, Jennifer Hornsby, Jennifer Hudin, Martin Jones, Menno Lievers, Jan-Tore L@nning,Per Martin-L@f,Alex Oliver, Peter Pagin, John Perry, Franqois Rbcanati, Ian Rumfitt, Mark Sainsbury, John Searle, Gabriel Segal, Timothy Smiley, Scott Soames, Barry Stroud, Rupert Summerton, Jamie Tappenden, Bruce Vermazen, Dag Westerstahl, and Bernard Williams for helpful comments and suggestions. I gratefully acknowledge the support of a Visiting Scholarship at Corpus Christi College, Oxford for Hilary Term of 1992. 1. The basic idea concealed beneath the surface of (T3) is that a sentence is an ordered pair consisting of a representation of surface syntax and a further syntactical representation of logical form ("LF"), where the latter is the sintactical representation relevantto semantical interpretation. The scope of an ex~ressionis evervthing it c-commands at LF. where c-command is essentiallv the formal (or trei-geo&etric) relationship that a sentential operator bears to ik operand(s) in the simplest formal languages, an idea exploited by (e.g.) Harman [1972], Higginbotham [1980], and Neale [1992a]. 2. The modal subthesis of (T2) is defended in detail Neale [1990]. 3. See Tarski [1956]. As far as natural language is concerned, the picture is complicated by the existence of (e.g.) indexicals and demonstratives and various types of temporal operators. For discussion, see (e.g.) Weinstein [I9741 and Taylor [1980]. 4. I here use 'sentence' to include open sentences. Since there is no space to go into this matter here, I shall simply stipulate that temporal expressions such as 'in 399 B.C.', 'today', 'now', 'before', 'after', 'sometimes', and 'always' are not Soperators. Two points: (i) Nothing of consequence turns on this claim here, but it makes it possible to avoid a lengthy detour from my main theme. (ii) There are syntactic and semantic reasons for thinking that it is, in fact, a mistake to treat such expressions as S-operators-some of these can be distilled from Davidson [1967c], Davies [1981], Evans [1984], Lewis [I9751 and Salmon [1989]. 5. In the terminology of tree-geometry, the scope of an S-operator (or any other expression for that matter) is the first branching node properly dominating it. 6. Quine [1953a, 1953b, 19601; Davidson [1967a, 1967b, 1967~1. 7. I use 'intension' in the strict and narrow sense that one associates with the work of many logicians and philosophers. To those who see virtue in talk of "possible worlds," the intension of a sentence can be viewed as a function from possible worlds to truth values. 8. The label is, of course, meant to be suggestive. To the extent that expressions

118 / StephenNeale such as 'it is true a priori that' and 'it is doubtful that' are S-operators, they are epistemic rather than intensional. If a semantical theory were to treat a verb of "propositional attitude" like 'bel'eves' as a constituent f (e.g.) 'Helen believes that' in a sentence of the form Helen believes that pg, and also treat 'Helen believes that' as a complex S-operator, then the S-operator would be epistemic. By contrast, a semantical eory were to treat 'believes' as a constituent of the verb phrase believes hat p , then there wou d be no epistemic S-operator in a sentence of the form Helen believes that p . On such an account, 'believes' would not be an S-operator because it would not combine with some number of sentences to form a sentence. However, it would be of value to call the attitude verb an epistemic operator because it would combine with some number of sentences (one) to form another expression the extension of which would not be determined by either the extension (truth-value) or the intension (truth conditions) of its operand. For the purposes of this paper, it is not necessary to accept either of these approaches to attitude verbs (or any other). All that is needed is an understanding of the uncontroversial idea of an expression lying within the scope (in the sense already defined) of an attitude verb or an epistemic S-operator (if such things exist). 9. It is tempting to claim that whether or not an expression occurs in an intensional or an epistemic context can be established as easily by syntax as by logic, and if this is correct it may well shed some light on the semantics of attitude verbs and hence propositional attitude reports. I cannot expand upon this remark here. 10. Subscribing to the idea of a class of expressions that are rigid does not involve committing oneself to any objectionable form of "essentialism." 1 1 . Throughout, I will be making the harmless (for present concerns) assumption that every name has exactly one bearer. 12. It has been suggested that the rigidity of names reduces to the fact that they demand largest scope in modal (and other) contexts, and that consequently Kripke does not show that names are not disguised Russellian descriptions (see, e.g., Dummett [1973]). However, as Kripke points out, this suggestion is surely incorrect because the rigidity thesis is "a doctrine about the truth conditions, with respect to counterfactual situations, of (the propositions expressed by) all sentences, including simple sentences" [1980, p. 121. Thus the rigidity of names is discernible even when there are no relevant operators with respect to which matters of scope arise as in (10) above. Not only are ordinary proper names rigid, they are not equivalent to, nor do they have their references fixed rigidly by, definite descriptions, even descriptions that demand largest possible scope, or descriptions that are "actualized" (or "rigidified" in some other way). On the phrase "rigid description," see section 7. 13. My phrasing here is heuristic and is not meant to suggest any sort of commitment to the view that temporal expressions like 'in 368 B.C.','before', 'after', and so on are nonextensional S-operators. My own inclination is to explore a modification of Davidson's view, on which such expressions are temporal predicates of events. While I am sympathetic to Davidson's postulation of events and his use of event variables in logical form, I am not moved by his argument to the effect that the aforementioned temporal expressions cannot be treated as nonextensional S-operators. His argument can, I believe, be defused in the same way that Quine's argument against nonextensional S-operators is defused in section 11. For a treatment of temporal expressions as nonextensional S-operators, see Salmon [1989]. 14. See Peacocke [I9751 and Kripke [1979]. 15. If names can be so substituted within the scopes of causal S-operators, this might lead one to propose a causal analog of rigidity. My own view, which I shall not defend here, is that the logic of causal contexts derives wholly from facts about events and facts about the logic of extensional and modal contexts. 16. By (T2), the same is true of natural language.

F

f

T

\

Term Limits / 119 1 7 . Notoriously, Quine [1953a, 1953b, 19601 has argued against the intelligibility of sentences like (18) in which a quantifier binds a variable across a modal operator. In the light of work by Smullyan [I9481 and others, it is clear that Quine's arguments do not pose a threat. For discussion, see Neale [1990], ch. 4. 1 8 . See, e.g., Wiggins [I9801 and Barwise and Cooper [1981]. 1 9 . Davidson [1967a]; Harman 11972, 19751; Wiggins [1980]. 20. See Neale [1992a]. 21. Chomsky [1986]; Higginbotham [1983a]; Higginbotham and May [1981]; May 119871. 22. i n his' review of Neale [1990], Linsky [I9921 claims that my treatment of descriptions as restricted quantifiers is incompatible with Russell's view that descriptions are "incomplete symbols." This claim is without foundation, as is Evans's [I9821 claim that facts about anaphora preclude a restricted quantifier treatment. For discussion of both claims, see Neale [1992c]. 2 3 . To the extent that we are interested in tracking an object through changes in its properties, interested in considering it with respect to alternative circumstances, and interested in properties beyond those that may initially draw our attention to it, and to the extent that we realize that we may have false beliefs about individuals and are concerned to correct some of them, Fallesdal suggests that names for those individuals will be introduced. I am not convinced there is enough in this characterization to isolate the class of names within the class of singular terms. More of what seems to be required can be found in Strawson [1974]. 2 4 . I disagree with F~llesdalon a number of further points. (1) Besides names, F@llesdalclasses definite descriptions on some of their uses-presumably, socalled "referential usesw-as singular terms. For reasons given in Neale [1990], I am thoroughly sceptical of the idea of a semantically significant referential use of descriptions that resists Russellian treatment. (2) In places, Fallesdal suggests that "rigid descriptions" are singular terms. For reasons given above, this seems to me unmotivated. (3) F~llesdalregards pronouns as singular terms by virtue of functioning like the variables of quantification theory. Such an account of the semantics of pronouns will not be adequate: for one thing, pronouns are sometimes used to refer directly to individuals; for another, it is not true that every occurrence of a pronoun functions as a term. At the outset, we may want to distinguish between demonstrative pronouns such as 'this' and 'that' and personal and impersonal pronouns such as '1'. 'you', 'he', 'she', and 'it'. This simple bifurcation is complicated by the fact that 'I' and 'you' have certain affinities with 'this' and 'that' (they appear to be both referential and contextsensitive), the fact that 'he' and 'she' have demonstrative (and thereby presumably referential) uses, and the fact that 'he', 'she', and 'it' can be anaphoric on names, quantified noun phrases, or other occurrences of pronouns. But a further complication arises because pronouns anaphoric on quantified noun phrases bifurcate into those that function as bound variables and those that themselves function as quantified noun phrases (as in 'Every man who owns a donkey beats it'). For discussion, see Neale [I9901 chs. 5 and 6. For present concerns, the main point is that every pronoun is either a rigid referring expression or a restricted quantifier. 25. As far as theoretical vocabulary is concerned, I see no straightforward objection to this latter position. Importantly, denying the possibility of reference change does not involve denying the possibility of semantic change. As far as theoretical vocabulary is concerned, it seems clear to me that many predicates have changed not only their extensions but also their meanings. 26. Distinct occurrences of R in a single spoken utterance will themselves be separated by some portion of time, and strictly speaking this highlights a problem in my use of (12) to exemplify the temporal rigidity of proper names. However, the use of an example involving two occurrences of the same name is not crucial.

120/ Stephen Neale 27. See Strawson [I9501 and Kripke [1977]. 28. On this account, in a truth definition that makes use of axioms such as "Ref('Achilles', s) = Achilles", it will be Whitehead and Russell's derived rule of inference for extensional contexts (PM *14.15, see section 10) rather than the Principle of Substitutivity for Singular Terms that is used in derivations. Like "f(a)" and "the referent of 'Achilles'," "Ref('Achilles', s)" is a definite description. Once modal operators are introduced, *14.15 cannot be appealed to freely; something similar-essentially a modalized version of *14.15-must be proved if the truth definition is to be adequate. On the assumption that languages have their semantical properties noncontingently, what is required is easily proved in normal modal systems. 29. An attractive consequence of this is a clearer characterization of the relationship between surface syntax and logical form. For discussion, see Neale [1992a]. 3 0 . I shall not discuss pronouns anaphoric on quantified noun phrases as I have discussed them at length elsewhere (Neale [1990, 1992a1). Such devices present no problems for (Tl): If a pronoun P occurs within the scope of a quantified NP Q upon which it is anaphoric, P functions as a bound variable; if P occurs outside the scope of Q it is understood as a quantified NP, typically a definite description. 3 1 . K a ~ l a n119771. 3 2 . ~ a ~ l i1989j. a n 3 3 . As Evans [I9821 points out, there are dialects of English in which phrases of the forms rthis ~1 and [that ~1 can be used nondemonstrativelv. as in 'I met this man at the pub last night' and 'Do you remember that house in the country we were going to build?' I shall put aside such uses of complex demonstratives here as it is straightforward demonstrative uses that give rise to the most pressing problem for the complexity sceptic (quantificational analyses of these other uses seem very plausible). 3 4 . See (e.g.) Kripke [1977], Sainsbury [1979], Davies [1981], Neale [1990]. 35. See, e.g., Domellan [1966]. 3 6 . See in particular the first seven chapters of Grice [1989]. 3 7 . See, e.g., Kripke [1977], Sainsbury [1979], Searle [1979], Davies [1981], and Neale [1990]. 3 8 . For important discussion of such examples, see Taylor [I9801 and Davies 119821. 3 9 . in some dialects 't does appear to be possible to bind variables inside phrases of the form [that F used nondemonstratively. Jamie Tappenden has suggested the following example: 'every man eagerly awaits that day when he retires'. Certainly an analysis that makes 'that day when he retires' equivalent to 'the day (when) he retires' looks plausible here. 4 0 . The sceptic, of course, denies that any NP has its referent fixed compositionally by description. 4 1 . Perhaps the description in question needs to be more elaborate, for example 'the actual F I am demonstrating (or attempting to make salient in some other way)'. This would help with examples like 'Thank goodness that man with the awful tie has left'. For simplicity, I will not use the more elaborate description. I am here indebted to Jamie Tappenden. 4 2 . Some fine-tuning will still be needed to handle sentences containing two (or more) demonstrative descriptions as in 'Bill thinks that man and that woman are police officers.' From a truth-conditional perspective the relative scopes of 'that man' and 'that woman' are not important, but from the point of view of providing a truth definition in one of the standard ways, one or the other must be assigned larger scope. To say this is not to say that it is impossible to devise nonstandard methods for deriving the relevant theorems without relative scopes being assigned. 4 3 . Russell [1905]. See Davidson [1967a], Higginbotham [1983a], and Neale [1990] for elaboration.

i

Term Limits / 121 44. For discussion see b n n i n g [I9871 and the papers in Pelletier [1979]. 45. See in particular Russell (1905), p. 47 and pp. 51-52, and Principia Mathematica * 14. 46. Or, in RQ notation:

,

[the x Fx] (x = a ) (i) (ii) [the x Fx] ([the y: Gy)(x = y)). 47. Forms of the argument in question are presented in Quine [1953a, 1953b, 19601. I shall focus on the version in Quine [I9601 because it is not susceptible to potential problems concerning the existence of classes and the interpretation of the class abstraction operator. 48. Quine's argument is examined by Anscombe [1969], Morton [1969], Sharvy [1970], Cummins and Gottlieb [1972], Mackie [1974], Davies [1978, 19811, Barwise and Perry [1981, 19831, and Sainsbury [1991]. Although each of these works throws light on details of the argument overlooked by Quine, most of them also end up muddying the waters because of a number of inconsistencies concerning PSST, definite descriptions, contextual definition, class abstraction, logical equivalence, and the notion of an extensional context. In effect, I will develop points made by Sharvy, Davies, and Sainsbury in such a way that it is clear the argument in intrinsically incapable of making its point. 49. Quine [1960], p. 148. 5 0 . On this matter, I think I am in almost complete agreement with Sharvy [1970]. (Quine [1953a, 19691 accuses Smullyan of begging the question and of misapplying Russell's Theory of Descriptions, but careful examination reveals that Quine's remarks are based on misunderstandings of both the informal theory of Russell [I9051 and also the formal treatment in Whitehead and Russell [1927]. This matter is discussed in detail in Neale [1990]. In his review of that work, Linsky [I9921 offers a partial defense of Quine but its substance turns on misunderstandings about incomplete symbols and logical form that I plan to address elsewhere.) Davies [1978, 19811 and Sainsbury [I9911 focus on the same error as Sharvy (though neither mention Sharvy's paper or the formal similarity with Quine's arguments for the referential opacity of modal contexts). 5 1. O r, in RQ notation: [the x: (x = 1 & p) v (x = 0 & Ip] ([the z = (z = 1 & q) v (z = 0 & ~ q ) (x] = z)). 5 2. Or, in RQ notation: ] = 1)) Premise [3] O([the x: (x = 1 & p) v (x = 0 & ~ p ) (x [4] [the x: (x = 1 & p) v (x = 0 & -p)]

Premise

([the z: (z = 1 & q) v (x = 0 & ~ q ) (x] = z)) 3,4,PSST [5] O([the z: (z = 1 & q) v (z = 0 & 7q)] (z = 1)) 5 3 . This point seems to be made with varying degrees of clarity by Sharvy [1970], Mackie [1974], Davies [1978, 19811, and Barwise and Perry [1981]. 54. Versions of the argument in Quine [1953a, 1953bl use expressions of the form '$(Fx)'rather than Kronecker descriptions. As stressed by Cummins and Gottlieb [I9721 and Mackie [1974], either such expressions are treated as definite descriptions of classes or else the class abstraction operator is provided with a contextual definition: ~ ( F X= ) ~ ( G x =) df Vx(Fx = Gx). Thus it is not open to argue that although the Kronecker description version of the argument of Quine [I9601 fails, the earlier class abstraction operator version succeeds.

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