Horwich's Schemata Meets Syntactic Structures

Horwich’s Schemata Meet Syntactic Structures John Collins

Paul Horwich (), following a number of others, proposes a schematic compositional format for the specification of the meanings of complex expressions. The format is schematic in the sense that it identifies grammatical schemata that do not presuppose any particular account of primitive word meanings: whatever the nature of meanings, the application of the schemata to them will serve to explain compositionality. This signals, for Horwich, that compositionality is a non-substantive constraint on theories of meaning. Drawing on a range of linguistic data, the present paper argues that while the bare idea of compositionality indeed does not presuppose any account of meaning, Horwich’s format is empirically inadequate. The argument here goes back to Chomsky’s early position on the descriptive inadequacy of rewrite grammars and the consequent need for transformations. It will also be seen that the data militates for a general claim that meaning relevant structure is projected from words rather than imposed on them schematically. Finally, it will be indicated how this reasoning from syntactic considerations is flush with a more traditional philosophical understanding of compositionality.

1. Introduction There is a common understanding that an adequate theory of syntax will, given a lexicon, specify a set of rules or schemata which, when applied to items of the lexicon, will issue in the set of well-formed (grammatical) constructions as defined over the lexicon. Complementary to this view is the thought that an adequate theory of meaning will ‘track’ the syntax; that is, the theory will assign a meaning to each lexical item and, for each rule/schema R, specify how R, when applied to words with such and such meanings, issues in a complex whose meaning compositionally devolves onto the constituent word meanings under R, that is, the theory provides a statement in which the meaning of the complex is given as a function (expressed by R) of the meaning of its proper constituents. There is a deep irony here. The common unquestioning appeal to rules and schemata within philosophy is simply not mirrored within syntactic theory. Indeed, modern generative linguistics was born in the realization that syntax must consist of more Mind, Vol. 112 . 447 . July 2003

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than a taxonomy of sentential frames and the means of their generation; further, the very status of rules and schemata has continuously been in question. Otherwise put, far from philosophical projects being able to exploit freely the resources of syntactic theory, the very basis of modern syntax fundamentally undermines the common understanding of such projects. My claim is not that the very idea of a compositional theory of meaning is inconsistent with our best understanding of syntactic structure. In the absence of a detailed consideration of many syntactic and semantic theories, any such judgement would be empty. The contention, rather, is that the simple-minded model of how to account for compositionality via word meaning and rules/schemata is undermined by syntactic considerations. Further, this is not a claim that relies upon particularly tendentious theses of the latest syntactic work; as intimated, the point goes right back to the origins of generative grammar. The principal target of the sequel will be the position of Paul Horwich, as expressed in his Meaning (), although, as we shall see, the points to be made impact equally on many others. Horwich () proposes a ‘deflationary’ format to account for what he calls meaning facts, that is, all facts of the form ‘X means P’, where ‘X’ is a lexical item or phrase and ‘P’ is a name for the meaning of ‘X’. For each primitive lexical item, the corresponding meaning fact is constituted by the item possessing a monadic property; for each complex phrase, its meaning fact is constituted by what Horwich calls a construction property: the application of a schema to the phrase’s constituent items that have such and such meaning constituting monadic properties. Horwich proposes that this format is best realized by monadic ‘use’ properties of words w: a community’s (conditional) disposition to assent to various sentences that include w, such that this disposition explains all other uses of w within the community. The construction properties are specifiable by the general schemata independently of one’s choice of what properties constitute the meanings of the primitive lexical items that instantiate the schemata. This is what makes the proposal ‘deflationary’: an adequate account of compositionality is independent of any particular account of what meaning is, just as, per deflationism about truth, an adequate account of truth is independent of any proposals in metaphysics, epistemology, etc. Horwich’s general format and his appeal to ‘uses’ in particular, has been variously questioned (for example, Higginbotham, , Fodor and Lepore, , and Collins, ); Horwich () has offered some defence. The sequel will pursue a distinct tack and suggest that the pro-

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posed deflation is empirically inadequate regardless of any issue to do with ‘uses’ and independent of any favoured account of meaning, such as a truth-conditional conception. The inadequacy arises precisely from the kind of considerations that led to, and continue to animate, generative grammar. In essence, to glimpse ahead, the moral of linguistic research is that (meaning relevant) linguistic structure is not imposed upon words via rules or schemata, but is an organization that arises from the inherent features of words meeting the demands they place upon each other. This notion of linguistic structure being inclusive to the constituent words is at the heart of the so-called minimalist program (locus classicus: Chomsky, , Ch. ); as we shall see, though, the failure of the alternative schema model has its origins in the initial development of transformational grammar: simple schemata fail to express a range of essentially systematic semantic phenomena; transformations that map between structures were employed to capture the systematicity as an effect of inter-structure relations. In essence, this insight is what has driven syntactic theory ever since, and the recent development of the minimalist program is but a fruition of this insight.

2. Horwich on compositionality For Horwich, the chief consequence of, and motive behind, his deflationary format is to show that compositionality is a non-substantive constraint on theories of meaning constitution, that is, a compositionality constraint may be satisfied independently of any particular account of meaning properties. Horwich (, p. ) loosely characterizes the compositionality constraint as follows: ‘An adequate theory of meaning must enable us to see how the meanings of complex terms may be determined, and thereby explained, by the meanings of their parts’. It is unclear whether Horwich here intends to characterize what others think compositionality amounts to or just what he thinks it amounts to. Pro tem, let us assume that there is no dispute about the described constraint. Horwich’s idea is that this constraint reduces to the trivial thought that to understand the meanings of the constituent words of a complex and how they are put together to form the complex just is, ‘automatically and without further ado’, to understand the complex (ibid., p. ). In turn, since this thought merely enjoins us to specify primitive meanings and their modes of combination, then, with construction properties in play, the constraint imposes no real constraint at all on what we might take meanings to be. This is because construction properties determine the meanings of complexes in terms of the mean-

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ings of their parts, and construction properties can be defined independently of whatever we take such simple meanings to be. Compositionality, therefore, cannot decisively militate for one theory of meaning over another. In particular, compositionality provides no argument for a truth conditional approach to meaning in opposition to Horwich’s own use theoretic approach. This amounts, in Horwich’s terms, to a deflation of compositionality: ‘all theories regarding the meaning-constituting properties of primitive terms are compatible with compositionality (Horwich, , p. –) … [C]ompositionality per se provides absolutely no constraint upon, or insight into, the underlying nature of meaning (ibid., p. ) … [whether] physical, mental, abstract, irreducibly semantic, monadic, relational, social, descriptive, normative or whatever’ (ibid., p. ). Horwich’s (ibid., p. ) proposal is that any theory satisfying three demands will be consistent with the compositionality constraint. First, for some language L, the theory isolates the primitive expressions and rules of combination (phrase structures) of L, and shows how application of the latter to the former results in well-formed complex expressions of L. Second, the theory specifies meaning-constituting properties p for each ‘meaning fact’ of each primitive item and combinatorial schema (we may balk at the idea that schemata are assigned meanings in the same respect as lexical items; we shall below). Take, for example, a subject-predicate sentence of the form a is F. An adequate theory will tell us the following: (i) ‘a’ means a = p(‘a’) (ii) ‘F’ means F = p(‘F’) (iii) ‘x is f ’ means ‘what it does’ = p(‘x is f ’) (where ‘=’ means ‘… is constituted by …’). Third, for each complex expression e, the theory states that e means what it does in virtue of the application of a meaningful schema to the meaningful constituents of e. In terms of the above example, the theory's statement would be (iv) ‘a is F’ means a is F = ‘a is F’ results from applying a schema meaning what ‘x is f ’ means to a sequence of words meaning what ‘a’ and ‘F’ mean. It follows from (i)–(iv) that (v) ‘a is F’ means a is F = ‘a is F’ results from applying a schema whose meaning-constituting property is p to a sequence of

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words whose meaning-constituting properties are p and p, respectively. In general, the idea is that the underlying meaning property of a complex expression (a ‘construction property’), such as what occurs on the right flank of (v), has the schematic form (CP): (CP) x results from applying P to words <W,..., Wn> with, respectively, constituting meaning properties , and each instance of (CP) is the underlying property which constitutes the meaning of some complex x. This, claims Horwich, is all there is to compositionality. The composition of complex meanings ‘automatically’ follows from an assignment of meaning properties to primitive expressions and a procedure P, embodied in a phrase schema, which applies to such primitives. If, then, the compositionality constraint is just the demand for an explanation of how the meaning of a complex expression is a function of the meaning of its parts (and their combination), as Horwich thinks it is, the proposal is perhaps optimally simple. It tells us that to understand a complex expression is to understand its parts, and to know that their combination is the result of an application of some procedure P. This is stated without any ‘uniform condition’ on what constitutes meaning in general, that is, given any determination of primitive meanings, a construction property is available for each formulatable complex, and so what explains the meaning of complexes is not uniform with what explains the meaning of primitives. This follows from the meaning-constituting property of a complex being an instance of (CP). What on earth, it might be thought, is the meaning of a schema? In Horwich’s initial discussion, as presented above, they are treated as lexical items, as if they have meaning properties just like dog or bark. This is especially curious given that Horwich thinks that meaning properties are constituted by (conditional) assertion dispositions towards a set of sentences featuring the given word, but how is one to be disposed to assert sentences answering to a schema? One asserts a sentence, presumably, because one thinks it is true, not because it has a particular grammatical structure (the exception which proves the rule is where the structure is in some way tautological). In short, schemata require a distinct treatment. Later, Horwich (, pp. –) suggests that schema meanings are functions from word meanings to complex meanings (or, more complicatedly, from words that mean such and such to a sentence, where the meaning of the sentence just is its being the value of

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the function. Horwich notes no significant difference between these two approaches; the disparity will not matter to the sequel.) For example, let [Ns V] be a function which, taking the pair as argument, produces DOGS BARK as value: () Ns V() = DOGS BARK Horwich does not venture any account of how this function might be constituted by a speaker’s disposition to assert the members of a set of sentences. Be that as it may, let us think about this proposal on its own terms. Horwich generalizes () in terms of what he calls a Fregean principle, which identifies the meaning of complexes with construction properties: (FP) The meaning of the result of applying combinatorial procedure P to a sequence of primitives = The result of applying P to the sequence of the meanings of those primitives. The substitutends of P are functions as just described. Thus, given the construction property of, say, ‘Dogs bark’, () follows from (FP): () ‘Dogs bark’ means Ns V() And from () and (): () ‘Dogs bark’ means DOGS BARK, which is the meaning fact we want to explain. Horwich’s functional proposal, then, is an analysis of construction properties which, he claims, ‘proceeds via the fact that the meaning of the complexes are generated by their constituents’ meanings’ (Horwich , pp. –). In effect, then, all that is required of the theory is that it assigns a construction property to each complex expression. Of course, telling the full story here is not trivial. Horwich’s point, however, is that if and however this is done, then an explanation of compositionality is trivial and compatible with whatever primitive meaning properties are. At no stage does Horwich so much as raise an eyebrow at his idea that one may specify the meaning relevant structure for each sentence in a schematic form. The recent history of linguistics suggests that nothing at all

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should be assumed on the matter.1 What is clear is that whether or not there is a level of structure that uniquely codes for meaning features, it could not be occupied by the kind of schemata hypothesized by Horwich. The sequel will support this claim. Most of the arguments below will be based on linguistic data, not on the basis of any thesis as to what constitutes meaning. Thus, as far as the arguments go, Horwich might well be right that compositionality does not substantively constrain what meaning is; equally, though, the arguments will establish that schemata cannot enter into an explanation of compositional linguistic understanding, again, independently of what meaning is. Put simply, Horwich’s proposal just gets the facts wrong. This empirical, as opposed to conceptual, approach to the question might seem to be orthogonal to the ‘philosophical’ issue. This appears to be Horwich’s position. Let us look briefly at this potential gambit. Horwich’s preferred instantiation of the deflationary framework is reductionist in the sense that he views meaning properties as non-sui generis: they have specifiable non-intentional constitutions in the shape of use properties. At the same time, Horwich takes himself to be cleaving to the character of our intuitive concept of meaning. First, Horwich (ibid., p. ) declares his general approach to be non-revisionary in that it targets (supposedly) platitudinous meaning facts such as ‘Dog’ means DOG. Secondly, he eschews the relevance of any cognitive theory of linguistic competence or wider conceptuality. For example, Horwich responds to the thought that the understanding of linguistic meaning involves complex unconscious inferential processes by, in effect, saying that no such processes, even were they to be concomitant with linguistic understanding, enter into the ‘conceptual analysis’ of meaning facts (ibid., pp. –).2 The real tension between these two strands is not so much that metaphysical commitments should not drive conceptual analysis, but that if they are at odds with the data, if the facts are misdescribed, then the naturalism and the analysis must either come apart or fall down 1 It has been an assumption of the dominant generative tradition in linguistics, throughout its many incarnations (apart from a blip in the early s), that there is a unique level of syntactic structure that bears on properties of meaning (as opposed to sound). In recent years, this level has been identified as LF (‘logical form’); see, for example, Chomsky () and Hornstein () (but see n. ). 2 Horwich () appears to have changed his position somewhat. He now claims that the issues are wholly empirical (ibid., pp. , –). Even so, as Chomsky (, pp. –) rightly points out, Horwich’s proposal has no serious empirical constraints at all, and seems to be wholly motivated by conceptual considerations.

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together. After all, no naturalism, unless it be a mere play on words, can withstand empirical refutation; trivially, the result of an analysis may, in the sense that analysis targets our conception of a phenomenon, not the phenomenon itself. As a prelude to more detailed considerations of what the data tell us, let us see how the advertised tension plays out in Horwich. First off, the vast majority of linguists, semanticists and psychologists who appeal to compositionality have not the least interest in the conceptual analysis of meaning or any other intentional or epistemic notion. Even supposing, then, that there is some fecundity in the effort to analyse meaning (or any other concept for that matter) and, to further suppose, that Horwich’s tale does indeed track our relevant intuitions, it remains, it seems, perfectly legitimate to think that compositionality is a substantive constraint on theories of linguistic understanding. Whether it is or not depends on what linguistic structure is actually like. Put simply, the matter is empirical, not conceptual; any conceptual deflation might spin free of theories and their results that bear on the structure of linguistic cognition. Indeed, it might be that our best theories of linguistic competence tell us that language is not compositional, at least not in the way philosophers have traditionally imagined (cf. Jackendoff, .) Now it is, of course, open to Horwich simply to disavow any interest in what linguistics and related disciplines tell us about language and meaning. Yet Horwich affects to be telling a tale about what meaning is, what underlies the fact that ‘dog’ means DOG rather than, say, CAT. Whatever this amounts to, it can not be read off our intuitive concept of meaning, for, as far as Horwich is concerned, the content of this concept is fixed by the set of trivial meaning facts. That is, the general format is non-revisionary; it leaves intuition as it is by taking the intuitive facts to be its explananda. The ‘facts’, such as ‘dog’ means DOG, however, are merely highfalutin ways of saying that a word means whatever it means. The ‘facts’, therefore, do not constitute any kind of substantive explananda; they neither record the native speaker’s intuitions on, say, synonymy, contradictoriness, entailment, etc., nor constrain the candidates for meaning constituting properties. It is, we may say, a mere notational remark to say that the compositionality of complex meaning facts is compatible with whatever primitive meanings are, for the description of construction properties is at such a high level of abstraction that their specification amounts to no more than a statement of compositionality for each complex. Since the principle of compositionality in general is neutral as regards any substantial account of meaning,

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so will be the particular statements. In effect, then, if the deflation of compositionality is just to do with our notion of meaning, as putatively captured in meaning facts, then the effort is otiose; the deflationary thesis appears to be wholly unsurprising and quite uninteresting.3 The account amounts to a neutral description of compositionality. That such a description is available might be of interest were it commonly held that the very notion of compositionality entails some proprietary conception of meaning. But this is simply not the case. No-one, for example, thinks that compositionality is ‘defined’ in terms of truth conditions.4 If, then, Horwich’s ‘deflation of compositionality’ is to be significant, it must extend beyond the bland thought that our notion of compositional meanings does not essentially involve some conception of what meanings are; it must amount to more than an ontologically neutral statement of compositionality. Let us agree, then, that the facts of how language is structured decisively bear on Horwich’s thesis; they cannot be ignored in the name of conceptual analysis.

3. Schemata and syntax In this section, it will be argued that it is best to understand Horwich’s schemata in terms of the structures of a rewrite grammar. As we shall review later, Noam Chomsky from his early works on, has demonstrated that rewrite grammars are fundamentally inadequate to the task of capturing significant patterns of sameness and difference of meaning, and so may not serve to encode the meaning relevant structure of complex expressions. Parallel problems, we shall see, lie in store for Horwich’s proposals. Horwich does not offer a general account of schemata; instead, he settles for examples. Thus, ‘x is f ’ above is presumably intended to realize all cases of a singular third person nominal as subject, in present tense, to a predicative adjective.5 It might be wondered why Horwich leaves the verb in place, unschematized, as it were. Horwich is perhaps only interested in capturing the relation of predication that is invariant 3 The point here is an echo of Fodor and Lepore’s () claim that, while the very notion of compositionality does not entail any particular account of meaning, as a matter of fact, only certain theories of meaning can explain compositionality. Also see Collins (). 4 Horwich does assume that many, including Davidson, think of compositionality as being essentially linked to a particular account of meaning. For a detailed corrective to this misreading, see Collins, (a). 5 Of course, ‘x is f ’ by itself is woefully underspecified, wholly unconstrained; it does not even determine that the ‘is’ carries the matrix inflection.

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between agreement/inflection features of the verb, but be is not meaningless, and it is difficult to see, on Horwich’s approach, why its agreement/inflection properties should not be schematized. For example, although both are cases of adjectival predication, ‘I is tall’ is perfectly acceptable in some dialects of English, but ‘I are tall’ is acceptable in none. Why shouldn’t this difference be somehow schematized so that the deviance of the latter sentence is revealed? Much more will be said about this question below; pro tem, it appears that Horwich simply stipulates schemata and leaves problematic words unschematized. Horwich’s only other example of a schema is ‘Ns V’, which is supposedly realized by all cases of plural nominals as subjects of intransitive verbs. Again, features of agreement and tense are ignored. A plural subject constrains the morphology of its verb (in languages of richer inflection than English, there are greater constraints) and so there is a restriction on the form of words that may fall under Horwich’s ‘V’. For example, the schema, as it stands, admits ‘Dogs barks’. We can already see that Horwich’s examples of schemata fail to reflect salient features of words; simply substituting words for their categorical labels ignores morphology all together, but morphology is precisely to do with what words mean in a sentence, what role they are playing. As we shall see, this is just the beginning of the problem. Let us, however, first see if Horwich’s schemata may fall under a general format. Horwich provides no principle for the generation of schemata nor identifies what their primitive components might be. He might, however, have something like a (context free) rewrite grammar in mind; it certainly seems so. Such a grammar is essentially a means of recursively enumerating a set of structural descriptions for symbol strings. Given a lexicon—a collection of words—a grammar may generate (define) the set of ‘well-formed’ sentences formed from the lexicon. Here is a simple example. (RG) (i) S t NP VP (ii) NP t Det N (PP) (brackets indicate that the flanked material is optional) (iii) VP t V ADJ (iv) PP t P NP (v) Det t the

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(vi) N t girl, boy (vii) V t is6 (viii) ADJ t blonde (ix) P t behind (RG) enables one to form an infinite number of sentences. Each rule says ‘Rewrite X as Y’. Assume that the lexical rules (v)–(ix) are given. (ii) tells one that The girl is a NP, that is, [NP [Det The] [N girl]] is well formed. (iii) tells one that a VP is formed from a V and an ADJ; given (vii) and (viii), this provides us with [VP [V is][ADJ blonde]]. (i) says that an S is formed from a NP and a VP; this gives one [ S [ NP [ Det The][N girl]][VP [V is][ADJ blonde]]]. (RG) is recursive with respect to (ii) and (iv).7 (ii) allows for NPs to include PPs; (iv) tells one that PPs are formed from Ps taking NPs: the output of (ii) includes the input to (iv), whose output is the input to (ii). Thus, from the NP [NP [Det The] [N girl]], one can form the further NP [NP [NP [Det The][N girl][PP [P behind] [NP [Det the][N boy]]]], which forms the NP of a further sentence when attached to [VP [V is][ADJ blonde]]. Transparently, the process iterates: for any finite n, there is a sentence generated from (RG) with n NPs, n- of them being the respective arguments of n- PPs. This sort of procedure provides Horwich with all he wants. It generates a schema for every well-formed sentence given a lexicon (as specifiable by the lexical rules of the grammar); think of a schema as formed by, first, a deletion of the words of a sentence to give one, say, [S[NP[Det][N]][VP[V][ADJ]]], and then a deletion of the phrasal labels: [[[Det][N]][[V][ADJ]]]. The schema will apply, with respect to a collection of words C (for example, ‘the’, ‘girl’, ‘is’, ‘blonde’) just if, for each categorical label of the schema, there is a member of C that 6 Strictu dictu, the entry should be be, which gets its agreement morphology (potentially zero) via an obligatory number transformation. Further, Chomsky did not treat ‘be’ as a verb in Syntactic Structures; rather, the copula is a constituent of an auxiliary category which is represented by a rule of the form: Auxt C(M)(HAVE)(BE).

Here, ‘C’ is an affix (marking tense, number) and ‘M’ is the modal. The copula became a verb, as it were, in the late s. Such difficulty in placing ‘be’ arose precisely because of the inadequacy of rewrite grammars to capture significant generalizations; for example, that the modal, perfect, and copula raise in (English) questions, while (main) verbs do not. 7 No single rule, it will be noted, is recursive. In Syntactic Structures, recursion, which was construed as a clausal embedding phenomenon, was provided by generalized transformations defined over the output of a rewrite base. The Aspects (Chomsky, ) model included recursive base rules over ‘S’ to the exclusion of generalized transformations. In certain respects, the minimalist program reverts to the early model in its rejection of (recursive) D-structure X-bar forms in favour of generalized Merge (see below).

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instantiates it such that the result is a string generatable by the grammar.8 Alternatively, we can think of a schema as embodying a principle that attaches words to each other to form coherent wholes; for example, the above schema attaches an adjective—for example, ‘blonde’—to the copula to form a VP which attaches to the NP result of attaching a determiner to a noun—for example, ‘the girl’, which forms a sentence. If we further assume that words have whatever meaning properties they have independent of a given schema applying to them, then the result of applying a schema to C will be a string with a meaning that is a function of the meaning of the members of C under the schema. It might be that Horwich would reject some or other aspect of this approach; perhaps he would object to its derivational format. From the above, however, it is difficult to see how Horwich could sensibly hold that the results of such a grammar fail to specify the kind of schemata he has in mind.9 For example, Horwich cannot have in mind flat schemata, a mere list of labels, [Det N V ADJ]. A schema must impose a hierarchical structure upon a collection of words, the very structure that determines broad semantic features of subject, predicate, object, modification, etc. Without such structure there would be no way, apart from an infinite list of stipulations, to differentiate well-formed from ill-formed schemata. For example, we might recognize that [Det N V ADJ] fits ‘The girl is blonde’, but there is nothing about the putative schema that tells us that, say, ‘the is blonde’ or ‘blonde the’, are illformed. The imposition of a left-right, non-disjoint linear constraint rules out these cases, but not ‘girl is’. Obviously, the number of illformed schemata consistent with a given flat schema will rise with the number of labels featured. The point here is not so much that the schemata must be recursively generated, but that however they are generated, they had better be hierarchical. A rewrite grammar is simply a well understood way of finitely generating an infinity of hierarchical structures, or, in our present terms, schemata. Here’s the rub. Even rewrite 8

As will be noted, the label ‘S’ is problematic here, for it is non-phrasal, or, in linguistic jargon, it is ‘headless’. This feature, in fact, marks a fundamental inadequacy of rewrite grammars. The technicalities need not detain us; intuitively, the problem is that ‘S’ (sentencehood) must be stipulated as an extra element, for it is not a projection from any word and its arguments. Ideally, all syntactic properties of a sentence should arise from the combination of the constituent words. This issue will be important in the sequel. 9 Horwich () entertains a model under which schemata appear to be construed as part of lexical items (essentially, argument frames), rather than independent entries, but he further appeals to combinatorial procedures that, as far as I can understand the proposal, embody the sort of schemata generatable from rewrite grammars. If this is a substantial departure from the proposal of Meaning, then it is not a helpful one (see n. ).

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grammars are essentially incapable of representing central structural features of sentences. 3.1. Horwich is not alone Though Horwich’s position is advertised as one of radical deflation, it shares many traits in common with a quite popular approach to compositionality. Before turning to the specific inadequacies of rewrite grammars, it will be useful to highlight these commonalities. The moral to draw here is that we should eschew the issues relating to deflation, which needlessly kick up dust as explained above, in favour of gaining a proper understanding of the empirical phenomenon of compositionality. The schemata/rules based approach to the question of compositionality is encouraged by the ‘text book’ definition: the meaning of a sentence S (usually read as truth conditions) is given by (/is a function of/ consists in, etc.) the meaning of the constituent words of S and how they are put together (see, for example, Hale and Wright’s (, pp. –) glossary entry for ‘compositionality’; Miller’s (, p. ) introductory text; and Larson and Segal’s (, p. ) more advanced text). This double clause ‘definition’ appears to tell us that complex meanings require both simple meanings and some way of putting them together, which itself contributes to a complex’s meaning. The temptation of this double clause understanding is easy to appreciate. Descriptively, it seems that that one must say what words mean and how they may be permissibly combined. These two burdens look to be separate precisely because the modes of combination appear to be indifferent to what words means, but nonetheless essentially contribute to what a complex means. As we shall see, this separation is not sustainable. It is not, of course, mandatory to follow the letter of one’s informal statements in one’s actual detailed theorizing. It will be suggested below that appeal to schemata can be innocently understood as a theoretical aid: schemata are used to describe the semantic effect of word combinations; they do not semantically contribute to the combinations, still less should they be seen as encoded in ‘psychologically real’ processes or structures. Larson and Segal’s () model, regardless of any other virtues or failings, is perhaps a clear example of this innocent approach, where while schemata are used in the derivation of truth-conditional theorems, the theory does not assign semantic values to the schemata as such. Still, oft-times not only is the double clause definition taken at face-value, but it is also built into the accounts offered, so that complex meanings just are instantiated schemata of the rewrite forms. Horwich’s

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proposal is an explicit case of such an approach, but it is not the only one. Field (), along similar lines to Horwich, seeks to usurp the centrality of truth conditions in an account of compositionality. As an alternative, he offers sentential frames, which, by principles of substitution, may issue in compositional statements of the truth conditions of sentences without appeal to referential or satisfaction conditions of words: a lexicon, syntactic schemata, and a deflationary truth predicate suffice. Brandom (, Ch. ) seeks to reconstruct the import of apparent referential vocabulary in accounting for linguistic structure. He presents substitutional principles defined over sentential frames that encode the inferential commitments implicit in the acceptance of a given sentence satisfying a frame. Brandom, to be sure, does not appeal to rewrite forms, although if the account is to scale-up, forms at least of the complexity of a rewrite grammar would be required. It should be noted that Horwich, Field and Brandom all set out to undermine truth-conditional semantics via an appeal to schemata/substitution. It is not to be inferred, however, that right and wrong views of compositionality respectively map onto truth-conditional and nontruth-conditional semantic approaches. The deflationary tendency to be explicit about the putative schematic nature of compositional phenomena derives from the thought that such a nature leaves open precisely what account of meaning we should favour such that compositionality by itself doesn’t mandate a truth-conditional approach. This, essentially, is what is argued by Field and Horwich. But it just doesn’t follow that a schematic model of compositionality is unique to ‘deflationists’. As made clear above, it is perhaps the general view (for non-deflationary theorists who appear to make essential appeal to schemata, see, for example, Evans, ; Davies, ; and Cummins, ). Indeed, if we think of syntax as autonomously determining the compositional structure to be interpreted, in rewrite form or not, then compositionality simpliciter entails no particular theory of complex meaning, and no-one is required to think otherwise.10 The 10 It may be noted that the issue of logical form versus grammatical/surface form is also orthogonal to the current issue. The notion of logical form, notwithstanding its many guises, is generally understood to be that structure which applies to a sentence/proposition whose content is compositionally determined. In other words, compositionality is logically prior to logical form. In effect, if one thinks, as Horwich and Brandom appear to do, that there is just ‘surface form’, then logical form simply is surface form. If one thinks there is a difference, then the former is determined by the later under compositional interpretation. On the other hand, a notion of LF, as understood in current syntactic theory, is a notion at odds with a schematic understanding of compositionality— see below.

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point of the sequel, therefore, will not be to defend a truth conditional position against a deflationary one via a premiss about the correct understanding of compositionality. It is true, though, that the deflationary proposals enjoy a specious radicalism precisely because it is assumed that the truth-conditional tradition seeks to define compositionality in the vocabulary of, say, satisfaction. As noted, this reading is simply mistaken: compositionality is broadly understood to be a general feature of linguistic understanding that neither stands nor falls on the basis of any particular account of that understanding. What will be suggested, though, is that a truth-conditional approach, understood aright, does not make essential appeal to schemata, and so, indirectly, is preferable to Horwich’s proposal (and any other, such as Field’s or Brandom’s, which depends on schemata), which is not to suggest that any such approach will be correct in toto. That is to come. Let us now see what is precisely wrong with a schematic approach to linguistic structure.

4. The neglected significance of Syntactic Structures The inadequacy of rewrite grammars was first properly articulated by Chomsky (/, ). Indeed, we might say that transformational grammar was born in the realization that mere taxonomic labelling or schemata generation was a fundamentally shallow approach to linguistic structure.11 It should be emphasized that though Chomsky is often portrayed as almost entirely eschewing meaning in favour of syntax, he is better understood as contending that much of what is thought to fall under the purview of semantics properly belongs under ‘syntax’. This approach is at the forefront of his latest theoretical/methodological remarks (Chomsky, ), and goes right back to Syntactic Structures. Contra the common understanding, a central thesis of the work is that 11 The claim here is not that Chomsky demonstrated the necessity for ‘transformations’ tout court. There are now a range of frameworks in syntactic theory that eschew transformations and retain a form of rewrite grammar: for example, Lexico-Functional Grammar (for example, Bresnan, ) and Generalized Phrase Structure Grammar (for example, Gazdar, et al., ). The issues here are far too technical for the scope of the present work. Still, while LFG accepts rewrite grammar forms (what Bresnan calls ‘c(onstituent)-structures’), these are essentially paired with f(unctional)-structures; together they work somewhat like a (non-derivationally linked) D-structure/S-structure pairing. Moreover, LFG is inclusive in the sense that the structure pair is projected from lexical items, it is not imposed upon them (see below). Similarly, the rewrite forms of GPSG come with a host of features that constrain potential structures, which go far beyond the simple structures Horwich appears to have in mind. Besides which, GPSG, at least as proposed by Gazdar, et al. is explicitly non-cognitive, and so it is moot what bearing it may have on the present issues. It is precisely for such reasons, I think, that Chomsky sometimes suggests that these frameworks are notational variants of the ‘transformational’ frameworks.

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patterns of meaning (‘felt relations’) may be understood in terms of a specified set of structures (‘kernel sentences’) from which other structures are transformationally linked. In principle at least, all patterns of sameness and difference of meaning could thus be explained by the kernels and transformations (Chomsky, , p. ).12 In a very real sense, then, the early arguments against the adequacy of rewrite grammars were as much semantic as they were syntactic. Let us go through some of these arguments and relate them to Horwich’s schemata proposal. (i) Ambiguity. The ‘surface’ forms of many types of construction are ambiguous between two or more readings. Scopal ambiguities are perhaps most familiar: for example, ‘Every student admires some teacher’; ‘Mad dogs and Englishmen go out in the midday sun’. For our purposes, what is interesting about ambiguity is not how speakers manage to communicate or detect one or other reading, but the independent fact that, in general, no given schema of the form we have been considering will capture all readings of any given ambiguous structure. Compositionality is not at issue: each reading, we may assume, is a function of what the words uniformly mean and how they are combined. The problem is that how they are combined to produce the respective readings is not given in the linear ‘surface’ forms, the forms the schemata depict. It thus appears that word meanings plus a schema do not determine sentence meaning, for what a sentence means is underdetermined by any given schema plus word meaning. A simple remedy to this problem, it might seem, is to say that associated with each n-way ambiguous sentence are n construction properties, each involving the application of a distinct schema. This seems promising where the ambiguity may be resolved by distinct bracketing and labelling as in, for example, [[mad [dogs and Englishmen]]…] in opposition to [[[mad dogs] and Englishmen]…]. Here, the bare string/ pronunciation would be invariant under either schema. But scopal ambiguity cannot be so resolved in general; it is necessary to appeal to structures distinct from the given linear form of either reading. Nor, typically, will any surface re-ordering capture a reading. For example, ‘Every teacher some student admires’ is a perfectly good NP with the truncated relative clause, ‘some student admires’, but it is not a sentence (the structure, of course, can be read with ‘every teacher’ topicalized, but that does not alter the present point). Schemata, therefore, appear 12 This claim was made explicit in the so-called ‘Katz-Postal hypothesis’, which, roughly, claimed that all transformations are meaning preserving (Katz and Postal, ). An adequate semantic theory, therefore, need only account for the base structures (soon christened, ‘Deep Structure’), and the transformations. This hypothesis was adopted by Chomsky ().

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to be otiose in that the ambiguity is not resolved by any structure that combines words into the order given; a fortiori, construction properties are at best redundant. If we want to account for the meaning relevant structure of n-way ambiguous sentences, it seems that we must appeal to a structure that departs from how the sentence itself is put together at the ‘surface’. (ii) Structural synonymy. Ambiguity teaches us that the structure which goes to determine what a sentence means cannot be simply read off the attachment of the sentence’s words one to another. Similarly, even if a schema does appear to capture the meaning relevant structure of a sentence, it does not tell us how the sentence relates to another one that means the same. Consider the following relations as a small sample of those which obtain in English: Active/Passive: Bob kicked the ball / The ball was kicked by Bob Dative movement: Bob gave flowers to Mary / Bob gave Mary flowers Nominal Extraposition: A fly is in my soup / There is a fly in my soup Clausal Extraposition: Bob is easy to please / It is easy to please Bob Topicalization: I like strawberries / Strawberries, I like Ellipsis: Bob went to the bank and Mary went to the bank / Bob went to the bank and Mary did too Echo Interrogation: Bob married who? / Who did Bob marry? (In terms of Syntactic Structures, the first member of each pair would be (very roughly) a kernel sentence from which the second member is transformationally derived. The general idea was that two sentences mean the same just if they are derived from the same kernel. Thus, in the null case, the above synonymy relations are explained. This idea, suffice it to say, has not survived, although the data still stands.) Although the members of the pairs of constructions exemplified often differ as far as emphasis or force is concerned, they are transparently synonymous in a way that does not depend on the presence of any synonymous words; they are structurally synonymous. 13 We should, of course, like this to be explained, and much of syntactic theory over the past half-century has focused on such pairs. The problem for Horwich’s 13 The situation is somewhat more complicated than suggested. For example, active/passive pairs often differ in their natural readings depending on the type of verb involved. Compare: ‘The Japanese build good TVs / Good TVs are built by the Japanese’. The passive may be read as saying that good TVs are only built by the Japanese, the active does not admit this reading. Suffice it to say, this kind of subtle difference offers no succour to Horwich’s position.

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proposal is not so much that it fails to explain the synonymy relations, but that it appears to be inconsistent with the very data. According to Horwich’s proposal, the meaning of a sentence is constituted by a construction property—a schema in application to a collection of words— but each member of the above pairs clearly has a distinct construction property associated with it, and so should have a distinct meaning. The synonymy clearly does not rest on the mere co-occurrence of words. After all, not any old rearrangement of words is well formed, for example, *‘Like Strawberries, I’.14 Besides which, the relations exhibit the introduction and deletion of words. Again, obviously, these lexical differences are not arbitrary. Horwich might be tempted to say that synonymy can fall where it may; all that is important is that each sentence has a construction property that constitutes its meaning, independent of the meaning of any other sentence (see Horwich, , p. ). If this were to be Horwich’s riposte, then he would be confused about what is at issue.15 Suppose that whatever property constitutes the meaning of a sentence, assuming such talk makes sense, does not relate the given sentence to any other. This rules out a holistic individuation of meaning, but the issue at hand has nothing to do with holism. The point is to do with data, not theory. We want the structural pattern explained, and to propose a theory that is constitutively unable to explain the data does not make it go away. Construction properties are not a given; they presuppose substantial claims about linguistic structure that we have no independent reason to think are true; we are presently seeing that they look to be false. If the whole account spins free of the kind of data presently under discussion, then it is difficult to see how one might judge it, right or wrong. (iii) Deviance. A rewrite grammar, in principle at least, may generate a structure for each well-formed sentence in a given corpus. Just so, for each well-formed sentence, we can find a schema (modulo the above problems) that will enter into the construction property that putatively constitutes the meaning of the sentence. But what can be said about deviant constructions, those which are unacceptable, anomalous? 14 The ‘*’ notation marks a sentence to be somehow anomalous. To tease apart just what is wrong with a sentence is a theoretical matter. See below. 15

In fact, the thought here is obviously incorrect. Consider Horwich’s favourite example, ‘Dogs bark’. The verb ‘bark’, like any other, admits prepositional adjuncts, as in ‘Dogs bark at night’. Plainly, one’s understanding the second sentence necessarily involves one’s understanding the first. Yet the two sentences have distinct construction properties. Thus, if the proposed line were to be followed, it would appear that one would be lumbered with the egregious claim that one might understand a sentence with an optional prepositional adjunct without understanding the sentence minus the adjunct.

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Again, much of modern linguistics has been concerned with the issue of which are the legitimate structures and which principles generate them to the exclusion of deviant ones. The problem for a mere rewrite grammar or Horwich’s schemata approach is that any deviant sentence or phrase at all can be seen to be the result of the application of a schema. Further, compositionality is unaffected. As Zadrozny () has shown, if, as Horwich characterizes it, compositionality just amounts to the idea that whatever meaning a whole possesses is a function of the meaning of its parts and how they are put together, then any structure at all has a compositional meaning; we require some independently motivated constraints on the permissible structures to distinguish the ‘proper’ compositional meanings. Of course, given assumptions about what are the meaningful constructions, we can find construction properties. But this is utterly trivial, not in the supposedly virtuous deflationary sense, but in the sense of being a non-explanatory stipulation, for, absent a set of stipulations to the contrary, construction properties would remain available for all manner of nonsense. A construction property is meant to constitute the meaning of a sentence, that is, possession of such a property is a sufficient condition for a sentence to be meaningful. This looks to be false. These remarks may be substantiated by a close consideration of the examples below.16 ()a i Damaging testimony is sometimes given about oneself. ii *Damaging testimony is sometimes given about each other. b i Whom does Bob think that Mary loves? ii *Who does Bob think that loves Bill? c i It is likely that Bob will leave t Bob is likely to leave ii It is probable that Bob will leave t *Bob is probable to leave d i Bob asked what time it was / the time ii Bob inquired what time it was / *the time In each of the pairs above, we find acceptable sentences and deviant ones that marginally differ lexically (explanation will be provided shortly). Transparently, however, if a schema applies to one member of the relevant pairs then it applies to the other, for the lexical differences are within the same grammatical categories of N, ADJ, etc. The availa16 The examples are chosen more or less at random to exemplify the points to follow. See Haegeman (, ) and Culicover () for excellent overviews of the data which have occupied recent syntactic theory.

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bility of a construction property, therefore, looks not to be sufficient for meaning, that is, it is not the case that, given a collection of words and an acceptable schema, then the application of the latter to the former results in a meaningful sentence. As before, this is not an a priori matter. After all, why shouldn’t ‘probable’ take both finite and infinitive clauses just like its near synonym ‘likely’?; or why shouldn’t wh-words freely front sentences from object positions? As it is, the above examples are simply data on the surprisingly subtle restrictions that determine grammatical acceptability, restrictions that a rewrite grammar or schemata do not capture. That they hold is a matter of fact. There is no a priori reason, gleaned from reflection upon what language must be like or what it is for, for these restrictions to be in place. Just so, whatever one’s account of meaning or linguistic structure might be, if it is inconsistent with such restrictions, then it should be rejected on the straightforward grounds of misdescribing the facts. A likely response from the defender of schemata is that the differences exhibited in () are to do with the differences in meaning between the relevant words: although the same schema applies in each pair, it produces deviance in one case but not in the other because of an antecedently determined lexical difference, or perhaps a difference in ‘conceptual role’ in the kind of pattern the complex may play in wider thought (cf. Horwich, ). For example, [S [NP [Det ADJ N]][ VP [V]]] applies to ‘The blonde girl runs’ as well as to ‘Every green idea swims’. Yet the difference in meaningfulness between the two sentences is not to do with the schema but with the meanings that go into it; the second sentence expresses certain category errors which bar it from playing a role in thought. Perhaps some story can be told about how the meaning of ‘idea’ excludes its colour modification and its being the subject of verbs that express activities such as swimming. Intuitively, at least, this seems to be on the right lines, for that a schema does apply gives the deviant sentence a certain sense. We can, for instance, understand it metaphorically, whereas ‘Green every swims idea’ is just gibberish. It might be thought, then, that deviant sentences of the kind under consideration do indeed have construction properties and it is precisely such properties that explain their deviance, not in terms of the constituent schemata but the exclusionary meanings they combine. One immediate problem here is that, for Horwich, the deflation of compositionality just amounts to the idea that there are no top-down structural constraints from sentence meaning to primitive meanings; it does not make any difference what we take the nature of the meanings to be that enter into schemata. The proposal at hand, however, is not so

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glib. It makes quite specific demands that words (open class words: nouns, verbs, adjectives, etc.) should express (somehow — we may abstract from details) certain category restrictions; for example, ‘idea’ might be marked [-animate, +abstract], whereas ‘green’ might be marked [ _ -abstract] and ‘swim’ [+animate _ ], that is, ‘idea’ (qua abstract) cannot be modified by ‘green’ or be the subject of ‘swim’. It is wholly unclear how these features might be accommodated by any old account of word meaning, including Horwich’s own use theory. The point of the challenge here is not merely to ‘describe’ the fact that ‘green idea’, say, is deviant, lacks a ‘conceptual role’ (whatever one of those might precisely be), but to ‘explain’ the fact in terms, presumably, which appeal to facts about ‘green’ and ‘idea’.17 Even if, however, the kind of minimal (but sufficient) features entertained above were readily realizable, the general tactic of locating deviance in exclusionary meanings would remain unavailable.18 There are two central problems with the tactic. Firstly, it does not generalize to all the cases in () and, secondly, even if we focus just on the cases where the deviance is due to lexical differences, the relevant differences are such as to vitiate the whole schemata approach. Let us now see this. The first two pairs of () exhibit structural restrictions that do not arise from category exclusion; there is no semantic or conceptual incompatibility between the lexical material. Consider first the pair ‘Damaging testimony is sometimes given about oneself / *Damaging testimony is sometimes given about each other’. In general, reflexives and reciprocals must have a local (a clause mate) antecedent from which they inherit their referent. In the first sentence, the antecedent of ‘oneself ’ is the understood subject of passive ‘give’. Thus, we have the active paraphrase ()a and the expanded ()b:

17 The demand here might be felt to beg the question against Horwich’s use/conceptual role theory. For example, Horwich (, p. ) says that ‘[i]t is not as if each token of [a word type w] … exhibits some characteristic meaning-fixing behaviour … It is rather that the variety of facts about [w’s] deployment are best explained by the properties of some of its tokens’. This position is self-defeating until it is specified which tokens are relevant for even a single type w, which features of the relevant tokens are salient, and then further shown how such features do not simply devolve onto the kind of lexical features Horwich is attempting to avoid (here I presume that ‘meaning-fixing behaviour’ is a confused understanding of the role of (substantial) lexical features). The cases marshalled in this paper suggest that this cannot be done. Chomsky (, pp. –) argues similarly and offers some other cases throughout his response. Horwich’s only examples of such a method in operation are ‘true’, colour adjectives, and logical constants (see Collins, b). 18 It need not be denied, pace Fodor and Lepore (), that lexical entries are decompositional feature clusters (see, for example, Pustejovsky, , and Jackendoff, ). The present question is whether some such view might ameliorate Horwich’s problems.

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()a Sometimes, one/*he/*they/*Bob give/s damaging testimony about oneself. b Damaging testimony is sometimes given by one/*me/*him/ *them about oneself. The pattern here shows that ‘oneself ’ requires a singular indefinite antecedent, even where, as in ()ai, no such antecedent is pronounced.19 We should expect similar reasoning to hold for ()aii, that is, ‘each other’ requires a clause mate plural antecedent. Consider (): ()a Sometimes, they/*one/*he/*Bob give/s damaging testimony about each other. b Damaging testimony is sometimes given by them/*one/*me/ *him/ about each other. Clearly, there is no kind of semantic incompatibility between the reciprocal ‘each other’ and the other lexical material of ()aii. Thus, per hypothesis, there should be no divergence between ai and aii of (), yet there is. The explanation of the difference is a theoretical matter, but the data indicate that only the singular indefinite reflexive can be bound by the unpronounced passive subject. For example, even though ‘himself ’ is singular, it produces the same pattern of deviance as ‘each other’: ()a *Damaging testimony is sometimes given about himself. b Damaging testimony is sometimes given by him about himself. c Sometimes, he gives damaging testimony about himself. The divergence arises through the nature of the available antecedents of ‘himself ’. In other types of construction, all may enjoy unpronounced antecedents; in the present type, where the unpronounced passive by a is antecedent, only ‘oneself ’ may be properly bound as the argument. This is a structural constraint on binding and agreement relations, it is not a matter of semantic incompatibility. The difference between ‘Whom does Bob think that Mary loves?’ and ‘*Who does Bob think that loves Bill?’ is a difference between questioning the subject or object of the embedded clause. The deviant sentence 19 The unpronounced argument here is an example of what are called ‘empty categories’. They come in a variety of types and are a relatively well understood phenomenon of syntactic structure. The empty category in the current case is an example of what is sometimes called an ‘implicit argument’; see, for example, Brody and Manzini (). It is worth noting that Horwich’s schemata cannot so much as acknowledge empty categories.

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can be rescued by so little as deleting the complementizer ‘that’. The difference, however, is wholly structural. Firstly, there is no semantic difference between the nominative and accusative wh-forms, just as there is no semantic difference between tokens of ‘Bob’ as the subject and object of a verb. Nor is there any bar on the occurrence of the whforms in argument position with the complementizer overt. Witness the echo questions: ()a Bob thinks that Mary loves whom? b Bob thinks that who loves Mary? Secondly, and consequently, there is no semantic incompatibility between questioning the arguments — object and subject — of an embedded clause with the complementizer overt, for the echo questions are semantically on a par with their wh-raised counterparts. Indeed, according to present theory, the complementizer must head the clause, whether pronounced or not. The difference thus lies in a restriction on empty (phonologically null) subject positions, which, as ()b demonstrates, is not a semantic matter. As with most syntactic features, there is no currently accepted explanation for why the deviance should arise. Be that as it may, an explanation will not be forthcoming from assuming the one schema and then searching for a lexical semantic incompatibility—there isn’t any. In general, therefore, construction properties will not account for all cases of deviance, for even where the same apparent schema does apply, deviance still arises without there being any incompatibility between the constituent meanings, as there is with ‘green ideas’ and the like. As it stands, then, construction properties still do not offer a sufficient condition for complex meaning or, which is the other side of the same coin, an explanation of deviance. The advertised argument we are considering is that the schema approach may be saved from the problem of deviance by explaining the contrast in acceptability between instances of the same schema as a difference arising from constituent word meaning. The second and perhaps more decisive problem with this tactic is that even where differences of acceptability between instances of the same schema can be located in a particular lexical difference, the only difference there in fact is between words brings into doubt the very idea of schemata applying to words. This argument, as we shall see, marks a departure from the reasoning of Syntactic Structures and looks ahead to work from the s and beyond.

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Consider the third pair of (), here repeated: ()c i It is likely that Bob will leave t Bob is likely to leave ii It is probable that Bob will leave t *Bob is probable to leave The first case is a paradigm of what is usually referred to as a ‘raising’ adjective; that is, ‘likely’ takes a single clausal complement, either finite or infinitive; if the latter, then the understood subject has ‘risen’. Thus, ‘Bob’ in ‘Bob is likely to leave’ is not a subject argument of ‘likely’: Bob himself is not likely (whatever that may mean); Bob’s leaving is what is likely. ‘Bob’, therefore, must be an argument of ‘leave’. Hence, we say that ‘Bob raises’ from the embedded clause where it belongs semantically, as it were, to matrix subject. The reason for this is a theoretical matter; one current explanation is that in a lightly inflected language like English, the tense of a clause needs to be ‘checked’ in relation to a subject NP at the surface. That is, there must be an explicit morphological agreement between subject and tense; in descriptive terms: English tensed clauses have overt subjects. We see this in ()ci where ‘likely’ takes a finite clause as argument: the matrix subject is the expletive (semantically empty) ‘it’, with ‘Bob’ obligatorily in place as subject of the tensed embedded clause. Compare this pattern with ()cii. Like ‘likely’, ‘probable’ has a single clausal complement; this is witnessed in the acceptability of the expletive subject. But ‘probable’ is not a raising adjective: it accepts only finite clauses, from which NPs cannot raise, if they were to raise, the tense of the embedded clause would be unchecked. Clearly, the difference between these two patterns resides in the difference between ‘likely’ and ‘probable’. Prima facie, this supports the schema tactic: the deviance of the ‘probable’ infinitive construction in contrast to the ‘likely’ one is explained by a difference between the adjectival meanings that enter into one and the same schema. Well, the impression is illusory. There is clearly no contrast in the exhibited cases between the conceptual compatibility of ‘likely’ and ‘probable’ with their surrounding lexical material. This is not a case of ‘green ideas’. Worse, in most English dialects the two adjectives are synonyms. If, therefore, the difference were a matter of the concepts expressed, then we should expect there to be no difference at all. Indeed, let the two adjectives be strictly synonymous, and nothing changes. The only relevant difference between ‘likely’ and ‘probable’ is just that the first takes both finite and infinitive clauses, whereas the second takes just finite clauses. The profound problem for the schema

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approach here is not that there is no difference between the adjectives, but that the difference there is makes redundant the very idea of words and/or meanings slotting into schemata. In some sense, words carry their own structure rather than it being imposed upon them; that is, the role a word can play in a sentence is inherent to it; a word is not a syntactically neutral item, which has its potential roles determined by independently specifiable structures. It is not open to Horwich or others, therefore, to subsume these structural features under the ‘meaning’ of the words, for then the schemata would be out of a job; the words themselves would select their possible combinatorial options independent of any pre-specified schema. On the other hand, if the structure is not credited to the words, then the schemata will not be able to explain the patterns of acceptability and deviance we have been considering. On the third hand, as it were, if we were to let the words carry their structure and allow schemata, then we would have a massively inflated theory; for if the schemata are to record the correct features, they would be required to encode precisely that information that is already carried by the words. Nor could it be said that this would engender but a marginal inflation; the kind of argument structure that differentiates ‘likely’ from ‘probable’ is present throughout the open class words, and perhaps also prepositions. ()d, repeated below, gives a nice verbal example. ()d i Bob asked what the time was/the time ii Bob inquired what the time was/*the time ‘Ask’ and ‘inquire’ are, to all intents and purposes, synonymous two place verbs; both take clausal interrogative complements, but only ask takes nominal complements. In effect, then, if we were to have both schemata and lexical structure, we would have a rule telling us that ‘a verb that takes either interrogative clausal or nominal complements is one to which the schema [NP V CPQ / NP] applies’, mutatis mutandis for all other cases. Such rules are wholly redundant.20 20 Horwich’s () ‘very simple picture’ of the language faculty appears to contain this problematic redundancy, with (i) ‘some lexical items be[ing] schemata containing “slots” into which items of specified functional types may be inserted’ (ibid., p. ) and (ii) ‘a combinatorial procedure imposed on a sequence of I-sounds’ (ibid., p. ). The proposed upshot is that being the result of the application of the latter to the former will be the underlying construction property of the complex meaning. The problem witnessed above recurs: to specify the correct procedure would precisely involve specifying those features which must already be specified as inherent to the lexical items, otherwise, the procedure would apply willy-nilly. It bears noting in this regard that Horwich’s ‘combinatorial procedure’ cannot be a generalized operation such as ‘Merge’ (Chomsky, ): ‘Merge’ is not imposed upon anything, let alone ‘I-sounds’ (a meaningless notion). ‘Merge’

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Throughout this section, we have been questioning the ability of Horwich’s meaning properties/schemata format to account for certain elementary features of linguistic structure. No alternative to the format has been essayed, nor has Horwich’s apparent separation of structure from meaning, which motivates the supposed deflation of compositionality, been questioned. What has been shown is that the kind of schematic structure Horwich employs is inadequate to describe some of the most basic characteristics of human language. Thus, if compositionality is trivial, it is not because it is engendered by schemata specifiable independently of meanings. We have, however, just seen that words carry structure with them. The notion behind this metaphorical way of talking has in fact been behind the major developments in generative linguistics of the past thirty years. As intimated above, it would be an error to attribute the above reasoning to Syntactic Structures. Although we have been considering the inadequacy of rewrite grammars, they still played a fundamental role in the theories of the s and s: they provided the base component upon which transformations operated. Further, in the Aspects model, a set of initial transformations (lexical rules) inserted lexical items (substituting dummy symbols, D) into schematic rewrite forms. The inadequacy of rewrite grammars, as far as Syntactic Structures was concerned, is that transformations are also required. It came to be seen, however, that the separation of the lexicon from syntactic structure is not coherent, for words carry structure with them. The fundamental idea is that syntactic structure is not a formal rule based format, such as a logical calculus, or, indeed, base schemata, which words incarnate, but a reflection of, or projection from, words realizing certain selectional options inherent to them. Quite literally, there just is no syntax, if by ‘syntax’ we mean a set of rules or schemata that combine words in accord with their categorical properties. A major piece in this development was first the ‘projection principle’ in the ‘government and binding’ (GB) approach and later the ‘principle freely forms complex ‘objects’ (sets of lexical items), which are legible or not at the interface, but a merged object is not, as such, legitimate or illegitimate, and certainly not so according to a fixed schematic pattern. Further, the idea of schematic lexical items, if meaningful, courts further redundancy. A lexical item is simply a cluster of features; if the result of Merge builds a legible object, then argument features (inter alia) of the merged items are satisfied. Thus, it is redundant to have lexical items ‘designed’—with slots—to fit with other words, when there is an operation—Merge—that freely fits words together. Further, to constrain Merge to fit the ‘right’ words together via the ‘slots’ would issue in the proliferation of redundant particular rules which it is the very purpose of generalized Merge to avoid. Unsurprisingly, Chomsky (, p. ) intimates towards this kind of reasoning, and rightly takes it to militate for a rich notion of lexical features, per inclusiveness (see below).

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of inclusiveness’ in the minimalist program.21 If we ignore technical differences between these two principles, we may express the core notion as (PI): (PI) The properties of any syntactic structure S are inherited from or licensed by the features of the lexical items that constitute S; the interpretability of S devolves upon all and only the inherent features of the words that comprise S. For example, in the GB approach, there are a number of levels of representation derivationally linked: D-structure, S-structure, PF and LF. The projection principle says that the inherent lexical features (for example, grammatical subcategorization and argument role assignment of the kind witnessed above) represented at D-structure are inherited by or projected to all representations at subsequent levels, even though the structures differ so that they may answer to the constraints proper to the given levels, for example, constraints of agreement met by raising to realize case properties at the surface. The crucial point of PI is that there is no importation of extra material from one level to the next. For example, the level of LF (misleadingly, ‘logical form’) was posited under the constraint that it employs no features not already present at S-structure and the principles that derive S-structure from D-structure are just those required to derive LF from S-structure: the ‘cost’ of LF is thus zero (for example, May, ). Under ‘minimalism’, there are just two levels—PF and LF— with all features directly inherited from a merged selection from the lexicon.22 The principle of inclusiveness is, in effect, the idea that PF and LF are simply the result of unfurling and selectively deleting the features inherent to the lexical items selected. This general derivational process is constrained only by the need for PF and LF to encode exclusively those features relevant to sound and semantic interpretation, respectively (the guiding hypothesis of the minimalist program is that all movement leading to is for the deletion—‘checking’—of illegible features: what looks like the ‘imperfections’ of uninterpretable features and dislocation induced by movement is a single design mechanism for the satisfaction of inde21 See, respectively, Chomsky (, Ch. ; , Ch. ) and Chomsky (, Ch. ). The projection principle applied in particular to argument roles as determined by theta-theory. Minimalist inclusiveness is a more encompassing principle which, for example, excludes intermediate projections, trace elements, indexes, etc. 22 In more recent developments of the minimalist program, even the levels of PF and LF have been questioned in favour of a cycle of ‘transfers’ from merged structures (phases of a derivation) to the external interpretive components (see, for example, Uriagereka, , and Chomsky, ). For present purposes, however, such developments may be sidelined (Collins, forthcoming).

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pendent interface conditions). For present purposes, minimalism is the purer idea, for it does without D-structure, which can seem to be an intermediary level or interface between the lexicon and syntax proper, and it also dispenses with S-structure; another level which might be taken to lend itself to a schematic representation of ‘surface form’. Such understanding, it should be emphasized, would be mistaken: neither D- nor S-structure is taken to be a set of schemata. Even so, minimalism banishes the very idea of schemata applying to words, and so fits more snugly with (PI). (If minimalism sanctions no schemata or rules of construction, then how are complex structures formed? A principal claim of minimalism is that there is a single, uniform operation — ‘Merge’—that freely combines any available lexical item to any other, marking one as a ‘label’ for the resulting complex—effectively, a maximal projection whose root constitutes the head of the merged object.23 If a merged object is legible, then we have what we might loosely call a well-formed structure; if the object is illegible, the derivation crashes at the interface. Merged objects, considered independently of the interface conditions, are all equal: Merge embodies no notion of well-formedness. See below.) We need not venture further into linguistic theory, for we have already seen enough to support (PI) against a schemata approach. Instead, if we look at Horwich’s favoured way of understanding schemata, his so-called Fregean approach, we may see how (PI) gains support from more traditional philosophical/semantic considerations.

5. Schemata: a category mistake Schemata do not mean anything; or at least not in the same way lexical items have meaning. Schemata are abstract descriptions of classes of phrases made from labels describing classes of words; it is the phrases and words they describe that are meaningful. The schema [NP VP], say, describes the class of sentences formed by a VP taking an NP as subject; ‘NP’ and ‘VP’ describe the classes of phrases that are headed by nouns and verbs respectively; and ‘N’ and ‘V’ are labels for the classes of nouns and verbs respectively. Now of course, verb phrases have a certain function f as expressed in the relational category of predicate of, but it is not ‘VP’ that has f, rather, it is the members of the class described that has f. So, to speak of VP expressing a characteristic function that 23 Merge is essentially a recursive operation of set formation: the merging of lexical items a and b results in {a{a, b }}, where the leftmost ‘a’ labels the structure such that, for further merge, the complex projects the features of a.

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takes NP values as arguments is not to assign a function to ‘VP’, it is to assign a function characteristic of the members of the class described by ‘VP’ to such members. This rough model may loosely be described as Fregean and perhaps less loosely as Carnapian or Montagovian (the tradition of categorical grammar also appears to fall under this characterization). But it is not Horwich’s idea. He appears to think that schemata themselves express or are (?) functions. That idea is unique to him. Similarly, a truth-conditional theory does not assign semantic values to schemata. Consider: () v(T, [S NP VP]) v (∃x)(v(x, NP) . v(x, VP)) (where ‘ v(x, y)’ means ‘x is the semantic value of y’).This does not tell us the conditions under which ‘[S NP VP]’ is true, for it is true under no conditions at all (it is a description, not a sentence). Rather, (), qua axiom schema, tells us that any sentence described as [S NP VP] is true just if the value of its NP is also the value of its VP: for example, ‘John is tall’ is true just if someone is John and that someone is tall. As with a function-argument theory, a truth theory only assigns semantic values to words and phrases. The role of semantic clauses for schemata is to capture the way in which the semantics of each complex of a given form is a function of the semantics of its parts; that is, their role is to detail compositional meanings. But again, it is not the schemata that composes word meanings, it is the meanings themselves, as it were, that compose, axiom schemata merely describe this. According to such a truth theory, of course, such composition is not achieved by an argument-function structure. Nevertheless, Frege’s notion of predicate meaning being ‘unsaturated’ or functional is reflected in the form of the axioms. The axioms specify the semantic values of predicates in terms of the values of NPs which compose with predicates: () v(x, ‘is F’) v x is F. Thus, the semantic value of a predicate is assigned in terms of a predicate’s composition with possible NP values. Horwich’s notion of assigning meanings to phrase schemata appears to be an unprecedented category mistake. Can we make sense of Horwich’s idea in some other way? Let us assume for argument that Horwich has something as follows in mind. We imagine a speaker to know the meanings of all the words in his idiolect (by definition); he also knows a host of schemata, whether independently specified, recursively generated or abstracted

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from some corpus of familiar sentences, or some other method (cf. Brandom’s, , notion of children learning a language by projecting sentential frames from a finite corpus that exemplify such frames). When it comes to understanding some complex, the speaker applies a schema to some n-tuple of word meanings, and this suffices to provide him with the meaning of the complex. On this model there is no inference from word to complex meaning: a speaker understands a complex just because he understands the constituent words and their composition, as enshrined in some schema. The understanding, as Horwich says, would be ‘automatic’. Consider, then, Horwich’s [Ns V]. This schema only applies to pairs of plural nouns and intransitive verbs. Now the speaker either knows what words of his idiolect fit these syntactic categories or he does not. If he does, then he need not apply any schema at all, for he will ‘know’ that an intransitive verb selects an external NP as subject, and if he recognizes ‘dogs’ as forming a plural nominal and ‘bark’ as an intransitive verb, then he will recognize ‘Dogs bark’ as a meaningful sentence, a sentence he in fact understands given his lexical knowledge, he does not require any other information. The schemata the speaker knows will simply be abstract descriptions of the complexes he understands. But if the speaker does not know the syntactic categories to which the words of his idiolect belong, then his purported schemata knowledge will not aid him to understand a complex, for the schemata we attributed to the speaker do not tell him whether or not ‘dogs’ and ‘bark’ are plural noun and intransitive verb respectively. He would as readily apply [Ns V] to the pair , as to the pair , or why not the pair ? This is obviously absurd. In line with (PI), syntactic categories do not apply to meanings, but are intrinsic features of words which project a structure which is then submitted to interpretation: semantics interprets syntax. Such an explanation tells us that the situation we envisaged for the speaker is absurd because, in effect, it is part of understanding a word that one knows its compositional options — what other words of one’s idiolect can be meaningfully combined with it. In minimalist terms, the claim here is that rather than requiring rules/schemata to construct just the well-formed structures, the language system freely generates merged complex objects; those objects whose constituent lexical items satisfy the demands they make upon each and check any illegible features are just those objects which are legible at the interface (get to be useable in thought). There is no redundancy of information and there is no independent structure that

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is imposed on the lexical items. We can, as is indeed common, label the parts of a given structure and treat it as a filled schema, but the result would be a partial, otiose taxonomy. The problems which beset Horwich’s account are avoided in principle. Here we see a nice concord between reasoning from linguistics and the more traditional reasoning from the Frege/Davidson tradition. It is moot, however, whether the (essentially empirical) linguistic reasoning supports a truth-conditional semantics, at least as usually conceived (Collins, forthcoming). We may more modestly conclude that there is a convergence against the very idea that linguistic structure is applied to words, and so reject the very idea that the meaning of a sentence is the result of applying a principle expressed by a schema to words that independently mean such and such.24

Philosophy, SOC University of East Anglia (Norwich) Norwich NR4 7TJ UK

john collins

References Brandom, R. : Making It Explicit: Reasoning, Representing, and Discursive Commitment. Cambridge, MA: MIT Press. Bresnan, J. : Lexical-functional Syntax. Oxford: Blackwell. Brody, M. and M. R. Manzini : ‘On implicit arguments’, in R. Kempson (ed.), Mental Representations: The Interface between Language and Reality. Cambridge: Cambridge University Press. Chomsky, N. : The Logical Structure of Linguistic Theory. Ms., Harvard University. Revised  version published by Plenum, New York, ; Chicago: Chicago University Press, . ——: Syntactic Structures. The Hague: Mouton. ——: Aspects of the Theory of Syntax. Cambridge, MA: MIT Press. ——: Lectures on Government and Binding. Dordrecht: Foris. ——: Knowledge of Language: Its Nature, Origin, and Use. Westport: Praeger. ——: The Minimalist Program. Cambridge, MA: MIT Press. ——: New Horizons in the Study of Language and Mind. Cambridge: Cambridge University Press. ——: ‘Beyond explanatory adequacy’. MIT Occasional Papers in Linguistics, , pp. –. 24

My thanks go to the non-schematic NP, Nina Power.

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