The Primacy of Grammar Part 10

(78) Every llama ate a banana.

(79) Every x ((x is a llama) ((by) y is a banana & x ate y)) In this notation, the phrase a banana is viewed rather as introducing a variable y, which in turn is bound by an ''abstract'' quantifier b. Similarly, a llama introduces a variable x that is overtly bound by the quantifier every. Finally, the existential clause is embedded within the scope of every to bring out the intuition underlying (78) that each member of the set of llamas ate a banana. Thus, the notation of logical theory, as used in (79), is a tool that helps in explicit representation of data, namely, what Grammar and Logic

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interpretation native speakers attach to (78); it does not give an account of the data.

The account ensues when the structure of (79) is exploited to provide a grammatical a.n.a.lysis of (78); it ensues because a phenomenon is now a.n.a.lyzed, not just represented, in terms of empirically significant theoretical postulations. As Diesing notes, (79) suggests that there could be a split in the underlying syntactic structure of (78) such that every llama and a banana are interpreted at dierent parts of the structure. This led to the distinction between the IP and the VP parts of a structure via the VP-internal-Subject hypothesis, as we saw. It took linguists several years to incorporate this specific syntactic idea within the general grammatical theory. Several steps, some of which we saw, were required. First, a general theory of clause structure was formulated (Pollock 1989) in which the VP-internal-Subject hypothesis (Koopman and Sportiche 1991) was incorporated. Second, a general theory of displacement had to be found (Case checking). Third, principles had to be designed to place strong quantifiers at specific locations outside the VP-sh.e.l.l (Mapping Principle), and so on. Logical theory played no role in this at all.

Furthermore, Diesing's representation of (78) as (79) shows that logical notation, like musical notation, can be changed abruptly and arbitrarily for convenience of exposition. This is not to deny that there is some element of convenience in any choice of notation whose arbitrary character shows up when theoretical explanations get deeper. It happened for parts of grammatical theory as well: ''A lot of uses of such devices as proper government and indices turn out to be pseudo-explanations which restate the phenomena in other technical terms, but leave them as unexplained as before'' (Chomsky 2000a, 70).

But this fact, common in science, cannot apply to logical notations since their uses do not even qualify as pseudo-explanations, as argued above. To emphasize, a new logical notation cannot show that the uses of old ''devices'' turn out to be ''pseudo-explanations.'' For example, the adoption of the new notation in (79) does not show that the old notation was a pseudo-explanation; it shows that the old notation did not even represent data perspicuously enough for a.n.a.lyzing the user's intuition.

So, why do we need the notation of logic anymore?

3.4.

Truth and Meaning For a large (and growing) number of linguists and philosophers, the notation of logic is still needed because the imposition of this notation 88

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facilitates systematic a.s.signment of truth conditions to sentences of a language. To feel this need is to entertain a conception of language theory that includes truth theory as a part. Although there is distinguished history to this conception (Wittgenstein 1922, 4.024; Strawson 1952, 211), it is dicult to find an explicit argument that supports this conception of language. To my knowledge, this issue was never fully raised in the literature since it was taken for granted-even by many pro-ponents of generative grammar-that it fails to include an adequate semantic theory.

What we find is that people simply proclaim a conception of language theory that contains truth theory by stipulation: ''Semantics with no treatment of truth conditions is not semantics'' (Lewis 1972, 169); ''construction of a theory of truth is the basic goal of serious syntax and semantics'' (Montague 1974, 188). If this is just an unargued a.s.sertion (Pietroski 2005; Stainton 2006), then the motivation for expanding the scope of grammatical theory considerably weakens: dierent people with dierent a.s.sumptions do dierent things, period. To ill.u.s.trate this crucial point, I will examine in some detail the origins and structure of the theory of meaning proposed by Donald Davidson.

In a cla.s.sic paper (Davidson 1967), which may well be thought of as having initiated the contemporary program of formal semantics, Davidson gave a new direction to a conception of semantics he traced to Gottlob Frege. Frege held the near truism that the meaning of a sentence is determined by the meaning of words in it.5 We would thus expect a theory of meaning to spell out how individual words systematically contribute to the meaning of a sentence, the meanings of sentences diering when (nonsynonymous) words in them dier. Given that the linguistic resources of users of a language L are finite, it is plausible to place the condition (M) on a theory of meaning of L such that the theory recursively generates, for each sentence s, a theorem of the form (M) s means m, where m gives the meaning of the sentence (Davidson 1967, 307). The trouble is that Frege's own conceptions of meaning fail to satisfy these requirements. If, on the one hand, the ''meaning of a sentence is what it refers to, all sentences alike in truth value must be synonymous-an in-tolerable result'' (p. 306). If, on the other, individual words and sentences have meanings distinct from their reference, then the most we can say is that the meanings of Theaetetus and flies are what they contribute to the meaning of Theaetetus flies, and the meaning of Theaetetus flies is what is Grammar and Logic

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contributed by the meanings of Theaetetus and flies. Since we ''wanted to know what the meaning of Theaetetus flies is, it is no progress to be told that it is the meaning of Theaetetus flies.''

Keeping this in mind, a number of consequences could be drawn from these results regarding the form and the scope of a putative theory of meaning. For example, why should Frege's choices exhaust the options for what is to count as the right ent.i.ties mentioned by the singular term m?

Suppose we hold that the concept of meaning, whatever it is, that figures in LF-representation(s) of a sentence exhausts the scope of a theory of language; as I proposed earlier, any other concept of meaning could then be viewed as either incoherent or falling beyond the scope of a theory of language.

Now recall that so far Davidson has placed two constraints on a theory of meaning: it has the form ''s means m'' where m is systematically correlated with s, and m cannot be Fregean. It is easy to see that these conditions are satisfied by the schema for grammatical meaning (GM), (GM) s means LFs, where s is a phonological form of s,6 and LFs names LF-representation of s, a theoretical expression systematically correlated with s. LFs is a genuine (abstract) singular term that mentions perhaps a specific state of the mind/brain. This should not be a problem for Davidson since his ''objection to meanings in the theory of meaning is not that they are abstract or that their ident.i.ty conditions are obscure, but that they have no demonstrated use'' (p. 307). Since LF-representations do have demonstrated use, we could say that grammatical theory generates each instance of GM. GM also escapes another objection to M. Davidson's objection to M is sometimes interpreted to suggest that M is uninformative. Someone may know an instance of M without knowing what the relevant expression means: one may know ''Theaetetus flies means what is meant by Theaetetus flies'' without knowing what Theaetetus flies means. In contrast, GM is not only noncircular, the conception of (overt) knowledge of language that gives rise to this objection does not apply to a theoretical formulation such as GM; only linguists have overt knowledge of GM.

Well-formulated recursive syntax and dictionary thus seem adequate.

Davidson, however, chooses a dierent course because ''knowledge of the structural characteristics that make for meaningfulness ( syntax) in a sentence, plus knowledge of the meanings of the ultimate parts, does not add up to knowledge of what a sentence means'' (p. 307). This is because just this much knowledge fails for propositional att.i.tudes where 90

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''we cannot account for even as much as the truth conditions of such sentences on the basis of what we know of the meanings of the words in them'' (p. 308). It is well known that the problem of propositional att.i.tudes persists even within semantic programs that have more resources than Davidson's own truth-theoretic semantics (Chomsky, Huybregts, and Riemsdijk 1982, 91); for that matter, it apparently persists irrespective of conceptions of meaning (Kripke 1979). In any case, the vexing, unsolved problem of propositional att.i.tudes (Schier 1987) cannot be the starting point for a general theory of meaning.

If Davidson's appeal to propositional att.i.tudes is merely an attempt to draw attention to the general point that syntax and dictionary together fail to show how the meaning of the complex is a function of its const.i.tuents-the ''contrast with syntax is striking''-then the objection does not apply to GM since syntax does generate LF-representations computationally from the lexicon. In that sense, whatever an LF-representation means is a function of the meanings of its parts. It follows that Davidson simply requires at least that a theory of meaning give an account of truth conditions of sentences.

The pretheoretical a.s.sumption shows up even more directly in the way Davidson formulates his theory. When Fregean conceptions failed, Davidson did not pursue the option of finding a non-Fregean singular term, as noted; he just a.s.serted that the only way to reformulate M is to change m to a sentence p. No argument is advanced for the totally artificial suggestion that the meaning of a sentence is to be ''given'' by another sentence in some language or other. If anything, it is natural to think of the meaning of a sentence as a property of the sentence to be described in some theoretical term; it is hard to see how another sentence carrying the burden of its own meaning can do the job. As we will see, there is exactly one way of not begging the obvious questions.

Setting the issue aside for now, the move from m to p enables Davidson to narrow down the options. In formulating a theory of meaning, we can no longer use the two-place predicate means to relate s and p; for that we now need a sentential connective. Davidson imposes an additional constraint that the theory of meaning must appeal only to extensional relations, since with the ''non-extensional 'means that' we will encounter problems as hard as . . . the problems our theory is out to solve'' (p. 309).

Once we stipulate that m be reformulated with a sentence p, and p and s be related by an extensional sentential connective, then for the whole thing to work as a definition of sentence meaning, schema (T) becomes inevitable: Grammar and Logic

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(T) s is T if and only if p, where s is a structure description of the sentence under study, p is a metalinguistic expression that is systematically correlated with s, and is T is a metalinguistic predicate that is recursively characterized by the theory for each sentence of L.

To see that schema T is inevitable recall that p has to bear a lot of weight: it needs to be both systematically and uniquely correlated with s, and it must give the meaning of s in some sense. This last condition rules out formulations such as schema G.

(G) s is grammatical if and only if there is a derivation that yields LFs.

This schema obeys much of Davidson's conditions: it ''provides'' s with its own predicate ''is grammatical,'' and it has a ''proper'' sentential connective that has a sentence to its right. G has the additional virtue that it carries exactly the import of GM without mentioning meanings, a virtue that Davidson claims for Convention T (310). However, there is no clear sense in which the entire sentence there is a derivation that yields LFs by itself ''gives'' the meaning of s; the derivation does not give the meaning, LFs is the meaning of s.7 Therefore, p can only be s itself if L is contained in the metalanguage ML, or p is a translation of s in ML. This forces schema T.

Despite these moves, we still do not know what is T is, since we have taken much care to detach the content of is T from that of means that.

However, it is somehow clear to Davidson that ''the sentences to which the predicate is T applies will be just the true sentences of L, for the condition we have placed on satisfactory theories of meaning is in essence Tarski's Convention T that tests the adequacy of a formal semantical definition of truth'' (pp. 309310).

(Convention T) s is true if and only if p.

No doubt schema T looks like Tarski's Convention T, and alternatives virtually die out once the preceding conditions are enforced. Yet, some independent argument is needed for us to view the identification of is T with is true ''in the nature of a discovery'' (p. 310). Otherwise, it is dicult to resist the thought that just those a.s.sumptions have been built into the form of a putative theory of meaning that filter out everything except Convention T. A theory of meaning, then, is what we get when we work backward from a theory of truth.

Davidson does provide justification for viewing a Tarski-type truth theory itself as a theory of meaning, but it comes after the ''discovery''

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has been made. So, it could have been proposed without taking recourse to the famous argument I just reviewed. Thus, it is suggested that Convention T will generate theorems such as ''snow is white is true i snow is white.'' Any competent speaker of English, namely, one who has already internalized the meaning of the metalinguistic relation is true i, will recognize that this instance of Convention T is true; in recognizing this, a speaker has displayed understanding of the sentence snow is white in some sense. Therefore, a recursive characterization of the truth predicate for each sentence of a language ''recovers'' something of the user's understanding of the language.

What is the sense in which competent users of English recognize that ''snow is white is true i snow is white'' is true? The answer is that, in giving a.s.sent to ''snow is white is true i snow is white,'' the users have indicated the right circ.u.mstance in which snow is white is to be used, namely, the circ.u.mstance in which snow in fact is white. In other words, by displaying the correct use of snow is white in the right-hand side of the formula, the users have displayed their competence of snow is white itself mentioned in the left-hand side of the formula. The bridging truth predicate is true i thus systematically matches sentences with descriptions of circ.u.mstances. In this sense, Convention T brings out the information-bearing aspect of language.8 From this perspective, Davidson's proposal concerning Convention T may be viewed as a philosophical clarification of the concept of meaning.

As competent speakers of a language, we need some common hold on what counts as the significance of a sentence in that language. Since it is generally believed that the most promiscuous use of language consists in talking about the world, the common notion of significance may be captured in formulations such as ''snow is white is true i snow is white''; thus, as Tarski saw, competent speakers of a language are likely to a.s.sent to it. In other words, native speakers a.s.sent to instances of Convention T precisely because it agrees with their folk conception of significance/ meaning. It follows that Davidson's proposal does unearth a folk conception of meaning. Not surprisingly, this part of Davidson's work set o one of the most interesting literatures in philosophy, which includes Davidson's own subsequent work on structure of beliefs, knowledge, truth, subjectivity, and the like.

However, philosophical clarification of a network of common conceptions-such as the ''triangularity'' of truth, meaning, and beliefs-is a very dierent activity from giving an empirically significant account of some properties of linguistic objects in the mind/brain. This is because Grammar and Logic

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folk conceptions of meaning themselves demand explanation, perhaps in a form of inquiry Chomsky (2000d) calls ''ethnoscience''; also, folk conceptions could be false with respect to-or inapplicable to-the properties of the mind/brain.

Davidson meets this objection by proposing a side project: the conception of meaning via Tarski's truth theory can be formulated as an empirically significant theory of meaning in consonance with grammatical theory we already have. For the rest of this chapter, I will be exclusively concerned with this project.

What sort of theory might ensue from the fact that native speakers a.s.sent to instances of Convention T? For Tarski, the task was to construct a theory for an entire language such that the eect of Convention T obtains for each sentence of the language. The task obviously requires that we are able to fully characterize a language L recursively such that its sentences can be explicitly identified. Tarski held that it can only be done for formal languages. Supposing it to have been accomplished, what is the character of such a theory? At its best, that is, for a suciently rich formal language, the theory could be viewed, as with any logical theory, as a ''rational reconstruction'' of the native speaker's informal intuition of the correct use of the truth predicate captured in Convention T. In other words, the theory would be an explicit generalization of the native speaker's intuition displayed in cases such as ''snow is white is true i snow is white.'' It will not be an explanation of the intuition: Tarski and, as we will see, Richard Montague never intended the project to be so (Stainton 2006).

For natural languages, even this much is hard to achieve since there is no prior characterization of a natural language: structure of natural languages are matters of fact, not stipulation. So the only route available here is to first focus attention on that fragment of a natural language that does match formal languages in the relevant respects under suitable abstraction: to use ''new'' English to throw light on ''old'' English. Then we proceed to extend the system to cover further fragments.

This part of the project is certainly empirical in the (very) narrow sense that we do not know in advance which structures will fall under the enlarging truth theory. In other words, the project is empirical in its attempts to catch up with Tarski in covering progressively richer fragments of these languages. At each stage of empirical progress, therefore, we have a more adequate rational reconstruction of the native speaker's original intuition; prima facie, no other notion of empirical significance attaches to the theory beyond a philosophical clarification of linguistic 94

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significance for fragments of natural languages. Here, empirical work in the syntax of natural languages provides the relevant structures to which Tarski-type (metalinguistic) structures are suitably attached.

This is exactly how Davidson proceeds. Davidson's general suggestion is ''to mechanize as far as possible what we now do by art when we put ordinary English into one or another canonical notation.'' After all, it would be a ''shame to miss the fact that as a result of these two magnifi-cent achievements, Frege's and Tarski's, we have gained a deep insight into the structure of our mother tongues'' (1967, 315). Frege showed how some of the quantificational idiom of English can be ''put'' into the canonical notation of first-order logic; Tarski (1935) showed how to give truth definitions for a variety of formal languages, including first-order logic. Davidson's suggestion is that we align these eorts. Invoke some canonical notation to ''tame'' fragments of English, then apply Tarski's method to the fragment so tamed-the project of logical form, as I envisaged it.9 Drawing on pre-LF work in generative grammar, Davidson invited ''Chomsky and others'' to join the project since they are ''doing much to bring the complexities of natural languages within the scope of serious semantic theory'' (p. 315).

Specifically, canonical notation of logic will accomplish two tasks.

First, we need to state ''semantic axioms'' such as ''John is wise is true i John is wise'' by means of satisfaction relation in a model whose domain contains John, and that enables us to characterize/construct the set of wise things. Second, rules of logical theory will enable us to compute the values of more complex sentences such as John is wise or snow is white from the values of their parts. I will attend only to the first part of the project.

We need not deny that this program ''works''; sometimes it does so extensively and elegantly, as in Larson and Segal 1995. In fact, as we saw for every llama ate a banana, an appeal to logical form might on occasion throw some light on how syntax may be organized; there are other notable (and more technical) examples in the literature (Heim and Kratzer 1998; Chierchia and McConnell-Ginet 2000). But caloric theory also worked elegantly for a wide range of thermal phenomena; otherwise, it is dicult to explain its popularity with distinguished scientists for hundreds of years (for more examples of this sort, see Bennett and Hacker 2003, 45).

As with caloric theory, the issue is whether the program is needed. For that, we need to see why attachment of a truth theory coherently falls within the explanatory program of generative grammar beyond the se- Grammar and Logic

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mantics already covered at LF. From what we have seen so far, the explanatory significance of the combined theory of LF and logical form does not exceed the explanatory significance the theory of LF already has.

3.5.

Limits of Formal Semantics In the post-LF era of generative grammar, the convergence between LF and logical form is typically motivated as follows. Robert May (1991, 336) thinks that the philosophical concept of logical form-that is, the concept of logical form that is concerned with ''the interpretation of language''-serves as an ''extrinsic constraint'' on language theory. For example, we will want LF to have a form such that (truth-theoretic) semantic rules can apply, and ''compositional interpretation'' can be articulated (Larson and Segal 1995, 105).10 Once we have done so, LF and logical form will jointly serve to determine the structure ''in the course of providing a systematic and principled truth definition for (a language) L.''

As a result, ''a fully worked out theory of LF will be a fully worked out theory of logical form'' (Neale 1994, 797).

Supposing that we have a ''fully worked out'' theory, what does the theory explain beyond the narrow sense of empirical significance discussed above? There are two prominent responses to this query in the literature: (i) formal semantics explains the external significance of language; (ii) it explains (mind-) internal significance of language beyond syntactic organization.

3.5.1.

External Significance It is widely held (Barwise and Perry 1983; Larson and Segal 1995) that one of the main goals of a semantic theory of human language is to furnish an account of the external significance of linguistic expressions: the fact that humans use languages to talk about the world. A semantic theory that does furnish such an account is then empirically significant. There is no doubt that grammatical theory is not empirically significant in this sense; the task is to see if theories of logical form are so significant.

I a.s.sume that it is plausible to hold a pretheoretical conception of language theory in which we give an account of how language relates to the world. As noted, I also grant that our grasp of the truth predicate indicates the significance we attach to this function of language. To that extent, I a.s.sume that there is a sense of ''understanding'' in which a user 96