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of L fails to understand a sentence of L if she cannot figure out the conditions in which the sentence turns out to be true or false. Since LF does not furnish an account of this understanding, LF needs to be supplemented by a truth-conditional theory in this sense.

Notice that this conception can be questioned: just which aspects of understanding a sentence is to be covered by language theory? It is certainly an aspect of a competent user's understanding of English (or some dialect of it) that the expression get out of here may be interpreted either as an insult or an endearment depending on who uttered it on what occasion.

It is unclear if such phenomena of language use fall under language theory per se.

Studies on autistic and aphasic patients dramatically ill.u.s.trate the point. Faced with the request Can you pa.s.s the salt please, an autistic patient said Yes and did nothing further. The saying Too many cooks spoil the broth elicited this response from an aphasic patient: Too many cooks, you know, cooks standing around the broth, they are talking and cooking (Gardner 1975, 79). In a famous work on the subject called Laura, Jeni Yamada (1990) found that Laura's language capacities were apparently intact, but her cognitive and pragmatic competence was limited. For example, Laura knew when she should describe herself and others as sad or happy, but apparently without the capacity to feel sad or happy. In each case, there is a clear sense in which a user fails to understand some English sentences. There is considerable evidence that such ''pragmatic'' failures are caused by selective impairment dissociated from the language area of the brain (Kasher 1991; Fromkin 1991); hence, these notions of understanding a sentence do not fall under language theory.

So, even if we agree with Larson and Segal (1995, 31) that understanding a sentence requires knowing its truth condition ''at the very least,'' we will expect some additional argument as to why this notion of understanding is to be covered by the ''general enterprise initiated by Noam Chomsky'' (1995, 10), unless it is held that every aspect of human understanding falls under the Chomsky-initiated general enterprise. In that event, the impairment cases just cited also fall under the enterprise. The issue clearly is: What falls under a version of the enterprise restricted just to some theoretically salient conception of language?

Holding onto the pretheoretical ( unargued) conception, nonetheless, we will expect an empirically significant theory of truth to attach somehow to grammatical theory, possibly as part of a general theory of language use. This additional theory will purport to give an account of the extremely complicated ability to relate items of language to aspects of Grammar and Logic

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the world, the ability that enables a user to determine if a sentence is true or false.

Notice that all I am currently discussing is whether the formal semantic truth conditions explain the external significance of language; the postulated properties of expressions under discussion will be those that bring out this significance. Therefore, an empirically significant account of these properties must tell us how these properties obtain such as to relate mind-internal ent.i.ties with those in the world. If formal semantics is not designed to do so, then either the program is a.s.suming what it needs to explain or it explains some other significance of language, to which I turn in the next section.

From this perspective, even superficial reflection suggests that a wide variety of cognitive capacities must work in tandem to connect items of language to aspects of the world. Keeping just to names such as John and Mt. Everest, not to speak of external significance of whole sentences, at least the following things are involved: a system of linguistic structure to place the name, and a system of conceptual relations and conditions, along with factual beliefs, to place the thing named (Chomsky 1975, 46; Malt, Sloman, and Gennari 2003, 8284). Hence, we need, if at all, a cl.u.s.ter of theories about the world, about linguistic practices, about formation of beliefs, and the like, to reach something like a naturalistic version of truth theory; then we find some way of attaching the cl.u.s.ter directly to grammatical theory.

It is important to note that each of these theories will be ultimately needed in a naturalistic explanation of external significance of linguistic expressions, for, together they explain just the abilities that enable a competent speaker to a.s.sent to instances of Convention T such as ''snow is white is true i snow is white.'' In other words, it is hard to see how a speaker who lacks these abilities can master the use of the truth predicate to a.s.sent to instances of Convention T. Needless to say, the desired cl.u.s.ter of theories is not even in sight.

Lowering our sights for now, the only issue that concerns us is whether the imposition of logical form is a desirable step toward the envisaged naturalistic theory. If it is not, then, granting that it is the only technique we know of for attaching a truth theory to a theory of language, we are either left with an ''incomplete'' theory of language in the form of grammatical theory, or we begin to doubt whether the pretheoretical conception of language theory is to be entertained at all.

So, how does a theory of logical form begin to account for the external significance of language? One answer, underlying much of the formal 98

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semantics literature, is that the recognition of diering truth conditions of the two readings of, say, (2) The king of France is not wise.

is in fact the relevant intuition to be explained by language theory ''at the very least.'' In other words, our recognition that (2) is structurally ambiguous is dependent on our intuition that (2) may be interpreted in two dierent ways and that intuition, in turn, rests on the fact that the interpretations dier in truth conditions. Since this last intuition is the one we ultimately need to give an account of to resolve scope ambiguity, we must begin with structural ambiguity and end by showing how the structural ambiguity results in diering truth conditions to which diering truth values may be systematically a.s.signed. Since the logical forms (4) and (5) motivate the desired progression, they are empirically significant.

We need not deny that expressions such as (4) and (5), or their informal English paraphrases, enable us to recognize that the readings of (2) dier in truth conditions; that, in other words, is data. Just what is achieved by the use of logical notation beyond this? The only constructive response that I can think of is that logicians have mastered a technique not only for representing the said intuition in structures such as (4), but also for characterizing that intuition explicitly. Thus, having reached (4), logical theory imposes a scheme of interpretation in a model. We define satisfaction conditions for each of the primitive terms and a.s.sign them compositionally to structures such as (4). Suppose we have two sentences, John is wise and Mt. Everest is a mountain. As noted, the model-theory part of the theory of logical form a.s.signs John to John, Mt. Everest to Mt. Everest, and so on. It is claimed that the resulting expressions in the semantic metalanguage will mimic the varying truth conditions. As far as I can see, the claim of external significance of truth theories ensues from these a.s.signments alone; once these denotations are plugged in, the rest is Tarski-style construction, as noted.

Just what is accomplished by picking John and mountain from a model such that John denotes John, or that mountain denotes the set of mountains, and leaving matters at that? Suppose we want to know how the external significance of John and mountain contribute to the external significance of John climbed a mountain. Clearly, we need to say something about John, mountain, and climbing, beyond saying that these things are denotations of John, mountain, and climbing. It is dicult to see how one can refuse to say these things while claiming that the expressions at issue have external significance.

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Denotational theorists will, of course, deny this. Concerning the sentence France is hexagonal, and it is a republic, Pietroski (2005) notes that speakers can use France to (simultaneously) refer to various things-a certain terrain, a particular nation, or whatever. However, according to Fodor and Lepore (cited by Pietroski), ''this does not yet show that semantic theories should mark such distinctions. Perhaps we should diag-nose such facts as reflections of what speakers know about France, and not what they know about France.'' Fodor and Lepore thus seem to allow that France is a hexagonal republic-which is dierent from, say, a triangular dictatorship-since that is what France denotes. The entire explanatory weight thus is on denotes.

What is denoting? Unfortunately, we have very little to work with here.11 In the formal semantics literature, denote is taken to be a primitive and is used in formulations such as ''John denotes John.'' This contrasts sharply with grammatical theory. Grammatical theory uses the term ''r-expression,'' where ''r'' abbreviates ''referring.'' In that sense, the theory uses some aspect of referring. But the aspect of referring it uses is theoretically characterized: an r-expression is A-free. Needless to say, the theory does not characterize-hence, does not use-other aspects of the common term. We would expect formal semantics to have taken over that unfinished task. Formal semantics fails us in using the common term itself.

It seems that people for whom ''John denotes John'' appears to be essentially a.n.a.lytic ( nonempirical) could have the right intuition. Suppose, by ''denotes'' we mean something like stands-for. Bertrand Russell (1919) held that a symbol stands for something. Hence, the knowledge that John is a symbol is the knowledge that John stands for something.

This general knowledge and the device of disquotation yield ''John stands-for/denotes John.'' On this view, the device of disquotation spells out that John is a symbol. One may know this without knowing what John (specifically) stands for or denotes; all we know is that John has external significance. The argument extends to common nouns like mountain: one may know ''mountain denotes mountain'' without knowing what mountain (specifically) means.12 We wanted to know the external significance of John and mountain to find out how they contribute to the external significance of John climbed a mountain; it is no progress to be told that John and mountain have external significance. It seems that the net situation is that what would count as a genuine theory of the external significance of language is not in hand; what is in hand is not a theory of external significance (Stainton 2006; Pietrosky 2006 for more).

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Common conceptions of denotation and designation, and cognate conceptions of truth and meaning, then, have little role in a theory of language. In fact, their lack of explanatory value puts significant pressure on the cla.s.sical notion of semantics-that is, the study of how language relates to the world. We may doubt whether this study applies to natural languages at all, whether or not there could be such a study for artificial languages or nonhuman signal systems. ''It is possible,''

Chomsky (2000d, 132) suspects, ''that natural language has only syntax and pragmatics.''

There is a certain irony here. We are discussing whether the concept of denotation interestingly captures the external significance of language.

According to Chomsky, only two kinds of systems may be viewed as ill.u.s.trating the common concept of denotation: animal call/signal systems and logical systems. The irony is that no significant notion of language applies to animal call systems, although the systems have external significance in the desired sense. Logical systems, on the other hand, may well be viewed as products or ''oshoots'' of the human linguistic system, but they do not have external significance. So, there is no case in which the notions of denotation, language, and external significance converge.

3.5.2.

Syntax of Thought?

The preceding observations need not immediately aect formal semantics in its entirety. Although formal semantics does indeed claim to address the external significance of language, arguably its more interesting parts can be viewed as concerning essentially the structural conditions that enter into computation of meaning. In other words, the program grants that words mean whatever they do; the program just looks at the general conditions they must meet on entering the semantic part of the computational system.

Of course the program need not be restricted to just this much. Having described the structural conditions, the program might try to link them up with the conceptual system; the conceptual system, in turn, might be viewed as linked up with items in the world. Chomsky (2001b) describes the full enterprise: the denotation relation holds between the internal semantic representation of books and its ''semantic value,'' which in turn relates somehow to books; ''the child acquires the denotation relation by virtue of causal properties of the world that relate external phenomena to mind-internal ent.i.ties, say 'concepts'. . . . We can forward further inquiries to the physics department, or maybe the sociology department.''

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Accordingly, the total program has three parts: (i) structural conditions on logical and nonlogical terms, (ii) conceptual characterization of nonlogical terms, and (iii) linking nonlogical terms to items in the world.

From what we saw, (iii) faces the problems discussed in the last section.

For (ii), I will a.s.sume, pace Chomsky 2002, 159, that ''n.o.body really has much of an idea about the computational processes right outside the language faculty. One could say there is a language of thought or something like that, there are concepts, etc., but there has never been any structure to the system outside the language faculty.'' We will study the prospects for a theory of conceptual organization in the next chapter. In any case, the program begins and is at its sharpest at (i), where it is concerned with the structural conditions that enter into computation of meaning.

This is done by focusing basically on what are generally called ''closed items'' of a language. Words of a language fall into two broad groups: closed and open. Closed items, such as prepositions and articles, form a fixed and restricted set-a few dozen in English, for example. Typically, though not always, they do not have a meaning standing alone; they must combine with open items, such as nouns and verbs, to form larger units that have independent meaning. It is reasonable to think of the semantic properties of closed items as ''wired-in'' such that vagaries of mind-external language use are not likely to aect their operations. The semantics of open items such as nouns and verbs, in contrast, not only involves the conceptual system directly, but the significance of these items is largely derived from the external contexts of their use, as noted.

The restricted attention to the structural conditions governing the (contribution of ) meanings of closed items raises the possibility that formal semantics need not be primarily viewed as giving an account of the mind-external significance of language. Instead, it may be seen as describing the mind-internal properties of language. With the change in perspective, formal semantics will no longer be semantics in the sense of relating language and the world, but as establishing systematic relations between language and some mind-internal ent.i.ties.

Chomsky has held this perspective on formal semantics for several decades. In Chomsky, Huybregts, and Riemsdijk 1982, 4647, he suggested that Montague semantics is ''not semantics really'' since ''it does not deal with the cla.s.sical questions of semantics such as the relation between language and the world.'' More recently (2003, 271), he has held that formal semantics should be regarded as a ''form of syntax.'' Hence, it is ''a study of symbolic objects and their properties-in this case, internal objects, 102

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linguistic expressions, and semantic values.'' ''Postulation of semantic values,'' he adds, ''faces the same challenges as postulation of other theoretical ent.i.ties: phonemes, atoms, whatever.'' Formal semantics thus extends the notion of syntax beyond grammar.

What do we make of the altered perspective even if, for Chomsky, formal semantics may not meet the standards of science? Can we think of the structures described by formal semantics as internal to the child's mind, an account of a cognitive capacity at all? To answer these questions, we need at least a cursory look at how part (i) of formal semantics in fact works.

Given the fixed, universal character of closed items, it is possible to use the abstract format of logical theory to spell out the conditions governing the semantic contribution of closed items to the overall meaning of the phrase in which they occur. As we saw, Russell invoked quantification theory to represent the contribution of the in a definite description. Once the contribution is spelled out in the logical format, the standard schemes of interpretation may then be attached to the expressions so constructed.

It stands to reason that the treatment could be extended beyond the usual quantificational part to any closed item of a language, including wh-items, p.r.o.nouns and anaphors, tense and agreement features, modality, and so on.

For a brief look at how all this is supposed to work, consider Richard Montague's treatment of every man walks (Dowty, Wall, and Peters 1981, 108109). As noted, the open items man and talk are viewed as nonlogical ''constants'' that are incorporated into Montague's formal system as man0 and walk0 respectively-that is, the latter are the ''primed variants''

of the corresponding English words. Although man0 is called ''Common Noun (CN)'' and walk0 is called ''Intransitive Verb (IV),'' both are viewed as semantic objects denoted by the type set of individuals, represented as he, ti ( semantic value), a map from ent.i.ties/individuals to truth values. Notice that the (vast) conceptual dierences between man and walk are simply set aside; these open items enter the system only as abstract semantic types.

The syntax of the sentence is displayed in terms of the usual phrase structure. The real action is on the closed item every. Keeping to the extensional part of the system, every is viewed as a logical constant belonging to the type 5e, ti, 5e, ti, t6, a map from sets of individuals to truth values. This is arrived at as follows. Every is viewed as an operation on two one-place predicates of the type he, ti. Let these arbitrary predicates be P and Q that range over constant predicates such as man0 and walk0.

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Figure 3.1 Montague tree Thus, we have the familiar first-order form Ex[Px ! Qx] for the general expression every P is Q. Next, we apply l-abstraction over the predicate expressions to yield lP[lQEx[Px ! Qx]], where l-abstraction turns a functional expression into an individual expression (Dowty, Wall, and Peters 1981, 98); in this case, lP[lQEx[Px ! Qx]] is an abstract determiner. We can view this expression as capturing the meaning of every since it has the desired type 5e, ti, 5e, ti, t6; it is desired because when the values for man0 and walk0 are inserted, the two he, tis cancel out and a t results. Thus, the logical form of every man walks is lP[lQEx[Px !

Qx]] (man0)(walk0). The derivation is represented in figure 3.1.

In frameworks that appeal only to (restricted) first-order notation, the general logical form for a sentence of the form every F is G is (every x: Fx) (Gx), with the ''truth clause'' jF a Gj 0, meaning the set of things that are F but not-G is empty (Neale 1990, 4243). So, the logical form and the truth clause for every man walks are (every x: man x) (walk x) and jMan a Walkj 0 respectively, where Man and Walk represent the cardinality of the sets {man} and {walk}.

The preceding sketch is enough evidence that formal semantics can be ''done,'' as long as grammatical theory keeps supplying enough structures for semanticists to attach logical expressions to. Much of the current work thus depends parasitically on linguistic theory to furnish fine-grained 104

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a.n.a.lyses of linguistic structures; once those structures are made available, say by Binding theory, the primitive basis of logical theory is suitably expanded to accommodate the new structures.

Could all this be viewed as describing the mind of the child? Consider the remark, once made by Chomsky, that Peano axioms are actually embedded in the (child's) mind. The postulation was supposed to explain why, pathology aside, children are able to acquire the standard number system without fail.13 Arguments from poverty of the stimulus suggest that children must have internalized a system that recursively generates numbers and other discrete infinities. With regard to numbers, Peano axioms also do the same. Yet, it will need a lot more than just these two facts-psychological and textual-to conclude that children have internalized these axioms. Peano axioms are ''rational reconstructions'' of some body of mathematics; hence they are essentially normative in character. They are useful for studying various formal properties of arithmetic; they are not intrinsically useful for studying the nature of arithmetical knowledge internalized by the child. If anything, Peano axioms are products of what Chomsky (1980) calls the ''science-forming capacity,'' whose object in this case is the body of arithmetic, not the child's mind. It is not at all obvious that the same ''axioms'' will show up when the capacity shifts its gaze to the child. What children do is a matter of fact, and a very dierent line of inquiry is needed to account for it.

In fact, Montague (1974, chapter 3) was very clear about the character of his project. He insisted that the theory is entirely mathematical in nature in that no psychological implications should be read in it. His goal was to treat English as a formal language with the ''usual syntax and model theory (or semantics) of the predicate calculus'' (p. 189). With Davidson, he regarded ''the construction of a theory of truth . . . as the basic goal of serious syntax and semantics.'' He was not giving an account of how English speakers in fact attach interpretations to sentences; he was merely a.s.signing logical interpretations to a cla.s.s of English expressions taken as objects of inquiry by themselves. According to Thomason 1974, 3, Montague never suggested that ''his work should be applied to topics such as the psychology of language acquisition.''14 A number of recent and influential monographs on the subject pursue the topic exactly as Montague did, diering only in the specific logical theory they adopt: Heim and Kratzer (1998) use the extensional part of Montague's model theory; Larson and Segal (1995) use only first-order logic and its familiar scheme of interpretation. But now the claim is that Grammar and Logic 105.

they are studying ''I-languages''-that is, they are studying ''knowledge''

of language as internalized by native speakers. Thus, a purely mathematical inquiry has turned into a psychological one without any noticeable change in the internal vocabulary of the enterprise. Constructs of formal semantics such as ent.i.ty, truth value, semantic value, and so on have now a.s.sumed an ''internalist'' character such that they are to be viewed as theoretical postulations uncovering aspects of the mind. Restricted to mind-internal aspects of language, what do the postulations of formal semantics now pick out? Given what ent.i.ty and truth value commonly mean, how do we conceptualize mapping of ent.i.ties to truth values internalistically?

The question is pertinent because it is natural to view postulations such as ent.i.ty, truth value and semantic value, as relating to the mind-external significance of language, as an attempt to explain the ''aboutness'' of linguistic expressions, whatever the merit of the project for a theory of language may be. No doubt, the ''world-bound'' character of formal semantics remains incomplete until several other steps are taken, as we saw. The world side of the language-world relation that obtains for Nixon simply uses Nixon: Nixon denotes Nixon; it tells us nothing about what denotation accomplishes. Nonetheless, the postulated relations of denotation, reference, and designation, intend to relate linguistic expressions to items in the world. Thus, in generating ''Arnold Schwarzenegger is big is true i (the individual) Arnold Schwarzenegger is big'' as a theorem, formal semantics is committed to the claim that Arnold Schwarzenegger designates Arnold Schwarzenegger, the famous bodybuilder, ''the actual, physical person'' (Larson and Segal 1995, 197, 203), not an ''internal representation'' of Arnold Schwarzenegger. It is hard to see what else designate could mean.

That is why fictional names such as Nixon-where Nixon names a pain that has ceased to exist-are a puzzle in semantics. Since it is unclear what Nixon means in a pain-free (state of the) world, we are p.r.o.ne to entertain the false belief that ''pains like Nixon never cease to 'exist' ''

(Kaplan 1989, 612). Given what we know about ''internal representations,'' it would not have been a problem if Nixon picked out ( just) an internal representation of Nixon. For the same reason, Chomsky's examples of the average man, the flaw in the argument, John Doe, and Joe Six-Pack are problems for formal semantics. Not only is it dicult to locate flaws and average men in the world, but some of these singular terms-the average man, John Doe, Joe Six-Pack-are used precisely for making 106

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general comments about the world, and not for picking out anything in particular. Hence, it is unclear what it means to have a model with John Doe and Joe Six-Pack occurring as individuals in it.

Constructs of formal semantics have an intrinsic urge to fly o the paper. No wonder major books on formal semantics are often full of pictures and hand drawings of people, dogs, cats, perambulators, and the like (Barwise and Perry 1983; Larson and Segal 1995). The contrast with syntax is striking. Postulates of grammatical theory such as noun phrase, anaphora, trace, c-command, and so on, make no reference to ent.i.ties outside the mind: there are no noun phrases or reflexives in the world. If anything, these are likely to be properties of the mind/brain. Notions like truth, reference, and the rest, on the other hand, do not seem to be ''psychological categories'' at all: it is better to think of them as ''modes of Dasein'' (Jerry Fodor, cited in Jackendo 1992, 159). From this perspective, it is implausible to a.s.similate truth and ent.i.ty with anaphora and c-command under the common head ''syntax.''

To summarize, the actual domain of formal semantics-structural conditions on closed items-raised the prospect of viewing it as restricted to language-external but mind-internal aspects of meaning; in that sense, it apparently enlarged the scope of language theory. However, its conceptual tools are suitable, if at all, for addressing cla.s.sical language-world relations. Given its conceptual resources, formal semantics cannot have it both ways.