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Chapter Six— Rejecting Nonconventional Syntax and Semantics for Symbols
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6.10—
"Pure Semantics" and "Abstract Languages"

The suggestion at hand, then, is that Tarski has employed notions of denotation and satisfaction and has characterized them for model-theoretic purposes in purely extensional (and nonconventional) terms—and, while his list-accounts do not provide any account of the nature of denotation or satisfaction (conventional or otherwise), the relations of denotation and satisfaction may yet be nonconventional in nature. And, moreover, the critic claims that the extensional characterization provided by Tarski is sufficient to show that we have notions here that can be applied indifferently to discursive symbols, thoughts, and mental representations.

I believe that this is the wrong moral to draw from Tarski's work. I further believe that the plausibility this thesis may enjoy derives from a common misunderstanding of what is going on in the formal (modeltheoretic) characterization of a language. Tarski himself differentiates between what he calls "descriptive semantics," which is concerned with describing how an actual group of people employs words, and what he calls "pure semantics," in which a language is considered in the abstract. Blackburn calls the domain of pure semantics "abstract languages," and this kind of locution, I submit, is the crux of the difficulty . For speaking of "abstract languages," as opposed to "languages considered in the abstract" suggests that there are these purely abstract entities called "languages," and it is to these that semantics applies, and the only job left for the descriptive theorist is to link a concrete community of speakers with the right abstract language. Thus many writers seem to see the problem of meaning as being identical to the problem of figuring out which abstract language a given community or individual speaks. Partitioning the problems in this way leads one to think that issues of semantics are all handled on the side of abstract languages which are, from the theorist's standpoint, stipulative in their semantic assignments. (I suppose from the metaphysician's viewpoint they are necessary and eternal.) Issues of conventionality, on the other hand, lie on the side of descriptive semantics. And if you view descriptive semantics as a matter of hooking up an abstract language, complete with semantics already intact, to a community of speakers, then it is natural to view the semantics of language per se as something outside of the web of convention and in the pristine world of abstract objects.

This story is alluring, but it is wrong. To see why it is wrong, it is necessary to tell a better story. The general moral is this: it is every bit as


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misleading to confuse languages-considered-in-the-abstract with "abstract languages" as it is to confuse material bodies-considered-in-the-abstract (e.g., in terms of mechanical laws) with "abstract bodies" (e.g., point-masses). Strictly speaking, there are neither abstract bodies nor abstract languages, and features that are bracketed for purposes of abstract analysis are not thereby proven to be inessential. In short, the belief that the domain of semantics is a kind of abstract object called an "abstract language" is to fall prey to another instance of the Fallacy of Reduction discussed earlier in this chapter.

The Fallacy of Reduction, you will recall, consists in giving an abstract description of a phenomenon as a model and then treating the properties that are clarified by the "reduced" model (e.g., the mathematical description) as precisely those properties that are constitutive of the original phenomenon. There are some cases, no doubt, in which the properties retained in the model are precisely those constitutive of the original domain, but such is not generally the case. The mathematics of thermodynamics, for example, does not tell you that the subject matter is heat . (Indeed, the same mathematics applies to information.) And in the case of abstractions such as point-masses, one is indeed faced with fictional entities that do not exist in nature. So long as one bears in mind that one is involved in a theoretical activity that involves abstraction, speaking of point-masses is completely benign. But if we forget the act of abstraction and treat point-masses as the real domain of mechanics—or even as a real part of the objects of mechanics—we have been deceived by our own use of language.

So what is one doing in giving a formal model of semantics for a language? What one is doing here is really just a special case of what one does in giving a model generally—for example, in mechanics or thermodynamics. (Tarski himself is really quite explicit about this, likening the relationship between metamathematics and particular mathematical domains to that between one of the natural sciences and the objects it studies.) In any of these cases, one begins with an intuitively characterized domain consisting of a set of objects one wishes to characterize (say, bodies or sentences) and a set of properties or relationships to rigorously specify (say, gravitational attraction or truth-functionality). One then abstracts or idealizes the objects in one's domain in a fashion that brackets those properties the objects have in vivo that are irrelevant to the problem at hand. One brackets features of bodies such as color, magnetism, and even size when one is doing a theory of gravitation, treating


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bodies as point-masses. And one brackets features of languages such as pronunciation, dialectical variation, nonassertoric sentences, linguistic change, and the conventionality of the symbols people really use when one is doing a theory of deduction. This kind of idealization is perfectly legitimate so long as the properties that are bracketed are truly irrelevant to the features one wishes to rigorously characterize. But of course the question of what may safely be bracketed depends entirely upon what aspects of the intuitively characterized domains one wishes to specify: a formal model of particle collisions should be sensitive to size and shape even if a model of gravitation is not, and a formal model of phonetics or pragmatics should be sensitive to features that are irrelevant to truth-functionality.

A formal model of a language (or of anything else) is thus a characterization of a language, viewed under a certain aspect and screening out other aspects of the language in vivo. It is, indeed, possible in some cases to construct artificial languages that actually lack some of the features that one idealizes away from in natural languages—for example, languages that lack lexical ambiguity, ambiguity in surface structure, notational variation, nonassertoric aspects, and change in usage. And indeed one usually constructs one's languages for mathematics and other deductive systems (Tarski's main interest) in a fashion that avoids these features. However, in the description of natural languages, one merely idealizes away from these features. Moreover, even with specialized languages, formal modeling idealizes away from other features—notably, those tied to the way the language is employed by its users. For example, what is called "denotation" in the model is bound up in what the language user does in referring in vivo, "satisfaction" is bound up with what the language user does in predicating in vivo, and so on.

As argued earlier in this chapter, there are two importantly distinct ways of looking at a model, corresponding to two different levels of abstraction one may adopt with respect to the intuitively characterized domain. At the first and milder level of abstraction, one views the model precisely as a model of the specified domain. One views Newton's equations as a model of gravitational interaction between bodies, or a Tarskian truth-definition as a model of truth in a language L . Here one is in fact looking at the initial domain, but viewing it abstractly through the lens of the model. One is making assertions about bodies, albeit bodies-considered-as-point-masses, or assertions about truth in a language L , but truth-characterized-extensionally. This is the "rich" characteri-


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zation of the model. Yet one may also perform a second act of abstraction and look at the model itself in abstraction from what it is a model of . One may, for example, look at Newton's laws simply as equations that can be satisfied under particular constraints and can be evaluated using particular techniques, or one may look at a Tarskian model simply in terms of the set-theoretic relations it employs and the valid deductions one may make on the basis of those. Here one has ceased to look at the mathematical construction that started out as a model as a model (for a model is a model of something), and treats it as an independent entity. This is the "sparse" interpretation of the model.

Now this does indeed have the consequence that formal modeling distills a purely abstract object—the construction that is the model sparsely characterized. However, it is incorrect to view this as an "abstract language," for it is not a language at all, but merely an object consisting of a set of expressions, a set of objects, and some mapping relationships between them. One applies the names 'denotation' and 'satisfaction' to some of these relationships, but that is simply an artifact of the process through which we got to the model sparsely characterized. There is nothing about the model sparsely characterized qua set-theoretic construction that makes particular mappings count as denotation or satisfaction. Indeed, there is nothing about the model sparsely characterized that makes them count as anything but arbitrary mappings. (This, I think, is the essence of Blackburn's point.)

Now indeed in the model richly characterized, we are entitled to speak of these functions as "denotation" or "satisfaction"—or, perhaps more correctly, as the extensional characterization of the denotations and satisfaction conditions of particular languages. But the reason for this is that we started out talking about such relations as the features of the intuitively characterized domain that we wished to speak about, and have merely constructed a model that gives a rigorous specification of these properties in a fashion that is "materially adequate and formally correct."

Compare the analogy with a theory of gravitation. If we look at Newton's laws just as equations—as a model sparsely characterized—they tell us nothing about what relationships they are supposed to describe. We may call the variables by names like 'mass' and 'distance', but they are no longer variables signifying mass and distance. Of course they do signify those properties in the model richly characterized, but again that is only because the model richly characterized is obtained by starting from an intuitively characterized domain, performing certain idealizations, and applying a rigorous description to what is left. A mathematization tells


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us only the relationships between the features we wish to describe—be they mass or denotation. It specifies only the form of the relations and not the nature of the relata.

As a consequence of this, it is important to see that a formal model of a language no more implies the existence of something called an "abstract language" than a formal model of gravitation implies the existence of things called "point-masses." The model richly characterized is precisely a description of a familiar intuitively characterized domain that uses an abstract object to describe certain properties of that domain. The "language" here is the full-blooded language we set out to describe, not some formal subset of it, and it is fraught with conventionality. The model sparsely characterized is not a language at all, even if we misleadingly use words like "denotation" for a mapping function it employs. All it is is a construction consisting of sets of expressions and objects and a set of mappings between them. Mappings in themselves no more add up to denotation than equations employed in mechanics or thermodynamics or the Mathematical Theory of Communication add up to mass or heat or information.

In short, there is no level at which we find what the critic needs: an "abstract language" that has genuinely semantic relationships but no conventionality. The model richly characterized has semantic relationships, but they are the conventional ones of full-blooded languages. The model sparsely characterized does not suffer from semantic conventionality (though it still presupposes the conventionally sanctioned symbol types that constitute its domain); but it does not involve genuine semantic relationships either, but merely the mathematical-logical form that those relationships in real languages share with many other nonlinguistic systems with which they are isomorphic. Tarskian semantics deals with (real, full-blooded) languages in abstraction from many features found in vivo, including their conventionality. But it does not succeed in uncovering "abstract languages" that can provide the domain for a "pure semantics."


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Chapter Six— Rejecting Nonconventional Syntax and Semantics for Symbols
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