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Dear Carnap, Dear Van: The Quine-Carnap Correspondence and Related Work

University of California Press

These three lectures are to be concerned with Carnap's very recent work only. His earlier book, Der Logische Aufban der Welt , must be excluded entirely, because, although a very important piece of work, it lies outside the direction of Carnap's latest book and articles; these lectures must, for lack of time, be confined to the new Carnap.

Carnap's central doctrine, which is the main concern of these lectures, is the doctrine that philosophy is syntax. In this hour I shall lead up to that doctrine by discussing the analytic character of the a priori . I will present none of Carnap's actual work this time, but will attempt only to put the mentioned doctrine in a suitable setting. In the remaining two lectures we can get into the details of Carnap's own developments.

The efforts of Carnap and his associates in the Viennese Circle have been directed in large part to showing us how to avoid metaphysics. Perhaps it will bear poor testimony to their success if I start out by discussing Kant. But a discussion of the analytic and the a priori starts us off with Kant.

According to Kant, a priori judgments and analytic judgments do not entirely coincide; for him all analytic judgments are of course a priori , but not all a priori judgments are analytic. A judgment is a priori if it has "the character of an inward necessity," as Kant says, and holds independently of any possible experience.

An analytic judgment is a judgment the truth of which may be established directly by analysis of the concepts involved. An analytic judgment can do no more than call our attention to something already contained in the definitions of our terms. Analytic judgments are consequences of definitions, conventions as to the uses

of words. They are consequences of linguistic fiat. Clearly they are a priori ; their truth does not depend upon experience, but upon vocabulary. Among analytic judgments are to be reckoned logic and the bulk, at least, of mathematics.

Analytic judgments are a priori ; but the converse, according to Kant, does not obtain. He holds that there are a priori truths, not dependent upon experience, which yet do not follow merely from the definitions of terms. He thus recognizes synthetic , or nonanalytic, a priori judgments. Among these a priori synthetic judgments he reckons the propositions of geometry.

But the development of foundational studies in mathematics during the past century has made it clear that none of mathematics, not even geometry, need rest on anything but linguistic conventions of a definitional kind. In this way it becomes possible to relegate geometry to the analytic realm, along with the rest of mathematics. This empties out the a priori synthetic. The analytic and the a priori become coxtensive. Thus Professor Lewis writes: "The a priori is not a material truth, delimiting or delineating the content of experience as such, but is definitive or analytic in its nature."1

It will be worth while, by way of examining this doctrine, to consider in detail the nature of the analytic. To begin with, let us distinguish two kinds of definition. First there is explicit definition, which is merely a convention of abbreviation. For example the definition of momentum as mass times velocity is an explicit definition: it is a linguistic convention whereby the word "momentum" is introduced as an arbitrary abbreviation for the compound expression "mass times velocity." The explicit definition is perhaps what we ordinarily think of as a definition.

An implicit definition is of an entirely different form. An implicit definition of a notion K is a set of one or more rules specifying that all sentences containing the word K in such and such a way are to be accepted, by convention, as true; their truth constitutes the meaning of K. For example, a set of postulates containing an undefined word K can be construed as an implicit definition of K: the postulates are adopted as true by convention, and the sign K is

Mind and the World Order , p. 231.

thereby partially or completely defined. An implicit definition, like an explicit definition, is a convention as to how the word in question is to be used. An explicit definition stipulates our use of the word, say "momentum", by referring us to our uses of certain other words, in this case "mass", "times" and "velocity", where the use of these words has presumably been already stipulated in the past. An explicit definition, unlike an implicit definition, is thus necessarily relative.

Often the word "definition" is restricted to explicit definition, and that has been my procedure elsewhere. But it will be convenient at present to use the word in the broader sense, covering both implicit and explicit definitions. This usage also has precedent; for the phrase "implicit definition" is not my own.

The analytic depends upon nothing more than definition, or conventions as to the uses of words. But in the ordinary uncriticized language of common sense we have little to do with deliberate definition. We learn our vocabulary through the usual process of psychological conditioning. We proceed glibly to use our vocabulary, and so long as we move among compatriots we get on without much difficulty: for their conditioning has been substantially the same as ours. At this level we feel no need of defining our terms, or introducing deliberate conventions as to the use of language. This comes only at a more sophisticated stagefor example in mathematics and in science.

Suppose now we start at a common-sense level, or an ultra-common-sense level, at which no conscious or deliberate definition has taken place. Then suppose we schematically run through the whole process of thoroughly defining the terms which we had been using without definition all along.

Let K be any word mathematical, logical or otherwiseperhaps the word "if", or perhaps "two", or "cat". Now let us consider the whole range of admittedly true sentences in which K occurs: true sentences, I mean, under the usual implicit, common-sense use of the word K, and true according to the given stage in the progress of science. The distinction between a priori and empirical does not concern me here. Let us call these accepted sentences the accepted K-sentences .

Now suppose we are confronted with the job of defining K. If we can frame a definition which fulfills all the accepted K-sentences,

then obviously we shall have done a perfectly satisfactory job. Nobody who was inclined to dispute the definition could point to a single respect in which the definition diverged from the accepted usage of the word K: for all accepted K-sentences would be verified.

Such a definition of K would be easily accomplished if there were only say three dozen accepted K-sentences. K could be given implicit definition by setting down those three dozen sentences, by fiat, and declaring that this was how you proposed to use the word K. Of course the definition might not be completely determinate; there might be several distinct notions all of which...