Analyticity

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ANALYTICITY

The idea of "analyticity"or truth by virtue of meaningcan be understood in two different ways. On the one hand, it might stand for an epistemic notion, for the idea that mere grasp of the meaning of a sentence suffices for knowledge that it is true. On the other hand, it might stand for a metaphysical notion, for the idea that a statement owes its truth value completely to its meaning, and not at all to "the facts." We may call the first notion "epistemic analyticity" and the second "metaphysical analyticity." On the face of it, these are distinct notions that subserve distinct philosophical programs. Willard Van Orman Quine, whose writings are largely responsible for the contemporary rejection of analyticity, failed to distinguish between them; as a result, many philosophers came to assume that the two notions stand or fall together. However, it is the moral of recent work in this area that this assumption is mistaken: epistemic analyticity can be defended even while its metaphysical cousin is rejected.

The metaphysical concept of analyticity is presupposed by the logical positivist program of reducing all necessity to linguistic necessity. Guided by both the fear that objective, language-independent necessary connections would be metaphysically odd, and that no empiricist epistemology could explain our knowledge of them, philosophers like Rudolf Carnap (1947) and A. J. Ayer (1946) attempted to show that all necessary truths are simply disguised decisions concerning the meanings of words. According to this view, there is no more to the truth of, say, "Either snow is white or it is not" than a decision concerning the meaning of the word "or." On this view, linguistic meaning by itself is supposed to generate necessary truth; a fortiori, linguistic meaning by itself is supposed to generate truth. Hence the play with the metaphysical notion of analyticity.

However, it is doubtful that this makes a lot of sense. What could it possibly mean to say that the truth of a statement is fixed exclusively by its meaning and not by the facts? Is it not in general true that for any statement S,

S is true if and only if (iff) for some p, S means that p and p ?

How could the mere fact that S means that p make it the case that S is true? Doesn't it also have to be the case that p (see Harman, 1960)?

The proponent of the metaphysical notion does have a comeback, one that has perhaps not been sufficiently addressed. What he will say instead is that, in some appropriate sense, our meaning p by S makes it the case that p.

But this line is itself fraught with difficulty. For how are we to understand how our meaning something by a sentence can make something or other the case? It is easy to understand how the fact that we mean what we do by a sentence determines whether that sentence expresses something true or false. But as Quine (1951) points out, that is just the normal dependence of truth on meaning. What is not clear is how the truth of what the sentence expresses could depend on the fact that it is expressed by that sentence, so that we would be entitled to say that what is expressed would not have been true at all had it not been for the fact that it is expressed by that sentence. But are we really to suppose that, prior to our stipulating a meaning for the sentence

"Either snow is white or it is not"

it was not the case that either snow was white or it was not? Is it not overwhelmingly obvious that this claim was true before such an act of meaning, and that it would have been true even if no one had thought about it, or chosen it to be expressed by one of our sentences?

There is, then, very little to recommend the linguistic theory of necessity and, with it, the metaphysical notion of analyticity that is supposed to subserve it. Epistemic analyticity, by contrast, is not involved in that futile reductive enterprise. Its role, rather, is to provide a theory of a priori knowledge.

Intuitively speaking, it does seem that we can know certain statementsthe truths of logic, mathematics, and conceptual analysis, most centrallywithout recourse to empirical experience. The problem has always been to explain how.

The history of philosophy has known a number of answers to this question, among which the following has been very influential: We are equipped with a special evidence-gathering faculty of intuition, distinct from the standard five senses, that allows us to arrive at justified beliefs about the necessary properties of the world. By exercising this faculty, we are able to know a priori such truths as those of mathematics and logic.

The central impetus behind the analytic explanation of the a priori is to explain the possibility of a priori knowledge without having to postulate any such special faculty of "intuition," an idea that has never been adequately elaborated.

This is where the concept of epistemic analyticity comes in. If mere grasp of S 's meaning by O were to suffice for O 's being justified (with a strength sufficient for knowledgehenceforth, we will take this qualification to be understood) in holding S true, then S 's apriority would be explainable without appeal to a special faculty of intuition: the very fact that it means what it does for O would by itself explain why O is justified in holding it to be true.

How could mere grasp of a sentence's meaning justify someone in holding it true? Clearly, the answer to this question has to be semantical: something about the sentence's meaning, or about the way that meaning is fixed, must explain how its truth is knowable in this special way. What could this explanation be?

In the history of the subject, two different sorts of explanation have been especially important. Although these, too, have often been conflated, it is crucial to distinguish between them.

One idea was first formulated in full generality by Gottlob Frege (1884). According to this view, a statement's epistemic analyticity is to be explained by the fact that it is transformable into a logical truth by the substitution of synonyms for synonyms. We may call statements that satisfy this semantical condition "Frege-analytic."

Quine's enormously influential "Two Dogmas of Empiricism," (1951) complained that there could not be any Frege-analytic statements because there could not be any synonymies. But, as Herbert P. Grice and Peter F. Strawson showed (1956), the arguments for this claim are highly disputable. And Paul Boghossian (1995) has added to this by arguing that Quine's negative arguments cannot plausibly stop short of his radical thesis of the indeterminacy of meaning, a thesis that most philosophers continue to reject.

The real problem with Frege-analyticity is not that there are not any instances of it, but that it is limited in its ability to explain the full range of a priori statements. Two classes remain problematic: a priori statements that are not transformable into logical truths by the substitution of synonyms for synonyms, and a priori statements that are trivially so transformable.

An example of the first class is the sentence "Whatever is red all over is not blue." Because the ingredient descriptive terms do not decompose in the appropriate way, this sentence is not transformable into a logical truth by substitution of synonyms.

The second class of recalcitrant statements consists precisely of the truths of logic. These truths satisfy, of course, the conditions on Frege-analyticity. But they satisfy them trivially. And it seems obvious that we cannot hope to explain our entitlement to belief in the truths of logic by appealing to their analyticity in this sense: Knowledge of Frege-analyticity presupposes knowledge of logical truth and so cannot explain it.

How, then, is the epistemic analyticity of these recalcitrant truths to be explained? The solution proposed by Carnap (1947) and the middle Ludwig Wittgenstein (1974) turned on the suggestion that such statements are to be thought of as "implicit definitions" of their ingredient terms. Applied to the case of logic (a similar treatment is possible in the case of the other class of recalcitrant truths), this suggestion generates the semantical thesis we may call:

Implicit definition: It is by arbitrarily stipulating that certain sentences of logic are to be true, or that certain inferences are to be valid, that we attach a meaning to the logical constants. A particular constant means that logical object, if any, which makes valid a specified set of sentences and/or inferences involving it.

The transition from this sort of implicit definition account of grasp to an account of the apriority of logic can then seem immediate, and the following sort of argument would appear to be in place:

  1. If logical constant C is to mean what it does, then argument-form A has to be valid, for C means whatever logical object in fact makes A valid.
  2. C means what it does.

Therefore,

  • 3. A is valid.

Quine's "Truth by Convention" (1936) and "Carnap and Logical Truth" (1976) raised several important objections against the thesis of implicit definition: first, that it leads to an implausible conventionalism about logical truth; second, that it results in a vicious regress; and third, that it is committed to a notionthat of a meaning-constituting sentence or inferencethat cannot be made out.

Even the proponents of implicit definition seem to have agreed that some sort of conventionalism about logical truth follows from implicit definition. However, Nathan Salmon (1994) and Boghossian (1997) have argued that this is a mistake: No version of conventionalism follows from the semantical thesis of implicit definition, provided that a distinction is observed between a sentence and the claim that it expresses.

Quine's second objection is also problematic in relying on a defective conception of what it is for a person to adopt a certain rule with respect to an expression, according to which the adoption of a rule always involves explicitly stating in linguistic terms the rule that is being adopted. On the contrary, it seems far more plausible to construe x 's following rule R with respect to e as consisting in some sort of fact about x 's behavior with e.

In what would such a fact consist? Here there are at least two options of which the most influential is this: O 's following rule R with respect to e consists in O 's being disposed, under appropriate circumstances, to conform to rule R in his employment of e.

According to this view, then, the logical constants mean what they do by virtue of figuring in certain inferences and/or sentences involving them and not in others. If some expressions mean what they do by virtue of figuring in certain inferences and sentences, then some inferences and sentences are constitutive of an expression's meaning what it does, and others are not.

Quine's final objection to implicit definition is that there will be no way to specify systematically the meaning-constituting inferences, because there will be no way to distinguish systematically between a meaning constituting inference and one that is not meaning-constituting but simply obvious. However, although this is a serious challenge, and although it remains unmet, there is every reason for optimism (see, for example, Peacocke 1994 and Boghossian 1995).

Quine helped us see the vacuity of the metaphysical concept of analyticity and, with it, the futility of the project it was supposed to underwritethe linguistic theory of necessity. But those arguments do not affect the epistemic notion of analyticity, the notion that is needed for the purposes of the theory of a priori knowledge. Indeed, the analytic theory of apriority seems to be a promising research program, given reasonable optimism about the prospects both for a conceptual role semantics and for the idea of Frege-analyticity.

See also Ayer, Alfred Jules; Carnap, Rudolf; Conventionalism; Frege, Gottlob; Grice, Herbert Paul; Knowledge, A Priori; Moral Epistemology; Quine, Willard Van Orman; Strawson, Peter Frederick; Wittgenstein, Ludwig Josef Johann.

Bibliography

Ayer, A. J. Language, Truth and Logic. London: Gollancz, 1946.

Boghossian, P. A. "Analyticity." In A Companion to the Philosophy of Language, edited by C. Wright and B. Hale. Cambridge, U.K.: Blackwell, 1997.

Carnap, R. Meaning and Necessity. Chicago: University of Chicago Press, 1947.

Dummett, M. Frege: The Philosophy of Mathematics. Cambridge, MA: Harvard University Press, 1991.

Frege, G. Die Grundlagen der Arithmetik: eine logisch-mathematische Untersuchung uber den Begriff der Zahl (1884). Translated by J. L. Austin as The Foundations of Arithmetic. Oxford: Blackwell, 1950.

Grice, H. P., and P. Strawson. "In Defense of a Dogma." Philosophical Review 65 (1956): 141158.

Harman, G. "Quine on Meaning and Existence I." Review of Metaphysics 21 (1960): 124151.

Pap, A. Semantics and Necessary Truth. New Haven, CT: Yale University Press, 1958.

Peacocke, C. "How Are A Priori Truths Possible?" European Journal of Philosophy 1 (1993): 175199.

Peacocke, C. A Study of Concepts. Cambridge, MA: MIT Press, 1992.

Putnam, H. Mind, Language and RealityPhilosophical Papers 2. Cambridge: Cambridge University Press, 1975.

Quine, W. V. O. "Carnap and Logical Truth" (1954). Reprinted in The Ways of Paradox, Cambridge, MA: Harvard University Press, 1976.

Quine, W. V. O. "Truth by Convention." In Philosophical Essays for A. N. Whitehead, edited by O. H. Lee. New York: Longmans, Green, 1936. Reprinted in The Ways of Paradox, Cambridge, MA: Harvard University Press, 1976.

Quine, W. V. O. "Two Dogmas of Empiricism." Philosophical Review (1951). Reprinted in From a Logical Point of View, Cambridge, MA: Harvard University Press, 1953.

Quine, W. V. O. Word and Object. Cambridge, MA: MIT Press, 1960.

Salmon, N. "Analyticity and Apriority." Philosophical Perspectives (1994).

Wittgenstein, L. J. J. Philosophical Grammar (19321934). Berkeley: University of California Press, 1974.

Paul Artin Boghossian (1996)

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