The Paradox of Analysis

The Paradox of Analysis

Another problem with the entire program was raised by Langford (1942): why should analyses be of any conceivable interest?

After all, if analysis consists in providing the definition of an expression, then it should be merely providing a synonym for it, and this should be wholly uninformative, as un-informative as the claim that unmarried males are unmarried.

But the proposed reductions of, say, material object statements to sensory ones were often fairly complex, had to be studied and learned, and so hardly seemed uninformative.

So how could they count as seriously analytic?

This is “the paradox of analysis,” which can be seen as dormant in Frege’s own move from his (1884) focus on definitions to his more controversial (1892) doctrine of sense, where two senses are distinct if and only if someone can think a thought containing the one but not other, as in the case of the senses of “the morning star” and “the evening star.”

If definitions preserve sense, then, whenever one thought the defined concept, one would be thinking also the definition.

But few of Frege’s definitions, much less those of the Positivists, seemed remotely to have this character (see Bealer 1982, Dummett 1991 and Horty 1993, 2007 for discussion).

A related problem, discussed by Bealer (1998), is the possible proliferation of candidate analyses.

The concept of a circle can be can be analyzed as the concept of a set of co-planar points equidistant from a given point and as a closed figure of constant curvature.

Not only do both of these analyses seem informative, the equivalence between them would need to be shown by some serious geometry, which, especially since the advent of non-Euclidean geometries and Einstein’s theories of relativity, could no longer be assumed to be justified merely on the basis of logic and definitions.

These problems, so far, can be regarded as relatively technical, for which further technical moves within the program might be made. For example, one might make further distinctions within the theory of sense between an expression’s content and the specific “linguistic vehicle” for its expression, as in Fodor (1990a) and Horty (1993, 2007); and maybe distinguish between the truth-conditional content of an expression and its idiosyncratic role, or “character,” in a language system, along the lines of a distinction Kaplan (1989) introduced to deal with indexical and demonstrative expressions (such as “I,” “now” and “that”; see Demonstratives, Narrow Mental Content and White 1982). Perhaps analyses could be regarded as providing a particular “vehicle,” having a specific “character,” that could account for why one could entertain a certain concept without entertaining its analysis.

However, the problems with the program seemed to many philosophers to be deeper than merely technical. By far, the most telling and influential of the criticisms both of the program, and then of analyticity in general, were those of the American philosopher, W.V. Quine, who began as a great champion of the program (see esp. his 1934), and whose subsequent objections therefore carry special weight. The reader is well-advised to consult especially his (1956/76) for as rich and deep a discussion of the issues as one might find. The next two sections abbreviate some of that discussion.



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