Wolfgang Schwarz

Explicating Analyticity

Some expression can't be properly understood unless one believes certain things: In some sense you don't understand "irrational number" unless you believe that no natural number is irrational; You don't understand "grandmother" unless you believe that grandmothers are female; Maybe you don't understand "cat" unless you believe that cats are animals.

This is all quite vague because "understanding" and "believing" are vague. I now want to suggest that a sentence is analytic iff you can't understand it unless you believe it. Analyticity is also vague, so the vagueness of the explicans is fine for this purpose.

Perhaps my notion of analyticity is unusually tolerant. It is certainly more tolerant than for example Frege's, who requires that analytic truths be deducible from logical truths and definitions. I think it's useful because at least to a certain extent it can be tested: S is analytic if the common (or at least, adequate) response to somebody asserting not-S would be to say that he must have misunderstood what (some component of) S means. The test is even better for the opposite concept of analytic falsehood: A sentence is analytically false iff you can't understand it and still believe it. For example, if somebody told me that all even numbers are irrational, or that cats are round, yellow fruits that grow in Africa, I wouldn' say that he really believes this: Either he isn't serious or he doesn't mean what he is saying.

To put it slightly differently, S is analytically false if, whatever somebody believes, it wouldn't be right to ascribe to him the believe that S. And S is analytically true if, whatever somebody believes, it wouldn't be right to ascribe to him the believe that not-S.

Unfortunately, it seems that the hard cases of apriori truths can be coherently denied, so they don't come out as analytically true. This is a pity because analyticity would probably be a good explanation of apriority. (I'm not so sure about this. An explanation of apriority would presumably have to say something about the experience-independent justification of the relevant beliefs, and I'm somewhat inclined to say that my belief that all grandmothers are female, or that Modus Ponens is truth-preserving, is not the kind of belief that even requires justification for it to be knowledge.) For instance, I think it would be correct to ascribe to Hartry Field the believe that there are no prime numbers smaller than 10, and that Hume's Principle is false. To defend the analyticity of Hume's Principle, one would have to argue why somebody who claims to deny it must have misunderstood it.

[Update 2003-05-16: I've inserted a "not" that Sam noticed was missing. He also offers a couple of putative counterexamples to my explication (unfortunately only in private mail), which I think do not work. There are two interesting cases, however, that I still have to think about: extremely complicated logical truths and extremely trivial synthetic truths.]

[Update 2003-05-17: The story continues here. Now I think that Sam brings up not two, but three interesting cases. I'll say more as soon as I found some time to think about it.]