Dummett's Backward Road to Frege and to Intuitionism - Tripod

It seems, then, that intuitionism cannot explain away our sense of mathematical discovery even
as a mere appearance. I mean that if what is proved is meaningless until it is proved, we cannot
meaningfully look for anything. Phenomenologically, the intentionality is gone. Is not human creation,
such as intuitionists take mathematics to be, normally a teleological process with an end in mind? Is not
trying to prove a thesis a paradigm of having an end in mind? 37
If different proofs provide or constitute different meanings for a theorem (see Dummett 1981:
674–75), the question arises whether they prove the same theorem, or whether the theorem is
ambiguous. But this question is meaningless for the intuitionist unless there is an actual, specific
second-order proof of sameness of the theorem. And if there are different second-order proofs of
sameness of the theorem, and so on, then there is a vicious regress involved in proving whether
different provers are ever proving the same theorem.
Perhaps Dummett’s belief in intuitionism has influenced his interpretation of Frege, or vice
versa. Perhaps his own contextualism and his forced choice argument have influenced both. Dummett
makes it clear that Frege is no intuitionist (1981: 586–87, 589). 38 But intuitionism and Dummett’s
program have something essential in common. Namely, both take the backward road. Intuitionism
holds that only a proof of the truth or falsehood of a mathematical theorem can provide a thought for
the theorem to express. Dummett’s program holds that for Frege, the truth-condition of a statement
wholly determines which thought the statement expresses.
In any case, Dummett takes the backward road in all three traditional areas of logic: terms
(senses via references), statements (propositional senses via truth-conditions), and inferences (theorem
senses via proofs of truth), in his Frege scholarship and/or his philosophy. 39
It may not seem so, but I agree with most of Dummett’s views on Frege. Whatever merit this
paper has is largely due to Dummett. For over a quarter of a century, I have regarded him as my Frege
teacher from afar. I owe more to him for my understanding of Frege than to anyone except Frege
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