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

even if we could say it, since there would be a Quinean compensatory adjustment of “color” and
“shape” as well.
Are not the concepts red and round differently principled and therefore different mapping
functions? The premise is true but the conclusion does not follow. They are differently principled by
the senses expressed by “red” and “round.” More precisely, incomplete senses contain modes of
presentation which are the mapping principles of functions.
Dummett’s program fails even if we provide truth-conditions for all possible sentences of L as
used to describe all possible truth conditions. Even if such a procedure were correct in principle, it
would be unworkable in practice. No human can learn that “is red” expresses the sense of a color by
working through all possible sentences of English as used to describe all possible truth conditions.
Dummett would be the first to tell us that we cannot even work through all actually used sentences of
English, but must be able to use only a finite fragment of a language to learn senses and references. Yet
his view implies just the opposite:
Suppose, then, that we have two sentences which are analytically equivalent, but have
different senses. Since they have different senses, they must, on a view of Frege’s kind,
have different truth-conditions. Since they are analytically equivalent, the world cannot
be so constituted that one is true and the other false: the set of possible worlds in which
the one is true is the very same set as that of those in which the other is true. How can
there be room for Frege to distinguish the truth-conditions of the one from those of the
other? (1981: 588)
Here Dummett adduces a nonexistent problem from a strange view of Frege’s truth-conditions.
If Dummett thinks that difference in sense implies difference in truth-conditions, then perhaps that is
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