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

same extensional in sense (2) mapping function. Our world of four objects logically could be the actual
world. Thus even if logical equivalence were Frege’s criterion for the identity of thoughts, the problem
of sensial underdetermination would remain for indefinitely many logically contingent statements in an
ideal scientific language (compare Dummett 1981: 228, 636).
But I reject the suggestion, and I accept Dummett’s view that sensial identity is given. Perhaps
all analytic truths have the same general truth-condition, true under any condition. But even if
necessary truth is the same as purely general truth for Frege, the specific or proper truth-conditions of
“2 + 2 = 4” and “(x)(x = x)” are different, consisting of different specific functions and objects in
different specific relationships. Strictly, even “2 + 2 = 4” and “4 – 2 = 2” have different truth-
conditions and express different thoughts. As to sensial identity, Frege’s plea that we must allow
transformations of the same thought in logical inference can be substantially preserved by glossing
transformations as changes to new thoughts which are substantially the same and differ only
holistically in their slicing. But on pain of vicious cognitive regress, it is essential that all senses
logically can be directly given, no matter how indirect the sense. Dummett is absolutely right that given
sensial identity is fundamental and trumps transformations (1981: 631–37). But then even sameness of
truth-condition does not imply sameness of sense, since Frege’s specific truth-conditions are
extensional in sense (2), exactly like the customary references they consist of, while his given senses
are intensional in sense (2). This is why Frege would reject even C. I. Lewis’s definition of a
predicate’s intension as (in effect) the class of all possible objects satisfying it (Lewis 1946: 39). For
on that definition, the senses of “= (1 + 1)” and “= (4 – 2)” are the same.
The actual world is only the actual set of compossible truth-conditions. But even if we knew all
possible truth-conditions as composed of all possible customary references in all possible worlds, why
assume that the problem of sensial underdetermination would somehow magically vanish? Even if to
give all possible customary references is to give all their possible modes of presentation via each other
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