[FOM] Platonism, Realism, Formalism

Peter Apostoli apostoli at cs.toronto.edu
Wed Oct 29 09:24:55 EST 2003

JS: What I'm interested in is how Realism can fail to entail Platonism: how
can we make sense of "the truth value" of a sentence like "there exists a
measurable cardinal" (henceforth: "MC"), which we know is independent of any
assumption necessary for "ordinary mathematics", without being Platonists?

This recalls Kriesel's famous dictum that its the *objectivity* of
mathematical statements, not the existence of mathematical objects, that the
realist properly defends. See the first few pages of C. Wrights On Frege's
Conception of Numbers as Objects for the Kriesel reference and a brief
discussion. I suppose the influence of Kriesel's dictum on Dummett's idea of
realism (= bivalence) with respect to a given discourse may be obvious to
listmembers, but I am not aware of the history of infuences here.

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