[FOM] Semantical realism without ontological realism in mathematics
Stephen Yablo
yablo at mit.edu
Wed May 28 10:00:22 EDT 2003
On ontological vs. semantical realism, see also Crispin Wright,
_Frege and the Conception of Numbers as Objects_ (1980), especially
the introduction.
S =/=> O: "The [semantic] realist has a choice. He can take it that
these aspects of number-theoretic language -- the fact that we use
apparent numerical names etc. -- ...reflect genuine aspects of
mathematical reality...[Or] he may argue that the grammatical
machinery in terms of which we give expression to arithmetical truths
is of a systematically misleading form; that it it distorts the real
structure, as it were, of the facts described...apparently
existential theorems of number theory are not genuinely
existential...their truth does not require the existence of some sort
of special object" (xviii)
O =/=> S: "someone could hold both that it is correct to think of the
natural numbers as genuine objects -- as genuine as buildings and
trees -- and that there are decisive objections to the realist's way
of thinking about the truth and falsity of statements concerning such
objects" (xviii).
Steve
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Stephen Yablo
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Linguistics and Philosophy, MIT
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