[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).


Stephen Yablo
Linguistics and Philosophy, MIT
office phone: 617-258-0740
website: http://www.mit.edu/~yablo/home.html

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