Saturday, March 12, 2011

Platonism is not the problem

Thomas Tymoczko, introduction to New Directions in the Philosophy of Mathematics (1986, rev. 1998), p. xiii:

To account for the indubitability, objectivity  and timelessness of mathematical results,  we are tempted to regard them as true descriptions of a Platonic world outside of space-time.  This leaves us with the problem of explaining how human beings can make contact with this reality.

Well, yes, that is indeed a question;  but not a new one.   The same conundrum confronts us in the Mind-Body problem; the problem of Free Will; and more simply, the problem of how you and I can communicate at all.  There are even puzzles at the level of mid-level objects.  The thesis of Mathematical Realism may or may not be valid, but it does not introduce a problem which we might otherwise avoid.

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