[FOM] Falsify Platonism?
Timothy Y. Chow
tchow at alum.mit.edu
Mon Apr 26 12:43:18 EDT 2010
On Mon, 26 Apr 2010, rgheck wrote:
> I was not trying to draw any complicated distinction that should be
> controversial. Surely we can all agree that there is a rather large
> difference between stars and our concept of stars.
The distinction you're drawing is not at all complicated or controversial
*to a philosopher*. It's something you expect your better undergraduate
philosophy students to grasp without much difficulty. But I maintain that
this is *not* the sort of distinction that a mathematician is accustomed
to having to draw in order to think clearly about mathematics. As a
mathematician, I know that I have to distinguish carefully between
different but isomorphic copies of a field F embedded in another field K.
I have to distinguish between a manifold and its embedding in R^n. I have
to distinguish between a random variable and the value it takes in a
particular trial. These are subtle distinctions but I know it's important
to keep them straight.
But why should it be important, in the practice of mathematics, to
maintain a distinction between N and the concept of N? Why are the
philosophers telling me that I can't define N to be "anything that
satisfies the Peano axioms" and that only the "concept of N" can be so
defined? This represents an intrusion of philosophy into mathematics that
does not currently exist. I still say that if you're right about the
distinction between N and the concept of N being of critical importance,
then some version of platonism is falsified by PA, even if it's true that
a slightly more sophisticated version of platonism isn't.
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