[FOM] Falsify Platonism?

W.Taylor@math.canterbury.ac.nz W.Taylor at math.canterbury.ac.nz
Fri Apr 23 02:46:09 EDT 2010

Quoting Richard Heck <rgheck at brown.edu>:

> Why would that falsify Platonism?

Oh sorry, I thought that was obvious enough not to need stating.

> It seems to me that it would simply
> show that PA is the wrong theory of the numbers.

But it is clear to us what basic properties numbers have.  PA.
If Platonism is to mean anything worthwhile, it must mean this -
that knowing "what" numbers are, means knowing their (basic) properties.

So from a Platonistic PoV, PA "can't" be wrong!

> The point is clearer with ZFC.

Yes indeed.  The universe of sets is clear to some, or so they say,
but it is certainly NOT clear to me.

> If ZFC is inconsistent, that doesn't falsify Platonism; it
> just shows that ZFC is not a true theory of sets.

Quite so - supposing there IS a true such theory, which is not clear.

In sum, I am NOT a set-theoretic Platonist; though I am a numerical Platonist,
or, as I would prefer to say, a numerical realist.  I think ALL mathematicians
are, (except for a few weird ultrafinitist hold-outs).

-- Bill of Basics.

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