[FOM] Falsify Platonism?

[Al Bernstein]

Platonism is a metaphysical construct that allows us to communicate
objectively using numbers. We can't build a perfect cube because there will
always be imprecision in our tooling. However, a perfect cube can exist in
our minds and we can calculate cubic numbers x^3 corresponding to the
volumes of various cubes. Anybody calculating x^3 for a given x will come up
with the same answer if we stick to integers to avoid talk about round-off
errors.

Platonism allows us to have a number system to begin with. I don't see how
Platonism is preventing us from exploring any concept we want to. We need a
starting point for a number system to exist. It seems that anything we would
use as an alternate starting point effectively provides the same function as
Platonism. If we suppose that Platonism is wrong, what would we replace it
with ? 

Al Bernstein

-----Original Message-----
From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf Of
W.Taylor at math.canterbury.ac.nz
Sent: Thursday, April 22, 2010 11:46 PM
To: Richard Heck
Cc: fom at cs.nyu.edu
Subject: Re: [FOM] Falsify Platonism?

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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