[FOM] Falsify Platonism?
meskew at math.uci.edu
Sat Apr 24 04:11:31 EDT 2010
I'm sorry, but I find this whole style of argument to be ridiculous.
Look at the axioms of PA. I need not list them here. They are such
basic and bone-headed statements. They follow from the concept of
natural numbers. If you disagree with this statement please tell me
which of the axioms could possibly be false while its negation could
still purport to describe something deserving of the title "natural
numbers" (whether fictional or real).
The kind of total abstraction from the subject matter into general
truisms about metaphysics and epistemology is exactly what's wrong
with academic philosophy. It gives people's arguments a loophole
around their own standards of intellectual honesty and allows them to
make claims that are just plain silly.
once a philosopher
On Fri, Apr 23, 2010 at 9:17 AM, Richard Heck <rgheck at brown.edu> wrote:
> I'm sorry, but I still don't see this. Platonism is a metaphysical view,
> a view about what the truth of mathematical statements consists in. It
> says that mathematical objects exist objectively, independently of our
> thought (or capacity for thought) about them, and that their properties
> are equally independent of our knowledge (or capacity for knowledge) of
> them. Such a view is in no way committed to any claim about what the
> truth about numbers is.
> Granted, we tend to suppose that we "know" what the basic properties of
> the numbers are. But maybe we don't know. Maybe we only think we know.
> That, indeed, is one of the central worries that people have about
> Platonism: It looks at least conceivable that the mathematical facts, as
> they are in mathematical heaven, could come arbitrarily apart from what
> we think we know.
> In any event, claims about what we know, about what could or could not
> prove to be false, are epistemological and so their relation to the
> metaphysical claim is not at all straightforward.
> Of course, if you want to use "Platonism" as a name for some view other
> than the metaphysical one described, that's up to you. But you're likely
> to confuse a lot of people.
> Richard Heck
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> FOM at cs.nyu.edu
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