[FOM] Falsify Platonism?
David Auerbach
auerbach at unity.ncsu.edu
Thu Apr 22 20:27:08 EDT 2010
A feature of the hard tests, in the sense I think intended, is that failing the test was a relatively clear matter (at least retrospectively). For example, the soundness of reasonable formalizations of arithmetic being provable by finitistic means is relatively clear hurdle that, modulo some quibbles, that Hilbert's program fails. (i.e., not finitistically provable Prf(A) --> A ....)
I'm not seeing how CH possessing a truth value is susceptible to such an articulatable test. We would need an good account of when a statement can fail to have a truth value and one that doesn't beg the question. (Pointing to the independence of CH from ZFC obviously won't (hasn't) done the job.)
The least question begging method I can think of for arguing for a lack of truth value is pointing to a failure of reference. Thus,
Sherlock Holmes lives on Baker Street
is a candidate for lack of truth value. But if that's the analogy, then what's needed is an argument for the non-existence of sets. In which case, we've refuted set-theoretical Platonism without a detour to the specifics of CH.
David Auerbach auerbach at unity.ncsu.edu
Department of Philosophy and Religious Studies
NCSU
Raleigh, NC 27695-8103
On Apr 22/10, at 6:20 PM, Brian Hart wrote:
> One way to falsify set-theoretical Platonism might be by demonstrating
> that CH does not posess a truth value since it is a presumption of
> Platonism in general that all mathematical statements possess such a
> value.
>
> On Wed, Apr 21, 2010 at 10:34 PM, Bill Taylor
> <W.Taylor at math.canterbury.ac.nz> wrote:
>> Lucas Kruijswijk <L.B.Kruijswijk at inter.nl.net> wrote:
>>
>> -> Hilbert's program contains hard tests, which are mostly
>> -> proven to be impossible. Is there any hard test that can
>> -> falsify Platonism?
>>
>> Yes.
>>
>> If a contradiction is derived from PA, that will falsify Platonism.
>>
>> (Strictly speaking, that falsifies numerical Platonism; it might be easier
>> still to falsify set-theoretic Platonism.)
>>
>> W. Taylor. (Basics Bill)
>>
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