[FOM] Falsify Platonism?
Staffan Angere
Staffan.Angere at fil.lu.se
Fri Apr 23 04:54:49 EDT 2010
I do not think that it is possible to falsify Platonism. A theory has to be falsifiable in order to be falsified, and Platonism as such is certainly not specified in the kind of exact, observational language that means that it could be falsified. Certain specific formulations of it may be falsifiable, however.
The same thing holds, in my opinion, for other theories of the foundations of mathematics. The general problem is philosophy, and there are no knock-down arguments in philosophy. While Hilbert's formalism may be said to be falsified by the incompleteness theorems, these do not really hinder some other version of formalism from being viable. Logicism, in Frege's sense, is falsified by Russell's paradox, but Logicism in another form (e.g. with Hume's principle instead of Basic Law V) is still a live option.
There have been several of findings that "should" have falsified Platonism, but since it (and other foundational programmes) are as vaguely stated as they are, it is always possible to reinterpret it in order to avoid the problems. Even the discovery of a contradiction in PA can be met by the assertion that PA, in that case, did not actually capture the "real" structure of mathematical reality.
Staffan Angere
Lund University
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Från: fom-bounces at cs.nyu.edu [fom-bounces at cs.nyu.edu] för Bill Taylor [W.Taylor at math.canterbury.ac.nz]
Skickat: den 22 april 2010 04:34
Till: fom at cs.nyu.edu
Ämne: [FOM] Falsify Platonism?
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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