[FOM] Re: Platonism and Formalism (a reply to Podnieks)

[T P Uschanov]

On Sat, 6 Sep 2003, Torkel Franzen wrote:

> But of course Wittgenstein didn't actually work in logic or
> mathematics or computing.

It depends on how one defines logic and mathematics. Wittgenstein was a 
certified engineer and architect; it was his postgraduate studies in 
aeronautic engineering which first brought him to problems in FOM. In 
1913 Russell wrote of his hope of leaving to Wittgenstein all the 
eventual updating of Principia Mathematica for the second edition. 
Wittgenstein personally knew, and had FOM-related discussions with, a 
good number of professional logicians and mathematicians such as Frege, 
Ramsey, Louis Goodstein, H. D. Ursell, Georg Kreisel, W. H. Watson, 
Peter Geach, and others. Most of them disagreed with him regarding FOM, 
often fundamentally, but as far as I know, none of them ever suggested 
that he "didn't actually work in logic or mathematics".

> A consistently non-Platonistic point of view with regard to mathematics
 > is much like a consistently skeptical view of human knowledge: it has
 > a certain appeal to the intellect, but it has no apparent relation to
 > how people, including professed non-Platonists or skeptics, actually
 > go about their business.

Of course, Wittgenstein agreed quite heartily with this, with the slight 
difference that he would have said exactly the same about a consistently 
Platonistic point of view; in his (largely correct) view, most working 
mathematicians are no more Platonists than they are non-Platonists -- 
just like most men in the street are no more scientific realists than 
they are skeptics -- since the whole issue (thankfully) is not and has 
never been a live one with them. ("The mathematical problems of what is 
called foundations are no more the foundations of mathematics for us 
than the painted rock is the support of the painted tower.")

-- 
T. P. Uschanov, Research Assistant        | e-mail:
Department of Philosophy                  | <tuschano at cc.helsinki.fi>
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