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

Torkel Franzen torkel at sm.luth.se
Wed Sep 17 22:05:51 EDT 2003

T. P. Uschanov says:

  >It depends on how one defines logic and mathematics. 

 It depends rather on how one defines "work in".  I think that if you
had asked Wittgenstein at the time, he would not have said that he worked in
logic, mathematics, or computing.

  >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. 

  No more is the issue of skepticism vs non-skepticism an issue with
the vast majority of people who use or produce human knowledge. They
simply take for granted that we know (some) things. Similarly, people
who use or produce mathematics simply take for granted that the
question how many factors some large number has, or whether RSA can be
broken, or whether P=NP, or whether ZFC+some large cardinal axiom is
consistent, is a factual question that we may or may not be able to
answer, whatever the mathematical facts may be. That they do take this
view is something that emerges in innumerable contexts, in many
different ways, just as in the case of people taking for granted that
we know things.

  A "consistently Platonistic" view of (all of) mathematics can hardly
be found, in philosophy or elsewhere, and has not been under discussion.

Torkel Franzen

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