[FOM] Wittgenstein?

Torkel Franzen torkel at sm.luth.se
Tue Apr 22 06:13:57 EDT 2003


Harvey Friedman says:

 >*DID LW WRITE ANYTHING THAT CAN AT LEAST BE REASONABLY INTERPRETED AS 
 >BEING SIGNIFICANT FOR THE FOUNDATIONS OF MATHEMATICS? IF SO, EXACTLY 
 >WHAT?*

  There is no obvious reason why somebody who regards Wittgenstein's
writings in the philosophy of mathematics as enormously significant
should regard those writings as significant for the foundations of
mathematics, since many comments of Wittgenstein's can be interpreted
as saying that the foundations of mathematics are no concern of his,
that he merely takes mathematics as he finds it. On the other hand,
Russell shrewdly observed that much of what Wittgenstein says in
the _Philosophical Grammar_ is constantly "in danger of becoming what
Brouwer has said, and has to be pulled up short whenever this danger
becomes apparent". But the whole matter is moot, and a capitalized
NO to your question is fully compatible with the view that Wittgenstein's
work in the philosophy of mathematics is enormously significant.

  For myself I would say that Wittgenstein's consistent anti-realism with
regard to mathematical statements is philosophically interesting and useful,
in bringing out the weaknesses of the view that statements decidable "in
principle" have a "determinate truth-value" in some sense that statements
involving quantification over infinite totalities do not.

  PS: I have seen on the net the absurd claim that Wittgenstein understood
Gödel's theorem better than Gödel did, but unfortunately Wittgenstein
enthusiasts who take this view are unlikely to contribute to the list.

---
Torkel Franzen



More information about the FOM mailing list