[FOM] FOM posting-Wittgenstein?

[Juliet Floyd]

re: Wittgenstein and Steiner

There is much more to say, historically and philosophically, about
Wittgenstein than I shall not attempt to say in this posting.  But I think I
ought to say here that Steiner has somewhat mislead readers of the FOM about
my particular interpretation of Wittgenstein on the Goedel theorem, which is
historical and philosophical.  I do NOT read Wittgenstein has having
established, or tried (unsuccessfully) to establish, that Goedel's
incompleteness theorems are "of no interest" to philosophy of mathematics,
as Steiner suggests.  To hold that these theorems have been misconstrued by
philosophers, that they are not of the significance that certain
philosophers are inclined to think they have, is also at the same time to
hold that they are of tremendous philosophical significance--or so my
reading of Wittgenstein is intended to suggest, as well as the reading I
proposed with Hilary Putnam in a recent paper in the Journal of Philosophy
(November 2000).  I do not hold that Wittgenstein "understood Goedel better
than Goedel"--that is a ridiculous assertion that I hope and expect readers
of the FOM will not associate with my readings of him.  The
situation--historically, mathematically, and philosophically--is more
complex.

I am inclined to agree with Bill Tait that Wittgenstein's relevance for
recent philosophy of logic and mathematics is, in direct terms, minimal,
though it is unquestionable that his philosophy of logic influenced in
fundamental ways the philosophies of Russell, Ramsey, Carnap, C.I. Lewis,
and many others (the dictionary meaning of "tautology", associated with
truth-functionally valid schemata, is due to Wittgenstein's philosophical
bent of mind and his particular construal of the truth-tables as an
alternative notation for propositions generally--on this cf. Dreben and
Floyd, "Tautology: How Not to Use a Word, SYNTHESE, 1991). To at least this
extent, his place in the history of general philosophy is unquestionable.
That he came to his views through a consideration of the philosophical and
logical works of Frege and Russell makes his remarks instructive for
philosophers and logicians nowadays, even if the conceptual difficulties
facing Frege and Russell were not identical with the conceptual and
mathematical difficulties facing logicians today.  I would add that
Wittgenstein seems to have been one of the first (wrongly) to conjecture a
decision procedure for all of logic, i.e., for validity, a point that,
somewhat ironically, links him with the tradition of analyzing the intuitive
notion of algorithm that culminated in Turing (during LW's lifetime).

I am inclined to think that Wittgenstein's thought will likely prove
fruitful precisely through the negative reactions to his remarks that
logicians and mathematicians are bound to have, reactions such as Harvey
Friedman reports of himself.  But that is still a contribution,
philosophically and mathematically speaking.


Juliet Floyd
Associate Professor of Philosophy
Boston University
745 Commonwealth Avenue
Boston, MA 02215
617 353 3745
FAX: 617 353 6805
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