[FOM] FOM posting-Wittgenstein?

[Mark Steiner]

Juliet Floyd writes:

 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.



What I wrote in my posting was:

  I also read LW as arguing that
Goedel's theorems have no significance for the philosophy of mathematics--a
disastrous error even from LW's own point of view, as I understand it (cf.
my remarks on Juliet Floyd's views in Philosophia Mathematica, vol. 9,
257-279).

    I think this says, and certainly intended it to say, not that Juliet
reads LW this way, but that I do (this would follow immediately from LW's
pronouncement in Philosophical Investigations that no advance in mathematics
can contribute to philosophy in any way).  I apologize for any
misunderstanding caused by this passage.  I hope the article in question
correctly reflects the high regard I have for Juliet's work.  Our agreements
on interpreting LW far outnumber our disagreements and I would like publicly
to thank her and the late Prof. Burton Dreben for long discussions on these
matters in their house during the years 1997-8.

    In my article I also read LW as suggesting that Goedel's proof of the
theorem is invalid, since he presents an argument for the proposition "There
are true sentences in Principia Mathematica  that are not provable in
Principia Mathematica" very much like the informal argument (the one
analogous to the liar paradox) Goedel himself presents in the Introduction
to his theorem, and then proceeds to attack the argument.  Obviously Juliet
has another reading of this "notorious passage" and so does Prof. Hilary
Putnam.  I think Goedel himself read the passage my way, which is what
raised his ire against LW.

Mark Steiner