[FOM] Fw: Wittgenstein,Putnam, Floyd, Godel

[mjmurphy]

MessageT. P. Uschanov wrote:

I have read the recently mentioned Floyd/Steiner exchange in Philosophia
Mathematica over five times -- it is a truly excellent and entertaining
pair of papers -- and I have to say that I side with Floyd about
practically everything. Regrettably the exchange is not available
electronically (perhaps Floyd and Steiner will respond to Harvey
Friedman's request for summation?), but Floyd's earlier (2000) joint
paper with Putnam actually is available in PDF form at:

http://staff.washington.edu/dalexand/Putnam%20Readings/Notorious.pdf

I think it is the best brief paper on the issue published so far,
and I'd love to see discussion of it here.
------------


Thanks for pointing out this fascinating paper.  Some comments, and a
question for anyone willing to answer.

 I'd be inclined to reconstruct the argument in the paper (at least in its
"for dummies" version) as follows.  Godel gets a formal result in Russel's
symbolism (PM) which he would like to translate into English as "P is not
provable in Russel's system."  I guess English here is to be regarded as
seperate system, and moreover the system in which we "do" the philosophy of
mathematics in.  In fact I wonder if it would be fair to say that English is
standing in here for "Natural Language" or "Ordinary Language" as LW tends
to use these terms (especially the latter term.  See below)?   The paper's
authors (and LW) allow Godel the formal result,  but do not accept  the
proposed English translation of the formal result.  Their claim is that,
when speaking English, we would be prepared to give up "P is not provable in
Russel's system." as the translation of the formal result under certain
circumstances.  For this reason, Godel is unjustified in giving that
sentence as the English counterpart of the formal result.  Presumably it is
in English that any metaphysical claims (philosophy of math claims) must be
couched, so rejecting the sentence as an English translation means that
Godel is unjustified in making metaphysical claims based upon it.  I say
"presumably" English is the system into which philosophy of math claims must
be cast because otherwise you could demonstrate the philosophical
significance of Godel's theorem by simply giving the proof itself.  But
Godel wants to say something "broader" than the proof itself.

Put this way, the "notorious remark" looks like a variant of LW's contention
that technical philosophical languages are "de-linked " from Ordinary
Language, to the detriment of technical philosophy.  This seems to be the
point behind Hempel's statement, quoted in the paper, that all formal
languages are "explained in" ordinary language, and that formal language
should/ought to bear a "hereditary" relationship to Natural Language.  In
the absence of such a relationship the move from the formal result to some
Natural Language counterpart is a leap across the abyss, as it were, and
need not be accepted.

Cheers,

M.J.Murphy