[FOM] Floyd, Putnam, Wittgenstein

[Timothy Bays]

Re:  The Floyd and Putnam piece being discussed here by Floyd, Steiner 
and Franzen.

I'm afraid I find this paper rather baffling.  Early on, the authors 
seem to argue that, if we were to discover that PM proves ~P (here, P 
is the  "I'm not provable" sentence from the proof of Godel's first 
incompleteness theorem), then we would/should *abandon* N as the 
canonical model for interpreting arithmetic and begin interpreting 
arithmetic on the non-standard models which satisfy PM.  (And, when we 
notice that P doesn't reliably evaluate to "P is not provable" when 
interpreted on such non-standard models, we would/should ``give up'' 
the  interpretation of P as "P is not provable").

But surely this isn't right.  If PM turns out to be w-inconsistent 
(e.g., because it proves ~P),  then it seems far more likely that we 
would modify PM rather than accept non-standard models as canonical for 
arithmetic.  Even if PA---a far more widely accepted system than 
PM---turned out to be w-inconsistent, we would hold that against PA 
(and look for some modification of PA's induction scheme which lets us 
regain soundness).    I simply can't imagine that we would keep PA as a 
standard axiomatization of arithmetic, and (therefore) accept 
non-standard models as canonical.

So, I'm puzzled on this one.

For those who are interested, I have a short paper on this topic which 
lives on my website (http://www.nd.edu/~tbays/papers).  It's still 
(very) drafty, but it's there for any who happen to be interested.

Timothy Bays
Assistant Professor of Philosophy
University of Notre Dame
timothy.bays.5 at nd.edu
http://www.nd.edu/~tbays