[FOM] FOM posting-Wittgenstein?

[Harvey Friedman]

Reply to Floyd 4/26/03 11:10 PM and Steiner 4/28/03 10:27AM.

Floyd:

>...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.

It would be valuable for the FOM list to have some sketch, however 
brief, of your reading and/or Putnam's reading of LW regarding the 
incompleteness theorems. Many readers will be interested in this, 
even if they do not have the time to go look up and carefully read 
subtle philosophical papers. Moreover, I am sure your paper(s) were 
not written for f.o.m. experts, but rather a more general 
philosophical audience, and so couldn't take certain things for 
granted.

I am interested because it will be a very efficient way of causing me 
try to strengthen some features of the incompleteness theorems.

>
>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.

Additional fruitful negative reactions may come from the discussion I propose.

Steiner:

>
>
>     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).

"No advance in mathematics can contribute to philosophy in any way" 
is quite interesting. For me, the trouble is that I can find a 
reading of this so that I can almost agree with it. However, change 
it to

"No use of mathematical thought can be a primary component in a 
contribution to philosophy"

and then my negative reaction becomes unbounded.

The discussion I am proposing could even spill over into questions like

what is philosophy?
what are philosophers trying to accomplish?
what could philosophers accomplish?
what are the most promising research projects in philosophy at this time?
what are the most important achievements in philosophy ever?
what are some of the most important developments in philosophy since 
1800? Since 1850? Since 1900? Since 1950?
what could philosophers of science accomplish?

This might well get too far from the scope of the FOM list. One could 
restrict this to philosophy of mathematics.

>
>     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.
>
Maybe Steiner can tell us more about the readings of Floyd and Putnam.