[FOM] Wittgenstein?

[William Tait]

On Monday, April 21, 2003, at 11:47  PM, Harvey Friedman wrote:

> *DID LW WRITE ANYTHING THAT CAN AT LEAST BE REASONABLY INTERPRETED AS 
> BEING SIGNIFICANT FOR THE FOUNDATIONS OF MATHEMATICS? IF SO, EXACTLY 
> WHAT?*

Harvey, I think that the answer is `yes', although I don't think that 
LW understood how his ideas applied to foundations of mathematics---his 
conception of the latter was inappropriate for the time he was writing 
(1930's, '40's). In the first place, his _Philosophical Investigations_ 
provides a (to me) convincing naturalistic conception of language and 
of logical and mathematical norms. Secondly, in the context of that 
conception, he argues (and again I am convinced) that questions of 
existence (Do physical objects really exist? Do other people/minds 
really exist? Do numbers, functions sets, etc. really exist?), when 
these are understood to be questions _about_ the language (as opposed 
to questions _within_ it, where they have trivial affirmative answers) 
simply spin their wheels. He sums it up in Section 402:

\begin{quote} For this is what disputes between Idealists, Solipsists 
and Realists  look like. The
one party attacks the normal form of expression as if they were 
attacking a statement; the others
defend it, as if they were stating facts recognized by every reasonable 
human being. \S 402
\end{quote}

That he excluded the mathematical Nominalist on the one side and the 
mathematical Realist on the other was, as I have already stated, 
because he did not really believe that discourse about sets and 
functions was an established part of mathematics and thought (quite 
contrary to the actual state of things by 1930) that it was just 
`language in holiday'.

If he is right about the wheel-spinning,  then  questions of 
`ontological commitment' in mathematics that are not based on issues 
_internal_ to mathematics (e.g. consistency) are suspect.

I hesitated to send this response because it seems to me that the fom 
list gets easily distracted from truly foundational questions. My 
compromise with myself in sending it is that I will not respond on the 
list to further questions about Wittgenstein. I just wanted to indicate 
that at least I thought that, with all of his pretense and arrogance 
and down-right ignorance, he in the end did have something to say of 
value in foundations.

Bill Tait