[FOM] Wittgenstein?

[Harvey Friedman]

When I posted my original message about Wittgenstein, 4/22/03 
12:47AM, I asked the question

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

I may have given the impression that I expect a simple negative 
answer to this question. I don't, because I had in mind (at least) 
two different senses of "significant" here.

1. LW might have work of clear scientific value bearing directly on 
issues in the foundations of mathematics, say in the way that Frege 
and Godel have done. This seems doubtful from what I have heard and 
what people are posting.

2. LW might have work of clear philosohical value which has, or could 
generate work of kind 1 if followed up carefully.

Actually, when I asked this question, I was expecting not 1, but 2. 
An interesting enough "ism" put forth with real finesse would likely 
be an example of 2.

For example, is LW a major force in nominalism and related views?

Roughly speaking, as I understand it, this is the view that only 
objects which have been named are legitimate items of discourse. 
Quantifiers should range only over objects which have been named.

Of course, this leaves open the crucial issue as to just what 
constitutes an appropriate name - perhaps how are names to be 
presented, created, etcetera.

While writing this, I see clearly how relatively high powered work in 
f.o.m. due to Godel in his Princeton Bicentennial lectures can, to 
some extent at least, be viewed from the point of view of nominalism 
- and I believe this way of looking at things leads rather quickly to 
interesting f.o.m. with serious mathematical component.

Another possible example from LW concerns the apparently rather 
subtle interpretation of LW concerning the importance and meaning of 
the Godel 2nd incompleteness theorem.

Credible people like Hilary Putnam (smile) seem attracted to such 
interpretations of LW, even though, on the face of it, LW seems to 
make no sense about such matters.

I don't care at all what LW **REALLY** meant, at least once it 
becomes controversial just what he meant. I am willing to use the 
phrase "Wittgensteinian" or "arguably Wittgensteinian", instead of 
"Wittgenstein".

I haven't looked into just what these so called subtleties in Godel's 
2nd incompleteness theorems are, preferring to see someone expert in 
this sort of thing lay it out **INTERACTIVELY** on the FOM email list.

Also, there is a persistent almost-claim here on the FOM that LW had 
a view that protects us from the famous Paradoxes - Ruseell's, 
Tarski's, etc. Of course, this is trivial to do - e.g., just don't 
allow any formal reasoning of any kind. But the interesting thing is 
whether or not there is any germ of an idea that protects all, or at 
least a significant portion of the math we really care about, yet 
protects us from the Paradoxes.

As is clear, I am knee deep in research on this, and if I have 
something to learn by thinking about LW, I will.

A deep enough full scale assault on the very idea of doing f.o.m. or 
constsructing any formal systems would also count as 2.