[FOM] Wittgenstein?

[Alasdair Urquhart]

In reply to Harvey Friedman's 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 think one can give a qualified positive response.  The best evidence
for this is that LW had a fairly direct influence on some
logicians.  Here the early work had much more influence than
the later work.  I list the clearest cases of this.

1.  Frank Ramsey's formulation of simple type theory in his paper 
"The Foundations of Mathematics" is clearly inspired by the Tractatus
view of logic -- Ramsey is quite explicit about this.  The extensional
view-point so strongly espoused by Wittgenstein is at the heart of
Ramsey's approach.  More generally, I think Wittgenstein's strongly
held extensional approach had a broad influence, in model theory 
and elsewhere.

2.  Carnap's work on the semantics of modal logic clearly has its roots
in Wittgenstein's ideas in the Tractatus.  In particular, the notion
of state description can be traced back to the Tractatus.

The later philosophy had much less direct influence on logic, and this
is not surprising, given its generally anti-formalist bent.  
The only logician to have been quite deeply influenced by the later
philosophy (I believe) was R.L. Goodstein.  In his case, the influence
took the form of trying to make logic as concrete as possible.
The best known example of this is his clever reformulation of epsilon-0
induction as a problem in notation for integers, a very early example
of "miniaturization" in logic.  Harvey should find this particular example
interesting, as a lot of his own work is in the direction of making
logic more concrete.