[FOM] Goedel on Wittgenstein

[Alasdair Urquhart]

>From Hao Wang, "A Logical Journey" p. 179.

Commenting on the Remarks on the Foundations of
Mathematics:

"Has Wittgenstein lost his mind?  Does he mean it seriously?
He intentionally utters trivially nonsensical statements.
What he says about the set of all cardinal numbers reveals
a perfectly naive view. [Possibly the reference is to 
RFM: 132 and the surrounding observations.]  He has to take
a position when he has no business to do so.  For example,
"you can't derive everything from a contradiction."  He should
try to develop a system of logic in which that is true.
It's amazing that Turing could get anything out of discussions
with somebody like Wittgenstein."

"He has given up the objective goal of making concepts and
proofs precise.  It is one thing to say that we can't make
precise philosophical concepts (such as apriority, causality,
substance, the general concept of proof, etc.).  But to go
further and say we can't make mathematical concepts precise is
much more.  In the Tractatus it is said that philosophy can't be
made into a science.  His later philosophy is to eliminate also
science.  It is a natural development.  To decline philosophy
is an irrationalistic attitude.  Then he declines all rationality --
declining even science."

In reply to Menger 1972, on Wittgenstein's discussions of the
incompleteness theorem:

"It is indeed clear from the passages you cite [RFM:117-123,
385-389] that Wittgenstein did NOT understand it (or pretended
not to understand it).  He interpreted it as a kind of logical
paradox, while in fact it is just the opposite, namely a 
mathematical theorem within an absolutely uncontroversial part
of mathematics (finitary number theory or combinatorics).  
Incidentally, the whole passage you cite seems nonsense to me.
See, for example, the "superstitious fear of mathematicians
of contradictions." "