[FOM] Wittgenstein and FOM

[mjmurphy]

Harvey Friedman wrote:


Is there anybody on the FOM list prepared to outline the LW attack or
any other attack interactively?
-------

I don't see it as an "attack".  That is, it is not a matter of LW's
attempting to refute some piece of mathematics.  I would say vaguely that he
was "attempting to change attitudes" (towards consistency, for example) or,
if this were a different list, that he was engaged in a kind of "ideological
critique". (See below)

 Mark Steiner wrote:


>     Let me give an example of this.  Wittgenstein, in a face to face
>exchange with Turing (who attended his classes in 1939), argues that the
>obsession with consistency on the part of logicians (Hilbert) is a
>superstition.  Hidden consistencies he argues can never affect the
>application of mathematics, and when an inconsistency crops up no engineer
>would argue that "anything follows from this."  Turing, on the other hand,
>argued that "bridges could fall down" if we apply an inconsistent system,
>because there are ways of arguing for any conclusion q in an inconsistent
>system without actually going through the step "p and not-p".  E.g., by
>arguing from not-p to if p then q in one proof, and then proving p in
>another.

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Putting aside the issue of "hidden contradictions" for a moment, I think the
point LW was trying to make here with respect to the "obsession" with
consistency is something like the following.  He asks Turing: "Why should we
care if our system is inconsistent?"  Turing's answer is "Because in the
application of an inconsistant system we may cause a bridge might fall
down."  Another possible answer is "Because if we interpret the sentences of
the sysem as a set of instructions, then given the instruction "p & ~p", we
will not  know how to behave."  But LW would say that we should not allow
contingent matters of psychology (in the latter case) or physics (in the
former) to determine the proper focus of the philosophy of mathematics.   If
Turing's answer is convincing, then it would be okay to have an inconsistent
system at some future date if we were all made immortal and didnt't care if
our bridges collapsed.  But this too would be an irrelevant, external
consideration.

This kind of criticism doesn't refute anything.  LW is urging the FOM people
to "throw off their chains"; to consider roads untaken (maybe leading to
paraconsistent logic?) etc. etc.  It isn't like anyone has to do that, or
even be moved by the plea.

Cheers,

M.J.Murphy