[FOM] Re: Wittgenstein?

Torkel Franzen torkel at sm.luth.se
Mon Apr 28 03:12:11 EDT 2003

Mark Steiner writes:

     >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."

  The question whether a hidden contradiction can lead to bridges
falling down is a reasonable one, as is the more general question how
we do in fact handle inconsistencies and other forms of murkiness in
our thinking and theories. But note that Wittgenstein, according to
the students' lecture notes, says he "failed to tempt" Turing into
making certain further claims about consistency. Wittgenstein's views
on consistency were radical, and may well represent the only
consistent anti-realism with respect to elementary mathematical
statements to be found in the philosophical literature. In the
_Bemerkungen_, Wittgenstein says:

     But here I must make an important point: a contradiction is only
     a contradiction when it arises. People have the idea that there might
     at the outset be a contradiction hidden away in the axioms which
     no-none has seen, like tuberculosis...one day the hidden contradiction
     might break out, and then the catastrophe would be upon us. What I am
     saying is: to ask whether the derivations might not eventually lead to
     a contradiction makes no sense at all as long as I'm given no method
     for discovering it. ...There can be no such question as whether we
     will ever come upon a contradiction by going on in accordance with the
     rules. I believe that's the crucial point, on which everything depends
     in the question of consistency.

Torkel Franzen

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