FOM: indubitability (or "certainty")
jkennedy at bucknell.edu
Fri Oct 2 13:33:51 EDT 1998
Regarding M.R.Holmes remark:
>2. It is possible to doubt the correctness of something presented to
>one as a completely formal mathematical proof because one cannot grasp
>it all at once; one cannot tell whether it is such a proof or not.
>This is not a challenge to the indubitability of mathematics; it is a
>realistic problem with human capabilities.
Wittgensteinian skepticism challenges the part of Holmes' position stated
above. Wittgenstein's idea being (I think) that proofs that are too big to
grasp all at once DO present a challenge to the indubitability of
mathematics. He uses in support of this the example that there is no way to
know that the rule we use to multiply numbers is stable under the passage
from small to large numbers. Kripke's "Wittgenstein: On Rules and Private
Languages" gives an exposition of this. (Please forgive if this is not
exactly the right title.) It is a (to me) elusive and difficult argument
that seems at first glance implausible in the extreme. Does anyone have a
clear description of Wittgenstein's postion? I am not sure I understand
Wittgenstein's argument very well.
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