[FOM] Wittgenstein?
Torkel Franzen
torkel at sm.luth.se
Sat May 3 00:10:42 EDT 2003
T P Uschanov says:
>I did not intend to claim simply that "we should say" that "There are
>statements that are true within PA that cannot be proven within PA,"
>only that if someone wants to convey the notion which "There are
>statements that are true that cannot be proven within PA" is ordinarily
>intended to convey, then that would be a better way of putting it.
It's difficult to make anything of this claim without knowing what
"A is true in PA" is supposed to mean. In your response to Neil
you suggest the following explanation of "p is true in PA":
>4) p is in the language of PA; being where it is within this language
>generally leads the users of the language of PA to hold it true; which
>in turn leads them (not necessarily wholly groundlessly) to make
>assertions such as your candidate 1) above.
It's not clear why we should be better off invoking these problematic
notions instead of ordinary mathematical definitions when explaining
why and in what sense there are true mathematical statements not
provable in PA. On the face of it, your explanation is not helpful in
understanding anything connected with Gödel's theorem. In particular,
is is not even superficially relevant to such statements as "The Gödel
sentence G-T of a consistent extension T of PA is true", since there is in
this case no suggestion that anybody holds G-T to be true.
>I simply think that viewpoints like this
>follow naturally from Wittgenstein's extreme version of non-realism, if
>followed through completely (in cold blood, or so to say)
I'm all in favor of exploring what follows naturally from Wittgenstein's
extreme version of non-realism, but we can't make old Witters responsible
for the shortcomings of our own philosophical musings.
---
Torkel Franzen
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