reply to Friedman FOM: new inductions unimportant
kanovei at wminf2.math.uni-wuppertal.de
Tue Mar 2 13:52:19 EST 1999
> From: cxm7 at po.cwru.edu (Colin McLarty)
> Date: Mon, 1 Mar 1999 20:48:44 -0500 (EST)
> In the language of any consistent formal theory there are statements, which
> the theory cannot prove, but which you actually accept because of inductive
> arguments not available in that theory.
This observation sounds very ridiculous.
Indeed, take PA as a consistent formal theory.
There are statements of PA which PA really
cannot prove or reject: say Con PA, the
Paris--Harrington theorem, and many more.
Some of them are accepted as true theorems
just because ZFC (or say 2nd order PA) proves them
(although PA cannot prove).
In those ZFC proofs there may happen some
induction arguments, of course, which cannot
be justified in PA (say because they appeal
to real numbers).
So what ?
This is a mathematical routine.
Why one can be so pompous of his own
discovery of this form of Goedel incompleteness
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