FOM: Mathematical Certainty: reply to Silver

Joe Shipman shipman at
Tue Dec 15 14:01:31 EST 1998

Charles Silver wrote:

>         This criterion may be right in all cases that we know of, but it
> is still possible for it to come out wrong.  This establishes that
> agreement and correctness are distinct.

I agree with you of course, but Hersh doesn't; I am not defending Hersh's position,
just talking about what arguments can be used against it.

>         I think you are doing something very different from what Hersh
> wanted to do.  Hersh wanted to capture the *meaning* of mathematical
> truth.  For him, agreement of a certain sort simply *is* mathematical
> truth.  I don't think you are claiming that your criteria capture the
> *meaning* of mathematical truth.  The very fact that you are asking
> whether anyone knows any counterexamples shows that the concepts
> "mathematically true" and "satisfy the criteria" are distinct.

Yes; but if no counterexamples can be found Hersh can maintain that this is a
distinction without a difference!  The point is that a counterexample would show
that his notion of mathematical truth did not entail a property of mathematical
truth that we would all agree on (namely incorrigibility) and therefore could not be
correct; without such a counterexample he is free to redefine what mathematicians
are "really" doing.

More information about the FOM mailing list