FOM: Reply to Hersh: why isn't it a theorem?
Shipman, Joe x2845
shipman at bny18.bloomberg.com
Thu Jan 22 18:45:14 EST 1998
> Your question (1) was not, is this true, but is this mathematics?
> So my answer yes was correct, even though the statment in question
> is not a theorem but only a well justified conjecture.
> I don't see how reclassifying one statement as a conjecture rather
> than a theorem causes any difficulty for my philosophical position.
> Reuben Hersh
The difficulty for your position is that I am talking about the
activity of chessplayers, not the activity of mathematicians.
Even if no mathematicians cared about this problem, the community
of chessplayers has reached a reproducible consensus that meets your
criteria. You must either say that
1) There is no essential difference between the process by which
chessplayers have come to believe this is true (and take it from me,
they don't require any further proof than they already have to be
absolutely positively really truly sure) and the process by which
mathematicians have come to believe, say, Dirichlet's theorem ("If m
and n have no common factor then there is a k such that km+n is prime")
--they are both equally "mathematical" and both equally "theorems".
2) Although there is a difference between these two processes, it
doesn't matter because the chessplayers' process is interpreted by
mathematicians as strong evidence for the plausibility of the
conjecture and there is no essential difference between an extremely
plausible conjecture and a proved theorem
3) The experience of chessplayers doesn't count because you really
meant "reproducibility and consensus among mathematicians". But
there are sufficiently many chessplaying mathematicians that you'll
still need to say there is no difference between the way they believe
this conjecture and the way they believe Dirichlet's Theorem.
4) <Some other explanation which I look forward to seeing!)
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