FOM: Comment on Hersh

Moshe' Machover moshe.machover at
Sat Feb 28 19:07:52 EST 1998

R Hersh says:

>	Some people find this conclusion shocking.  One may point to
> some beautiful theorem of Lagrange and say, "Isn't it obvious that this
> was always true, before there were any humans?"

> 	You could just as well cry, "Listen to this wonderful symphony of
> Beethoven!  Isn't it clear that this was always beautiful, even before
> Beethoven was born?"

> 	It seems to be especially logicians, foundations-of-mathematics
> specialists, and academic philosophers of math who find this idea
> upsetting.

Not so much upsetting as erroneous. The analogy is false.

If we, lovers of Beethoven symphonies, meet people from another culture who
find that music ugly or boring, then the proper reaction is to agree to
differ, each culture respecting the other's different taste. Neither we nor
they are `wrong'. Reasonable people don't argue about taste.

If we come across people from another culture who think Lagrange's theorem
is false, then the proper reaction would be to debate the issue until it is
cleared up. Perhaps their culture is not as developed as ours, so they
don't understand the theorem or its proof; or perhaps they are more
advanced, and have spotted a fault in the proof, or discovered a
counter-example. They or we *must* be wrong. Reasonable people do argue
about truth.

A Beethoven symphony and a theorem of Lagrange both exist in social
consciousness. But there is a vast difference in their status. The
`validity' of the former is a matter of cultural choice. The validity of
the latter is not: there is right and wrong, superior and inferior.

I'm sorry to have to make such an elementary point.

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