FOM: Reply to Hersh

Moshe' Machover moshe.machover at
Mon Mar 2 17:37:14 EST 1998

R Hersh says:

>I attempted an analogy between music and mathematics; the point
>was that as they are both (as you agree!) part of our social
>consciousness, they both exist only while the human race exists.

>If you disagree with my claim that mathematics (in the sense of
>pure mathematics, not in the sense of counting physical objects),
>is a human creation which exists only while humanity exists,
>then you can challenge and argue with *that*.

I think my comments have not been properly understood. I never meant to
challenge the claim that mathematics, like music, is a human social
creation. I regard this as quite trivial. Of course mathematics can only
exist so long as there are humans (or other creatures) that mathematize.
And a single isolated human individual could never develop the brain power
to mathematize or, for that matter, to engage in rational thought.

Rather, my comment were intended to highlight the constraints that apply to
the *content* of mathematics, primarily to mathematical propositions. To
paraphrase a famous saying: humans make their own mathematics; but do they
make it as they please? Social constructivists often repeat the claim that
mathematics is a social creation; but inside this harmless truism is
wrapped the false implication that mathematical truth is a matter for
social negotiation or social convention. *This* is where the analogy with
music, law and similar *conventional* social creations becomes positively
misleading. My comments were intended as a warning against this.

Obviously, there *are* constraints; and they are extremely strict.
Moreover, they are *unique* to mathematics. In my view you start to say
something profound about mathematics only when you say something that
characterizes and explains the unique, sui generis, constraints that apply
to its propositions.

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