FOM: Platonism and social constructivism

Moshe' Machover moshe.machover at
Tue Mar 24 19:35:40 EST 1998

At 8:27 am -0700 24/3/98, Reuben Hersh wrote:

>I think I agree with everything in your message.
>It seems to me our only difference is of emphasis.
>In particular, I have written repeatedly that once a mathematical
>entity is invented, it has definite properties which we are not
>free to choose, and which may be difficult or impossible for us
>to discover.
>By your definition, I am therefore not a social constructiviist.
>But this is a label that I have never adopted.  Others have
>chosen to attach it to me, without my permission.

I prefer not to stick any labels on individuals; I am for
self-determination: let people choose their own labels.

But I think the difference between Hersh's position and mine is a bit more
than just a matter of emphasis. I tried to point it out in my previous
posting (to which Hersh responded as quoted above).

It is this. If I'm not mistaken, Hersh believes that by stating the things
on which we seem to agree (the social nature of mathematical activity, the
status of mathematical objects as human-social inventions) one is solving
or dissolving a big problem. I, on the contrary, hold that this is just
where one of the most profound problems of the philosophy of maths only
*begins*: how to account for the ineluctable, necessary, objective nature
of mathematical propositions.

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