FOM: Objectivity: reaction to Detlefsen and Hersh

Moshe' Machover moshe.machover at
Sat Dec 20 19:47:36 EST 1997

Since Michael Detlefsen has addressed a direct question to me, I must
reply. But first I wish to second his plea that

>this discussion group should be about ideas and arguments, not about
>>employment status or class membership.

I'm glad someone registered displeasure with ad hominem arguments and
personal attacks. (I would have thought the moderator would intervene to
calm immoderation.)

No, I do *not* count myself `among the social construction crowd', because
as I understand their position, it is relativist (or, to use a buzz-phrase,
post-modernist). They claim that mathematical truth is not truly objective,
but a social convention that could be other than it is. Thus they deny what
I, like Reuben Hersh, take for granted:

>"Mathematics" is what we call the supremely objective part of human

But I do accept their premiss that mathematics, and the very concepts
involved in deductive proof, are socially constructed. This is because both
language and rational thought, and indeed all human cognition, are socially
constructed. To MD's question:

>Why 'social'construction rather than, say, invariant individual
>>'psychological 'construction?

--my answer is: because I don't believe there is such a thing, in the
strict sense--that is, as something having its origin in an individual
psyche that could exist, develop and function in isolation from social

Mathematics is *not* distinctive in *this* respect. It *is* distinctive in
being objective but--unlike empirical science--not being `about'
objectively existing objects. (Like Solomon Feferman, I find platonism
unbelievable.) Hence the puzzle, which SF articulated very clearly.

RH says:

> That still leaves Kant's question, "How is mathematics possible?"  If
>that >question is ever answered, it will be answered by neurophysiologists
>sociologists, not by logicians or philosophers.

I don't really care to what trade union those who answer the question will
belong. The question itself I regard as being about FOM.

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