FOM: Re: Internal/External Characterizations. Response to Silver

Charles Silver csilver at
Sat Jan 24 19:42:59 EST 1998

	I said some mushy things about fusing mathematical consensus (its
"external" part) to what mathematics is about (its "internal" part) by way
of an "if and only if" or possibly just an "if".  In response, 

On Sat, 24 Jan 1998, Moshe' Machover wrote:

> The external part of Hersh's characterization, the
> special quality of consensus that is uniquely possible in mathematics (and,
> I insist, is qualitatively different from anything possible in the
> empirical sciences, let alone the humanities) would then have to be
> *explained* by the internal `aboutness' of mathematics. Thus the latter
> only is fundamental, and the former merely derivative. It is only the
> `aboutness' of mathematics that is really determinative of what mathematics
> is.

	That would mean that there would be only an "if" going in the
wrong direction for Hersh's purposes.

Moshe' Machover concludes:

> Therefore Hersh's sociological observations about consensus among
> mathematicians--whether or not they are correct--cannot in principle be
> used to characterize mathematics.

	I think this is correct.  I think Hersh needs to say that
consensus is a necessary but not a sufficient condition of mathematics. 
Hmmmm.  Is it even necessary?  Your remarks above seem to indicate that
you think it is (when you say there is a special quality of consensus due
to what mathematics is about). 

Charlie Silver
Smith College

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