FOM: Comments on Simpson on Hersh

[Moshe' Machover]

While agreeing with Steve Simpson's objectivist position *contra* Hersh, I
would like to question two of the former's statements.

1. Hersh is not an objectivist, at least not in the same sense as SS (or
me). But this does not make him a *sub*jectivist. Subjectivism makes truth
depend on the individual subject, which is the last thing Hersh would
accept. What his social-constructivist position re mathamtical truth does
imply is cultural *relativism* rather than subjectivism. If mathematical
truth is constituted by consensus, then presumably it could be other than
what it is. In biblical times the consensus among the Jews was that the
circumference of a circle was three times its diameter (this was not just
consensus, but holy writ: I Kings, vii, 23); so presumably in that society
it was true that pi = 3.

2. SS claims

> Our mathematics has flourished and will continue to flourish in the
> context of Western culture and civilization.

*Has flourished*--yes, certainly. But *will*? How can you be so sure that
Western culture and civilization, as it evolves and transforms itself, will
remain invariant w.r.t to its attitude to mathematics? From my experience
here in Britain I fear that there is a great and continuing decline in
support for pure mathematics and other theoretical subjects which are not
seen as economically useful, as finance for academic institutions is
decided more and more by those who (as Oscar Wilde's put it) know the price
of everything but the value of nothing. I am not sure what the situation is
in the US, but judging from some of what I have read (including fom
postings by Harvey Friedman, for example) I infer that there is perhaps a
similar decline in support in your country, although the starting point may
have been higher. Is this trend not part of Western culture and
civilization? And if the trend continues, will the active development of
pure mathematics (and other non-maketable pursuits) not be extinguished, as
happened to Greek pure mathematics after about AD300?

Moshe' Machover
Professor of Philosophy (formerly Reader in Mathematical Logic)
King's College, U of London
Research interests
	Past: logic, genralized recursion theory, nonstandard analysis
	Present: philosophy of maths, social choice (maths applied to
	political science)