Len Fehskens replies to me:

>>The theoretical basis of pure mathematics is of course no more (or
>>less) amenable to proof than that of a musical scale.
>
>I just can't make any sense out of this assertion.  Pure mathematics may
>be synthetic, but its foundations remain grounded in objective reality
>(counting).

I'm confused by your confusion.  Objective reality?  Pure mathematics
is synthetic, we agree; and what makes "counting" any more of an "objective
reality" than some of my fanciful wellsprings for music (to which I'll
now add the rhythm of the human heart, our old friend Crotchet=60)?

Without tripping the light fantastic down paths littered with very big
bear pits, can we not also agree that "counting" is conceptual, whilst
the heartbeat is apprehended through the only objective reality we can
truly rely on - our own senses?

Now our heartbeat may indeed be a subjectively experienced sort of
objective reality, as you suggest; but this still leaves music at least
as rooted in real world phenomena as the towering mental constructs of
pure mathematics.

As to real-world modelling, just because you can't build a cantilever
football stand using musical logic does not mean that it's any less utile
as a real world tool.  Take, for instance, the current research into the
well-established and perfectly quantifiable therapeutic effects of Mozart
on cows and students: a person, we might hope, is just as real as a
stadium!

All of which makes me worry that your "objective reality" and its
"subjective" antithesis may be double-edged tools which paradoxically
tend to blur at the edges the more we focus on them.  Not surprising,
really, as they too are just human concepts ...  which feeling, to return
to our onions, was probably why I took issue with you in the first place!

Christopher Webber,  Blackheath, London,  UK.
http://www.nashwan.demon.co.uk/zarzuela.htm
"ZARZUELA!"