[ExI] The "Unreasonable" Effectiveness of Mathematics in theNatural Sciences

[Lee Corbin]

Stathis writes

> I don't think mathematics is contingent on the existence of a material
> world. If it were, then 17, or its primeness, would disappear if
> enough of the universe disappeared. That would be an extreme form of
> anti-platonism.

I worry that you may be underestimating the incredibly drastic
counter-factual non-existence of practically everything that I
am reading into this.  No material world at all in this case would
not simply be one single vanishing set of six constants. This would
be *everything*. Nothing except the 17 electrons---no infinite
space, no electromechanical laws, no real numbers indicating their
separation---nothing. Just 17 things.

If I must be specific and guess at things we don't yet understand
about universes, then I can imagine a small topologically closed
one that is everything there is. It is not embedded in a larger space;
no observers; no concepts there; nothing.

I affirm, however, that if even 17 things were all that existed in this
way, an incredibly little bit of math would have formed as a result.
The evenness and the primeness of 17, and the other properties of
their subsets, say any 11 of them would have a very limited
extension (as we say in math, i.e. application or reference).
But we never have the concept of "how many subsets of the
seventeen particles exist", because no numbers of that
magnitude exist (in this extreme counterfactual world).

CLAIM:  The ancient riff/rift between mathematical platonists and formalists
(let's leave the logicists and the constructivist/intuitionists out of it for a moment
and let the big guys duke it out), is whether or not human beings or other
conscious entities have anything to do with the existence of numbers, shapes,
or math in general. 

TO WIT: The mathematical platonists say that intelligent minds have nothing
whatsoever to do with math; that math was preexisting long before intelligence
or subjectivity came into being (as most people take those terms), whereas
the formalists insist that math is the study of relationships and requires students
for its very existence. (Recall Jef's insistence on the importance of ***meaning***.)

Therefore, by asserting that math has only to do with the physical universe
it is completely  false to say that this is necessarily a non-math-platonic position.
(I agree that classical Platonism does see the physical world as mere shadows
of a higher abstract reality---but my guess is that even they may have divided
into factions over the question of whether or not not physical items brought
about those higher abstractions.)

I confess that I may be striking out into very new territory entirely on my own
here, i.e., that mine might be a minority position among the mathematical
platonists---indeed, most of them might concur with you that not the existence
of any physics, any universe, or any physical relationship is required for their
beautiful mathematical reality---their Platonia. But as for me, while agreeing
that mathematical relationships are timeless, they're still intimately tied up
with the existence of the physical universe and cannot be severed.

Moreover, although of course we PCR types hold that *all* conjectures
are tentative and provisional only, this is new enough for me that I may
have soon to admit error at your ruthlessly logical hands  ;-)

Lee