Date sent:      	Fri, 22 Dec 2000 11:52:10 -0400
Subject:        	re:  Philosophy of Mathematics
To:             	johnny at charm.net
From:           	mbillington at holton-arms.edu (M Billington)
Send reply to:  	johnny at charm.net



Mr. Green, you wrote:

>>In fact, your criticism of epicyclic theory that they are
>> blind to fundamental principles, sticks firmly to the correspondence
>> theory of truth.  I'll bet that you deny that the coherence theory
>> of truth (if I could explain it adequately) applies to science at all.

>I thought I was agreeing with you.  How am I disagreeing?

No disagreement that I can see.  I am still clarifying the parameters of
the discussion started long ago by Mr. Mark.  Here is where I think we are:

On the one hand, we have science.   Science makes models in the mind that
*correspond* to observed data.   Science makes progress by including more
and more observations in its models.   A model that hasn't been confirmed
by observation is just speculation.  Since the models are often
mathematical, math functions as a handmaiden to science.   Science tries
to find the unifying principles that underlie matter, energy, space, and
time, e.g., the inverse square law unifies more observations than do
epicyclic calculations.

On the other hand, we have mathematics.  Mathematics explores the
properties that flow from certain postulates.  Mathematics makes progress
by unfolding the implications of those postulates.   Mathematical truth is
*coherent* because its statements follow the logic created by our own
minds.  A system that does not possess a logic, even a new and/or weird
logic, is not a system.  Sometimes some mathematical systems have
real-world correspondences, but scientific application is a by-product of
mathematics.  Mathematics is a playground of the rational mind, e.g.,
Newton's fanciful force laws.

Now, what happens when fanciful mathematics produces a unifying principle
which results in a specific observation, e.g.,  Einstein’s predicted
apparent displacement of that star, or Gell-Mann’s "bold" prediction
of the top quark?    In that case, it is hard not to say that
mathematicians have got hold of something "real", maybe "more real".  Does
that kind of mathematics contain a knowledge of the deep structure of
reality?  

I was going to predict your answers, but I'd better let each of you answer
that.  Other answers:

Galileo and Newton say, yes, because God is the Great Geometer.  By
exploring physics, we explore the mind of God.  God is a given.

Pythagoras says, yes, because everything is Number.  Number is the
ultimate ground of both mind and matter, the rational and the observed. 
(Why?)  

Plato says, no, but practicing that kind of mathematics is good practice
for  apprehending the Forms.  The prior existence of the Good is a given.

Yes, because what's in our minds as microcosm is also in the world as
macrocosm.  We ourselves are outcroppings of the universe.  At bottom, we
are the universe.  

No, because there is no deep structure of reality.  It is only a
projection of our minds.  The deep "structure" of reality is Being.  It is
found in union with the One.  If you meditate enough, you can find this
out for yourself.

Maybe, because whatever we discover, we are limited by our senses.   We
can never be sure whether other realities exist outside what science can
capture.  An agnostic's answer.

----------
Marion L. Billington  SF'78