FOM: R: Connections between mathematics, physics and FOM

[Luigi Borzacchini]

-----Messaggio originale-----
Da: Jeffrey John Ketland <Jeffrey.Ketland at nottingham.ac.uk>
A: fom at math.psu.edu <fom at math.psu.edu>
Data: lunedì 31 gennaio 2000 20.23
Oggetto: FOM: Connections between mathematics, physics and FOM


Dear FOM members,
   just few remarks about the abuse of ancient mathematicians' opinions in
this and other debates.
For example, J.J.Ketland wrote:

>(A) Plato’s dictum: Mathematics is a science of abstract patterns
>and structures...
>....The crucial point is that these abstract structures exist outside us,
.....
>...This is meant to provide a rough explanation for the very possibility
>of applying mathematics ....Again, the idea goes way back to Plato and
>before (Pythagoras, of course).


I never read that dictum. Actually Plato's opinion was deeply different: he
did not build Forms of numbers, and, most of all, the "ideal numbers"
('arithmoi eidetikoi', terms which is employed by Aristotle), if any, were
different from the "mathematical numbers" for a simple reason: how could
"even and monad become odd" when the Forms are immutable?
Then, I do not believe that Plato actually gave to arithmetic more than a
methodological role in connection with dialectics. In addition, if he could
accept the existence of ideal numbers (for which there is no evidence), in
his approach they had nothing to do with mathematics and physics, but had to
play a role just in simple 'numerology'; and this seems to me the exact
opposite of the thesis ascribed to Plato by J.J. Ketland.

>(C) Galileo’s dictum: the book of Nature is written in the language
>of mathematics....Physical particles
>move along continuous curves in continuous spacetime. ...So, the
>book of Nature will contain lots of analysis and reference to real
>numbers, and functions thereon.


Actually the language of mathematics for Galileo was only geometry, and
there is no algebra or analysis in his Opera Omnia. His mathematics was
simple arithmetic, euclidean geometry, and something from Archimedes. His
continuum was an infinite mixture of points and gaps. Obviously no real
numbers, no continuous curves in continuous space-time, etc.

About Zeno I can only believe that the reference is to another Zeno,
different from the Eleat.

Every reasonable thesis is welcome, but it is not correct to falsify the
ideas of ancient mathematicians to advocate a continuity in the history of
the mathematical thought that is a respectable but very  controversial
opinion.
                                                       Luigi Borzacchini