Date: Jan 5, 2013 10:22 PM
Author: fom
Subject: Re: The Distinguishability argument of the Reals.

On 1/5/2013 4:32 PM, Virgil wrote:
> But mathematics is NOT a science. Its truths and values are in no way
> dependent on physical experimentation or scientific observations of the
> physical world


I would actually disagree with this. The meaning of the
word "science" changed significantly in the nineteenth
century as "scientist" became a profession.

Modern logic discusses belief in terms of propositional
attitudes. If you read Aristotle, there is a slightly
different organization. There are three books: Prior
Analytics, Posterior Analytics, and Topics.

Prior Analytics discusses what is shared between
Posterior Analytics and Topics. Posterior Analytics
concerns itself primarily with the nature of demonstrative
science. Topics concerns itself primarily with the
nature of dialectical argument (rhetoric). The latter
is the use of the deductive calculus arguing from
belief. The former is the use of the deductive calculus
arguing from principles (assumptions and definitions).

From my perspective, mathematics is the science.

As for what you are referring to as science, Bertrand
Russell once observed that all of the "soft" sciences
were trying to ground themselves in physics at the
same time that physics was grounding itself in
mathematically-defined entities.

Have you ever asked yourself what the topology
of general relativity should look like if the
time cones were to be taken as the basis of the
topology? My bet is on a non-metrizable Moore
space.

How does one even get a physicist (or a WMythologist)
to even see the possibility of something that cannot
be measured relative to the rigid motions of a
platinum bar in Paris?

But do not misunderstand me. There is an
astounding theoretical coherence to our current
physicalist understanding of the universe. And,
without measurement, it is difficult to see how
that could have been accomplished.