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.