Truth is a quality a proposition or set of propositions have to greater or lesser degree depending on the extent to which one predicts/believes they will not have to be altered to comport with new observations. 1+1=2 is true because it has withstood the test of time and one anticipates no circumstance in which it may not comport with observed reality. 1+1=2 is "true" because, given the evidence, it will very, very, very, very probably not be observed to be false.
But truth has no binary nature because the universe is not deterministic but probabilistic.
> b) Can you then show me that this truth is not relative but objective or
> at least universal? Not in terms of particulars but in universal
> scope?
Truth always has a sense of relativity because to establish truth you have to compare the prosposition to reality and reality is always changing.
> c) How do you define "superior"? Do you really think that astronomy is
> superior to astrology (for explaining the nature of the universe) in
> every sense? How do you expect to demonstrate that conclusively?
Atrology has little or no predictive value. Astrological systems fail again and again to predict anything about the universe. The propositions of astology do not comport with reality - except by pure chance.
The propositions of Astronomy do comport with reality and like all science, they get better and better with each observation. Astrology never improves because it is based on nonsense - a stopped clock that is right twice a day.
Therefore astronomy is superior to astrology in terms of truth, but astrology sells better.
> d) What does superiority have to do with truth? Ptolemaic system of
> planetary motion were probably superior to whatever it replaced. Does
> that make it "true"? Is Reimann geometry true?
Nature is at it is. Our propositions can only be partly true. At the time of Ptolemy, that system was a superior approximation that what had come before therefore it was more true. Reimann geometry is more true than Ptolemy's system or Newton's.
> e) What is meant by "validity" (of science)? Valid in what sense? In
> representing "truth"? In being "superior"? Or just in the mundane
> sense of being more reliable than a few other systems?
What's mundane about being able to predict what Nature will do rather than making random guesses? And there really is no system of observing the universe but science because science is agnostic to the content of its own propositions. It only asks that we measure these propositions against Nature.
Science does rely on mathematics, but mathematics is pure logic, again agnostic, other than proposing a few first principles which are still arguable and argued about.
> f) Can you define "science"?
The process of measuring propositions against Nature and mathematics
> g) When we abandon one system of explanation for another because the
> latter is more parsimonious or more elegant (easier to work with,
> etc), is this because the latter is more "true"? Or is it just a
> matter of "taste? (a preference for parsimony, elegance, etc).
Science constantly abandons systems of explaination, as you know. In fact, it is the process of permanent skepticism. Truth simply does not exist as a valid concept in science. Something is may be confirmed by observation, but that doesn't make it true. Confirmation by observation just makes it more likely to be true. New systems can be simpler and more complex - it doesn't matter. The only test is whether they comport with Nature and mathematics.
I really don't think there is any real contest between Science and any other system.