First off, in response to ** matt**:
Yeah, you may be right. It’s possible that axioms don’t have intrinsic value. Nevertheless, it would certainly appear that some axioms reflect Nature more accurately than others. That’s kind of what I’m trying to ask: given that we don’t have a standard by which we can compare axioms, how do we know which ones to choose? Or are we left to a kind of blind relativism?
I think part of my confusion with this question stems from the fact that I’m at this point no longer really sure about the difference between an axiom and a hypothesis. This is why I don’t know if I can find a good example for you. I can give plenty of examples wherein hypotheses have been proven false, and I’m sure you can too. But axioms? Let us say that before Copernicus, it was axiomatic that the earth was the center of the universe. That’s now been proven to be false (not really, but at least in the sense it was understood back then). Is that a good example? I’m sure you will point out the utility of Copernican astronomy as opposed to Ptolemaic, but even if Copernican calculations are simpler, that isn’t the only reason Ptolemaic astronomy was abandoned.
I’m not sure how utilitarianism fits into this discussion, except possibly as an expedient method to judge between competing axioms. Was that the sense of your statement?
Finally, regarding science, you state that it is based on faith. Religion is also based on faith. Does this make science a religion? 
Well, okay, now to tackle oldscratch, and hopefully demonstrate that his PROOFS are really based on FAITH….
I’ll take your points in reverse order. You ask for examples as to why you can’t assume that just because a chemical reaction occurs a certain way one time, it will occur that way again. Fair enough. First off, let me start with a disclaimer: I’m not stating a dogmatic position here; there are probably philosophers of science who would agree with you. (I’m not much of an expert in this field either.) However, to state it briefly: the problem with your assumption lies with the faults inherent in inductive reasoning. I referred to this above, briefly, when I mentioned Hume.
As I’m sure you know, inductive logic attempts to derive general laws from a limited number of observations. This is both its strength and its weakness. Inductive logic states, “If such-and-such happens see-and-so many times, then there’s gotta be a law.” Sure thing, except that induction has been found to be wrong on numerous occasions. The classic example, often used in introductory discussions on the subject, is the “black swan”: scientists see several hundred (or thousand) white swans and come to the reasonable conclusion that there’s no such thing as the black one. Then, suddenly, a black swan is discovered, and induction is proved wrong. ( This is used as an example because it’s historical, by the way: scientists actually believed there was no such thing as a black swan until they discovered a gob of 'em in the interior of Australia in the mid-1800s.)
But a simple thought experiment can perhaps demonstrate my point. Let’s say I’ve never tossed a coin before and am interested in discovering how coins behave when tossed. I toss one five times and it lands heads up every time. Am I then justified in positing that a coin will always land heads up? I’m sure you’d say, “Of course not Svinlesha, you ignorant slut” (or something to that effect). In point of fact, even if I were to toss a coin 100 times and by some miracle it was to land heads up every time, I still couldn’t establish that there is a natural law stating that coins always land heads up.
Inductive logic relies on the assumption that the past always repeats itself in the present and the future. But unfortunately, this is nothing more than an assumption, an act of FAITH on the part of the assumer. That was David Hume’s point.
Admittedly, now, this is somewhat counter-intuitive. I remember that it took me a while to get my head around the idea after I first discovered it. Imagine my surprise to discover that it also literally stumped most of the philosophers of the time. Anyway, from the viewpoint of strict logic, you can never assume a general law is in place ** no matter how many examples of that law you produce. ** And if you don’t like it, well, don’t blame me bub; I didn’t do it. You quite simply can never rule out that there’s some force, or influence, or whatever, of which neither you nor no one else is aware, that is influencing events. And that’s why you can’t ever prove that just because a chemical reaction occured in certain way one time, it will occur the same way next time.
This post has gotten too long, so I’m just going to touch on your other points very quickly. With regard to “repeatability”, apologies, I may have misunderstood your meaning. But remember that “real objects” are experienced too, and the dividing line might not always be that sharp.
As regards the voting patterns of San Franciscan rodents, I think we are actually in agreement. Although, it would be absurd for any rodent to vote for the Prime Minister of England; if I was a badger, I’d definitely vote Nader! But see comments to matt above regarding the difficulties posed by the fact that logic seems to be useless in determining the validity of axioms. You make the very accurate point that without any method of determining the truth value of axioms, absurdity results. That also happens to be my point; our differences stem from the fact that you believe you have solved the problem, whereas for me it’s still unresolved.
Finally, an apology for being so fuckin long-winded.
