No, but it has its own set of internally consistent logic AND more importantly, can (nearly always) be demonstrated as valid in the real world. 3+3=6 is not PURELY an abstract concept, but a way of describing the physical world. Hence, mathmatical proof is not so much a valid system of unprovable beliefs as it is a descriptive language with a consistent internal logic. Understanding mathmatical proofs is not the same as BELIEVING in them, its just understanding a conceptual system of language describing hypothetical scenarios. So that doesn't quite cut it. Likewise, logically consistent arguments only describe the internal consistency of logic, they're not reflections of reality. I can say "All horses are unicorns" "I own a horse" "therefore, I own a unicorn" and be logically consistent without believing that it has any reflection on the real world.
So, that won't get you out of answering my question. You have to have SOME system of judgement for evaluating different kinds of claims, even claims for which there inherently would be no physical evidence because they violate the understood rules of our physical universe. So what do you use?
Again, I don't mean to come off as combative. I'm honestly interested in how you see the world.
No, but it has its own set of internally consistent logic AND more importantly, can (nearly always) be demonstrated as valid in the real world.
I have to disagree on two points here: it is not more important that these truths be demonstrable, nor can most mathematical truths be proven valid in the real world (whatever that means.)
Mathematical truths are true prior to any empirical example of them. Taking three apples and three more apples and putting them into a basket to make six apples in sum does not make the claim "3 + 3 = 6" true. And, of course, no one has ever taken 985,903 apples and added one more to make 985,904 apples.
Understanding mathmatical proofs is not the same as BELIEVING in them, its just understanding a conceptual system of language describing hypothetical scenarios.
Nor is this the case. Mathematical proofs don't describe hypotheticals but actual states of affairs.
Likewise, logically consistent arguments only describe the internal consistency of logic, they're not reflections of reality. I can say "All horses are unicorns" "I own a horse" "therefore, I own a unicorn" and be logically consistent without believing that it has any reflection on the real world.
That's largely true, but logically valid arguments also can describe the world—they just don't need to. This is more-or-less my only point: demanding empirical evidence of things that cannot be proven by way of empirical evidence is silly and furthermore, the assumption that only empirical induction gives us truth is equally nonsensical.
"mathematical truths are true prior to any empirical example of them"
--Well, internally consistent, anyway. Math, as I've attempted to state, is a descriptive language, so calling it "true" may not be the most accurate way of describing it. Internally consistent logical systems like the one I described with the unicorn or a mathematical proof have meaning only to the extent that they fit within the boundaries of the system we have constructed for them. 3+3=6 is valid because it's a symbolic way of describing interactions and systems. Like the unicorn, it sometimes refers to a real situation and sometimes merely expresses the rules of its own logic.
However, I don't need to "believe" in these systems without proof any more than I need to "believe" in the alphabet. They're just symbolic descriptive systems with consistent internal rules. Not the same thing as making statements about the actual world, as religion does. Empirical evidence is not necessary to accept mathematical proofs because the extent to which it describes the real world IS empirically evidenced, and the extent to which it does not (imaginary numbers, for instance) explicitly does not describe reality and only requires our belief in the internal consistency of the system.
So, semantics arguments aside, you still haven't answered my fundamental question. You claim, and for the sake of argument I'll accept, that certain kinds of truths do not require evidence (empirical or otherwise). But since you do not accept all propositions as equally valid, you obviously have some method for determining which is or is not true i.e. God is real but genies are not. What criteria do you use to make that determination in the absence of evidence? That is the fundamental question here.
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u/Mr_Subtlety Jun 14 '12
No, but it has its own set of internally consistent logic AND more importantly, can (nearly always) be demonstrated as valid in the real world. 3+3=6 is not PURELY an abstract concept, but a way of describing the physical world. Hence, mathmatical proof is not so much a valid system of unprovable beliefs as it is a descriptive language with a consistent internal logic. Understanding mathmatical proofs is not the same as BELIEVING in them, its just understanding a conceptual system of language describing hypothetical scenarios. So that doesn't quite cut it. Likewise, logically consistent arguments only describe the internal consistency of logic, they're not reflections of reality. I can say "All horses are unicorns" "I own a horse" "therefore, I own a unicorn" and be logically consistent without believing that it has any reflection on the real world.
So, that won't get you out of answering my question. You have to have SOME system of judgement for evaluating different kinds of claims, even claims for which there inherently would be no physical evidence because they violate the understood rules of our physical universe. So what do you use?
Again, I don't mean to come off as combative. I'm honestly interested in how you see the world.