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Originally Posted by utabintarbo  Quote: |
Originally Posted by utabintarbo's link True axioms are more solid than that. They are not statements we merely believe to be true; they are statements that we cannot deny without using them in our denial. Axioms are the foundation of all knowledge. | |
I don't believe in this sort of thing. I'm a skeptic, and I don't believe in any kind of "certain" knowledge.
I also don't believe in such a thing as an axiom that I "can't deny without using it in my denial."
Unless by axiom you mean a paradox, like, "this sentence is false"...to deny that I have to affirm it.
I think that kind of thing is cool, but I don't see how to build knowledge on it.
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Originally Posted by utabintarbo When I referred to axioms previously (including in that post you quoted), I was referring to axioms in the context of philosophy (metaphysics/epistemology as opposed to mathematics), which was the context in which the original quote occurred. The wikipedia article seems to focus on the mathematical/physics application (ie. as a starting assumption) of the word. |
God only knows what I saw in secondary math classes.
However, I *like* the wikipedia definition of axiom better. As I said, I don't believe there is such a thing as a "certain" or "irrefutable" starting point. I think starting points can't be proven, only assumed...in that case, they can be arbitrary.
I'm looking for plausible ones (plausible to me), not arbitrary ones. Or maybe I'm looking for aesthetically pleasing ones? At any rate, I'm not looking for axioms which satisfy some inarguability criterion, because I don't think it's possible.