Quote:
Originally Posted by alexander
Kriminal, thank you, that makes for a much more engaging conversation... really does, seeing where you are coming from, helps build replies that cater to what it is that you seek.
The thing with math, as well as any science is the fact that the facts claimed are facts that are proven to any arbitrary case we can come up with at the current time. Not to be confused with theories, but you were not implying those anyways. These facts are to our understanding facts, axioms, something so fundemental to math that many later concepts are built on them. But like any science, and math is a science of numbers, in many things it is not certain, thus is prone to, and accepts change. Proofs are proofs, they prove the concept to some degree, some prove it to n'th degree, where for any value you can give it, the concept remains true, others are proven, sort of, beyond current reasonable doubt, though if your reasoning changes, the proof may fly out of the window. I think it takes an understanding of what science is to understand this difference between "facts" and "things we know"...
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This discussion is a bit abstract for me. It's not really clear what you are saying exactly. Give an example perhaps?
Or maybe I can. I can prove that 1 + 1 = 2 just by putting two apples together and seeing that there are two of them. One can still doubt, but to do so in this case is to doubt everything that a person sees and if you are going to do that then you have nothing to go on at all.
Other than these trivial cases, it seems a "proof"'s effectiveness has a lot to do with how much the audience knows - meaning you can "prove" things that are wrong to people who do not know much, and to prove something that is right you have to start with what the audience knows and go from there.
The best understanding I can make of "proof" in academia is that there is some "body of knowledge" that it is assumed everyone is up to date on up to a certain point, and it is from there the "proof" starts. If you aren't up to date, you are supposed to look back and find a sequence of proofs that gets you there.
The problem with this is that epistemology isn't fully included in this body of knowledge. Usually proofs stay pretty formal, but sometimes they slip into this sort of "storytelling mode" where the person stops manipulating symbols for a moment and starts talking about what they can and can't do and why. In this situation, it seems there is a strong danger of there being unrecognized assumptions and I find myself at every step asking "OH REALLY? Can we REALLY do that?". In other words, at this point it is just an argument and no longer a proof.
The thing that makes me different in this regard is my advanced skepticism, which does seem to be a trait necessary to do proofs at all and yet there does still yet seem to be a stage of it that is never reached by most in the field. I am guessing that stage is the one where you are skeptical of something even though the majority of people around you agree with it.
