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Old 01-04-2010, 07:48 PM   #439 (permalink)
cardboard adolescent
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Join Date: Nov 2005
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there just is, i didn't decide anything. it's not something that can be explained. an explanation is a series of logical steps from the statement in question back to an axiom, which is ultimately unexplainable. why does x=x? why is a point indivisible? what is a point? if you define a point in terms of something else, you then have to ask, well what is that? ultimately you hit a zero-level where the mode of rational explanations no longer works, and it simply is what it is. and since reason breaks down at this point, if there is any way of "knowing" what that thing is, it has to be by "feeling" it.

i will admit that there is a positivist way out of this paradox--which is by saying a point is that which can make a line, and a line is that which can make a square, and so on and so on, so that it doesn't really matter what a point is, you come to understand that by the things it does. what this way of reasoning actually does though, is take that bottom-level ambiguity and spread it all over the entire system. although a line might be that which allows you to make a square, you have to realize that when you refuse to say what a line is in itself you also can't say what a square is in itself. it's just a clever mode of deferring the paradox.

when euclid started axiomatizing mathematics, he actually did something very clever. he said a point is "that which has no parts." that's another clever way of avoiding the paradox--give the simplest elements in your system an entirely negative definition. however, i would suggest that that mode of dealing with the paradox implies that your entire system is built out of... nothing. which hegel fully embraces, by the way

maybe one of the most obvious places where the difference between "feeling" and "knowing" breaks down is in trying to answer the question: "what is existence?"

Last edited by cardboard adolescent; 01-04-2010 at 07:58 PM.
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