#Philosophy Euclids Axioms are Self-Explanatory: By self-explanatory I mean that which can be directly seen to be true from the intuited understanding of the concepts involved. I would suggest that many of the foundational concepts in language are not understood by their definitions. If this were the case, (a) language would be a self-supporting structure which would have no way for our understanding to get a foothold, and (b) its is plainly not the case, as can be directly seen from extrapolating the definition of almost any word, and each of the definitions involved, etc. Eventually you arrive at some words that are not defined by different words, but by synonyms which are in-turn defined by the original word. These concepts therefore cannot be understood by means of their definitions, but either by direct intuition, or not at all. This could include experiential concepts like pain, pleasure, red, cold, etc.--but also metaphysical and mathematical concepts like being, time, number, line, point, parallel, etc. I would suggest that all of Euclids postulates flow directly out of the directly-intuited concepts involved, and thus is self-explanatory a priori. What objections could be made to this idea? I am aware that objections will be made on the basis of the parallel postulate having supposedly been shown to be false. But I dont think it has been shown to be false, just that you can create geometry for curved space. But a line in curved space is not a line (by virtue of the space it is in being curved), anymore than a meridian on the earth is a line. Obviously you think it’s a straight line if youre standing on the earth, but by virtue of the fact that its curved (and thus not a line) do parallel meridians intersect. Thus it is with the crossing of parallel so-called lines in non-Euclidian geometry. Or am I misunderstanding?
Posted on: Fri, 21 Nov 2014 03:00:50 +0000
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