Hawking Radiation 3

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Consider demonstration that two sets A and B are equivalent. This means simple thing: construct a one-to-one map between them. Usually one is only interested in the existence of this map but one can also get interested on all manners to perform this map. All manners to make this map define in rather abstract sense a collection of paths between A and B regarded as objects. Single path consists of a collection of the arrows connecting element in A with element in B. More generally, in mathematical proof theory all proofs of theorem define this kind of collection. In topology all paths connecting two points defined this kind of collection. In this framework Goedel's theorem becomes obvious: given axioms define rules for constructing paths and cannot give the paths connecting arbitrarily chosen two truths.
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September 20, 2017
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