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Mathematics
Set Theory, Logic, Probability, Statistics
Are Time-Travel and Logical Paradoxes Connected?
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[QUOTE="andrewkirk, post: 5963826, member: 265790"] It's helpful to distinguish between veridical and falsidical paradoxes. The former are conclusions that are surprising and anti-intuitive, but not logical contradictions. The latter are logical contradictions. The grandmother paradox, like in Azkaban or in Heinlein's 'All you zombies', is veridical. It doesn't seem to make sense, yet it does. The 'rule' that it seems to contradict is something like [I]'every sequence of events must have a cause outside the sequence'[/I]. But that is just a natural expectation based on our observation of the everyday, non-time-travelling world. It is not a rule of logic. Lay people often describe quantum mechanics as paradoxical. What they mean is that it contradicts their intuitions, not that it generates logical contradictions. The 'paradoxes' of QM are veridical. The liar paradox is, depending on how presented, either meaningless or a falsidical contradiction. Most presentations of it are in natural language, and are meaningless. They defy attempts to formalise them. A successful formalisation of it is Russell's Paradox, formulated in the context of naïve set theory. The paradox is falsidical, meaning it generates a contradiction, and that contradiction tells us that naïve set theory is inconsistent, which is why it was replaced by Zermelo-Frankel and its successors. Other formalisations are possible using second-order and higher-order logic. Those formalisations lead to formal contradictions, which demonstrate that the particular version of logic being used is inconsistent. Quine has a third sort of paradox, called an antinomy. Kant also played around with antinomies. According to wiki, there's a fourth type of thing that is sometimes called paradox, that has been discussed since Quine. The [URL="https://en.wikipedia.org/wiki/Paradox#Quine's_classification"]wiki article[/URL] covering this is quite good. . [/QUOTE]
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Are Time-Travel and Logical Paradoxes Connected?
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