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ParagonProtege comments on [SEQ RERUN] Guardians of Ayn Rand - Less Wrong
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Are there any great explanations that show why this is true? Something that shows how to derive Aristotelian logic from the axioms of Bayesian probability theory?
A somewhat more detailed derivation was made in this post by komponisto. He derived the analogues of modus ponens and modus tollens from Bayes' theorem. If you want even more detail, the first couple of chapters of Probability Theory: The Logic of Science discuss it.
Aristotlean logic is obtained by assuming every probability to be either one or zero.
Interestingly enough most of his fallacies are actually valid Bayesian inferences that aren't capable of producing outputs of 1 or 0 even if all of their inputs are 1 or 0.
This is particularly interesting in light of how 1 and 0 "work" within a bayesian context.
Yes. Just try applying the sum and product rules to the possible combinations of probabilities 0 and 1. The results should look familiar.