Bayesian probability theory is the quantitative logic of which Aristotle’s qualitative logic is a special case
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.
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.
I don’t really know probability well, but I noticed when reading posts about it that all you need do is “round off” probabilities to 0 or 1 and you end up with simple two-valued logic.
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.
Yes. Just try applying the sum and product rules to the possible combinations of probabilities 0 and 1. The results should look familiar.
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.
I don’t really know probability well, but I noticed when reading posts about it that all you need do is “round off” probabilities to 0 or 1 and you end up with simple two-valued logic.