Today's post, Guardians of Ayn Rand was originally published on 18 December 2007. A summary (taken from the LW wiki):

Ayn Rand, the leader of the Objectivists, praised reason and rationality. The group she created became a cult. Praising rationality does not provide immunity to the human trend towards cultishness.

Discuss the post here (rather than in the comments to the original post).*This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Guardians of the Gene Pool, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.*

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.