komponisto comments on A cautionary note about "Bayesianism" - Less Wrong
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"What you believe after seeing the evidence depends on what you believe before seeing the evidence" is, I think, a decent "layman paraphrase" of (one aspect of) Bayes' theorem that I think people do need to understand. "Don't forget to consider other ways the data could have arisen" is another.
On TDT, I agree; I regard that as more of a specialized AI topic.