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KnaveOfAllTrades comments on Does Probability Theory Require Deductive or Merely Boolean Omniscience? - Less Wrong
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Basically the problem is that a Bayesian should not be able to change its probabilities without new evidence, and if you assign a probability other than 1 to a mathematical truth, you will run into problems when you deduce that it follows of necessity from other things that have a probability of 1.
Why can't the deduction be the evidence? If I start with a 50-50 prior that 4 is prime, I can then use the subsequent observation that I've found a factor to update downwards. This feels like it relies on the reasoner's embedding though, so maybe it's cheating, but it's not clear and non-confusing to me why it doesn't count.