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Odinn comments on Science as Attire - Less Wrong
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So is the conjunction of two contradictory phenomena not zero? I am confused. I believe if that is so the rest of bayes falls apart, no? Bayes requires that you give zero probabilities to contradictions, if you do not then you can be dutch booked, right? It also requires that you give a probability of one to logical tautologies, if you give more or less, then you can also be dutch booked. What am I messing up? Really, please help if you understand.
Even the simplest expression such as 2+2=4 should not be literally tautological. There is an infinitesimal possibility that the human brain has a fundamental flaw that causes us to read the expression incorrectly, or that every person or program that has ever attempted to calculate the sum of 2 and 2 has erroneously provided an incorrect answer, or that our universe is actually configured in a way that isn't mathematically accurate (despite what those pictures of apples in first grade textbooks claim.) Conjugate all of these extremely strange possibilities and your odds of 2 and 2 not equaling 4 are so small, so imaginary, that we can confidently and adequately use probability 1 for 2+2=4, but a perfect Bayesian formula still has no room for entries of P=1 or 0, especially since the formula just doesn't provide useful data that way.