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.
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.