Wait, are you an finitist or an intuitionist when it comes to the philosophy of mathematics? I don’t think I’ve ever met one before in person?
Clearly you have to deal with infinite sets in order to apply Bayesian probability theory. So do you deal with mathematics as some sort of dualism where infinite sets are allowed so long as you aren’t referring to the real world, or do you use them as a sort of accounting fiction but always assume that you’re really dealing with limits of finite things but it makes the math and concepts easier?
Do you believe in the Axiom of Choice? Would the Banach-Tarski paradox make you less likely to?
Does the two envelopes problem make you less likely to believe the Bayesian theory of probability?
Can you justify your acceptance of the Bayesian theory of probability or the other mathematical axioms to which you hold through pure evidence?
Does it bother you that (as shown by Godel) no theory which contains elementary arithmetic (addition and multiplication of the natural numbers) can be both consistent and complete, and that no theory that contains elementary arithmetic and the concepts of formal provability can include a statement about its own consistency without being inconsistent? Does this evidence cause you to reject elementary arithmetic, based on the importance of consistency, rational logic, and the need for all true statements to be proved?
have you ever actually seen an infinite set?
Wait, are you an finitist or an intuitionist when it comes to the philosophy of mathematics? I don’t think I’ve ever met one before in person?
Clearly you have to deal with infinite sets in order to apply Bayesian probability theory. So do you deal with mathematics as some sort of dualism where infinite sets are allowed so long as you aren’t referring to the real world, or do you use them as a sort of accounting fiction but always assume that you’re really dealing with limits of finite things but it makes the math and concepts easier?
Do you believe in the Axiom of Choice? Would the Banach-Tarski paradox make you less likely to?
Does the two envelopes problem make you less likely to believe the Bayesian theory of probability?
Can you justify your acceptance of the Bayesian theory of probability or the other mathematical axioms to which you hold through pure evidence?
Does it bother you that (as shown by Godel) no theory which contains elementary arithmetic (addition and multiplication of the natural numbers) can be both consistent and complete, and that no theory that contains elementary arithmetic and the concepts of formal provability can include a statement about its own consistency without being inconsistent? Does this evidence cause you to reject elementary arithmetic, based on the importance of consistency, rational logic, and the need for all true statements to be proved?