Of course my honest advice to others is that they should follow my axioms! :-)
For example, let’s say I have an axiom that the winning lottery number is either 1234 or 4321. You’re thinking about playing the lottery, and have an opportunity to snoop the first digit of the winning number before making a bet. Then in my opinion, the best strategy for you to achieve your goal is to bet on 1234 if you learn that the first digit is 1, or bet on 4321 if you learn that the first digit is 4. Learning any other first digit is in my opinion impossible for you, so I don’t have any advice for that case. And if you have an axiom of your own, saying the winning number is either 1111 or 4444, then in my opinion you’re mistaken and following your axiom won’t let you achieve your goal.
That seems like the only reasonable way to think about beliefs, no matter if they are axioms or derived beliefs. Symmetry considerations do matter, but only to the extent they are themselves part of beliefs.
But I’m not sure why my advice on what you should do is relevant to you. After all, if I’m right, you will follow your own axioms and use them to interpret anything I say. The only beliefs we can agree on are beliefs that agree with both our axiom sets. Hopefully that’s enough to include the following belief: “a person can consistently believe some set of axioms without suffering from the problem of criterion”. Moreover, we know how to build artificial reasoners based on axioms (e.g. a theorem prover) but we don’t know any other way, so it seems likely that people also work that way.
Of course my honest advice to others is that they should follow my axioms! :-)
For example, let’s say I have an axiom that the winning lottery number is either 1234 or 4321. You’re thinking about playing the lottery, and have an opportunity to snoop the first digit of the winning number before making a bet. Then in my opinion, the best strategy for you to achieve your goal is to bet on 1234 if you learn that the first digit is 1, or bet on 4321 if you learn that the first digit is 4. Learning any other first digit is in my opinion impossible for you, so I don’t have any advice for that case. And if you have an axiom of your own, saying the winning number is either 1111 or 4444, then in my opinion you’re mistaken and following your axiom won’t let you achieve your goal.
That seems like the only reasonable way to think about beliefs, no matter if they are axioms or derived beliefs. Symmetry considerations do matter, but only to the extent they are themselves part of beliefs.
But I’m not sure why my advice on what you should do is relevant to you. After all, if I’m right, you will follow your own axioms and use them to interpret anything I say. The only beliefs we can agree on are beliefs that agree with both our axiom sets. Hopefully that’s enough to include the following belief: “a person can consistently believe some set of axioms without suffering from the problem of criterion”. Moreover, we know how to build artificial reasoners based on axioms (e.g. a theorem prover) but we don’t know any other way, so it seems likely that people also work that way.