I don’t consider “can have probabilities assigned” to be an exception that requires a special case. It gets treated the same as any other logical uncertainty. You can either handle logical uncertainty or you can’t.
Then what is it about the assertion “a proof exists” that calls out to have a number attached to it? Why is it similar to “a written proof will exist by tomorrow noon” and not similar to “the exquisite corpse will drink the new wine”?
In case it wasn’t clear, I rejected this line of reasoning. “A proof exists” is not a special case that needs justification.
Please refer to my first few comments on the subject. They constitute everything I wish to say on the (rather unimportant) subject of whether “a proof exists” is permitted. I don’t expect this conversation to produce any new insights.
I don’t consider “can have probabilities assigned” to be an exception that requires a special case. It gets treated the same as any other logical uncertainty. You can either handle logical uncertainty or you can’t.
I don’t understand. You’re saying you do have a prior probability for every grammatically correct assertion?
No, that isn’t something I’ve said.
Then what is it about the assertion “a proof exists” that calls out to have a number attached to it? Why is it similar to “a written proof will exist by tomorrow noon” and not similar to “the exquisite corpse will drink the new wine”?
In case it wasn’t clear, I rejected this line of reasoning. “A proof exists” is not a special case that needs justification.
Please refer to my first few comments on the subject. They constitute everything I wish to say on the (rather unimportant) subject of whether “a proof exists” is permitted. I don’t expect this conversation to produce any new insights.