″ Suppose you have beliefs A, B, C, and belief D: “At least one of beliefs A, B, C is false.” The conjunction of A, B, C, and D is logically inconsistent. They cannot all be true, because if A, B, and C are all true, then D is false, while if D is true, at least one of the others is false. So if you think that you have some false beliefs (and everyone does), then the conjunction of that with the rest of your beliefs is logically inconsistent. ”
But beliefs are not binary propositions, they are probability statements! It is perfectly consistent to assert that I have ~68% percent confidence in A, in B, in C and in “At least one of A,B,C is false”.
Most people, most of the time, state their beliefs as binary propositions, not as probability statements. Furthermore, this is not just leaving out an actually existing detail, but it is a detail missing from reality. If I say, “That man is about 6 feet tall,” you can argue that he has an objectively precise height of 6 feet 2 inches or whatever. But if I say “the sky is blue,” it is false that there is an objectively precise probability that I have for that statement. If you push me, I might come up with the number. But I am basically making the number up: it is not something that exists like someone’s height.
In other words, in the way that is relevant, beliefs are indeed binary propositions, and not probability statements. You are quite right, however, that in the process of becoming more consistent, you might want to approach the situation of having probabilities for your beliefs. But you do not currently have them for most of your beliefs, nor does any human.
″ Suppose you have beliefs A, B, C, and belief D: “At least one of beliefs A, B, C is false.” The conjunction of A, B, C, and D is logically inconsistent. They cannot all be true, because if A, B, and C are all true, then D is false, while if D is true, at least one of the others is false. So if you think that you have some false beliefs (and everyone does), then the conjunction of that with the rest of your beliefs is logically inconsistent. ”
But beliefs are not binary propositions, they are probability statements! It is perfectly consistent to assert that I have ~68% percent confidence in A, in B, in C and in “At least one of A,B,C is false”.
Most people, most of the time, state their beliefs as binary propositions, not as probability statements. Furthermore, this is not just leaving out an actually existing detail, but it is a detail missing from reality. If I say, “That man is about 6 feet tall,” you can argue that he has an objectively precise height of 6 feet 2 inches or whatever. But if I say “the sky is blue,” it is false that there is an objectively precise probability that I have for that statement. If you push me, I might come up with the number. But I am basically making the number up: it is not something that exists like someone’s height.
In other words, in the way that is relevant, beliefs are indeed binary propositions, and not probability statements. You are quite right, however, that in the process of becoming more consistent, you might want to approach the situation of having probabilities for your beliefs. But you do not currently have them for most of your beliefs, nor does any human.