But an important property of mathematical deduction is the second incompleteness theorem: no reasonable proof system X can prove that X doesn’t prove false statements.
True, but it also can’t prove that it does prove false statements. It can prove that the pseudorandom number generator does prove false statements, so it’s clearly at least as bad.
I don’t think your method of self-trust is very complete. Sometimes, your errors will correlate. For example, if you see one thing as stronger evidence of god than it really is, you’ll see the same of something else, until you have what you believe is overwhelming evidence.
I suppose you’d have to have some idea of how much the errors correlate. You might give some weird probability distribution for it, which would result in the probability distribution getting wider tails for each piece of evidence added. The middle would represent the errors being independent, and the tails would represent them correlating.
True, but it also can’t prove that it does prove false statements. It can prove that the pseudorandom number generator does prove false statements, so it’s clearly at least as bad.
Agreed, but trying to make correct deductions takes energy. If your deductions aren’t helping you, you are better off not talking.
I don’t think your method of self-trust is very complete.
The question was: what sort of evidence could you have for your own correctness. I don’t yet know any way of expressing such self-trust at all.
Sometimes, your errors will correlate.
You can express more complicated types of self-trust by looking at your beliefs about other conjunctions of A, B, believing A, and believing B. I believe that this actually expresses all of the possible information. For example, you can look at the probability you assign to “I believe A and B, but neither is true”, etc.
You can express more complicated types of self-trust by looking at your beliefs about other conjunctions of A, B, believing A, and believing B. I believe that this actually expresses all of the possible information.
No, you could also ask about your belief of (A & B), which is different from the conjunction of believing A and believing B, as you could believe A to be correlated with B. You could also try recursing farther: “do I believe that I believe A?”.
True, but it also can’t prove that it does prove false statements. It can prove that the pseudorandom number generator does prove false statements, so it’s clearly at least as bad.
I don’t think your method of self-trust is very complete. Sometimes, your errors will correlate. For example, if you see one thing as stronger evidence of god than it really is, you’ll see the same of something else, until you have what you believe is overwhelming evidence.
I suppose you’d have to have some idea of how much the errors correlate. You might give some weird probability distribution for it, which would result in the probability distribution getting wider tails for each piece of evidence added. The middle would represent the errors being independent, and the tails would represent them correlating.
Agreed, but trying to make correct deductions takes energy. If your deductions aren’t helping you, you are better off not talking.
The question was: what sort of evidence could you have for your own correctness. I don’t yet know any way of expressing such self-trust at all.
You can express more complicated types of self-trust by looking at your beliefs about other conjunctions of A, B, believing A, and believing B. I believe that this actually expresses all of the possible information. For example, you can look at the probability you assign to “I believe A and B, but neither is true”, etc.
No, you could also ask about your belief of (A & B), which is different from the conjunction of believing A and believing B, as you could believe A to be correlated with B. You could also try recursing farther: “do I believe that I believe A?”.