my beliefs are always the outputs of real-world embodied algorithms (for example, those associated with remembering previously proven axioms) and therefore not completely reliable.
there exists a non-empty set S1 of assertions that merit a sufficiently high degree of confidence that it is safe to call them “true” (while keeping in mind when it’s relevant that we mean “with probability 1-epsilon” rather than “with probability 1”).
I would also say that:
there exists a non-empty set S2 of assertions that don’t merit a high degree of confidence, and that it is not safe to call them true.
the embodied algorithms we use to determine our confidence in assertions are sufficiently unreliable that we sometimes possess a high degree of confidence in S2 assertions. This confidence is not merited, but we sometimes possess it nevertheless.
Would you agree with both of those statements?
Assuming you do, then it seems to follow that by “what I truly believe” you mean to exclude statements in S2. (Since otherwise, I could have a statement in S2 that I truly believe, and is therefore definitionally true, which is at the same time not safe to call true, which seems paradoxical.)
Assuming you do, then sure: if I accept that “what I truly believe” refers to S1 and not S2, then I agree that truth is what I truly believe, although that doesn’t seem like a terribly useful thing to know.
FWIW: I agree with you that:
my beliefs are always the outputs of real-world embodied algorithms (for example, those associated with remembering previously proven axioms) and therefore not completely reliable.
there exists a non-empty set S1 of assertions that merit a sufficiently high degree of confidence that it is safe to call them “true” (while keeping in mind when it’s relevant that we mean “with probability 1-epsilon” rather than “with probability 1”).
I would also say that:
there exists a non-empty set S2 of assertions that don’t merit a high degree of confidence, and that it is not safe to call them true.
the embodied algorithms we use to determine our confidence in assertions are sufficiently unreliable that we sometimes possess a high degree of confidence in S2 assertions. This confidence is not merited, but we sometimes possess it nevertheless.
Would you agree with both of those statements?
Assuming you do, then it seems to follow that by “what I truly believe” you mean to exclude statements in S2. (Since otherwise, I could have a statement in S2 that I truly believe, and is therefore definitionally true, which is at the same time not safe to call true, which seems paradoxical.)
Assuming you do, then sure: if I accept that “what I truly believe” refers to S1 and not S2, then I agree that truth is what I truly believe, although that doesn’t seem like a terribly useful thing to know.
Yes, I think you managed to put my thoughts into words very well here. Probably a lot more clearly than I.