Beliefs are procedural, you don’t need them all written out explicitly. This allows to hold infinite number of beliefs, each of them equipped with a specific level of certainty. I never before thought about the question of what the value of 385+23 is, but I still have a belief that 385+23=408 and also that 385+23 is not 409.
I reservedly agree. Taken to extremes your position implies logical omniscience—that I already have a belief one way or the other about the truth of the Riemann hypothesis because I know the basic axioms of complex mathematics, for example.
On the other hand, if I have a random number generator about to spit out a number between 1 and 10^12 I do assign an implicit probability 10^-12 to each number in that range, even though I (couldn’t possibly) explicitly list them out.
The way beliefs are “procedural” includes the requirement that you must be able to instantiate them, but permitting this bounded step vastly increases the number of possible beliefs. Beliefs are answers to questions, and epistemic mind is a question-answering engine. Without logical omniscience, the process of computation increases information about statements over time (even without learning new facts from environment). When first confronted with a question of what 385+23 is, the one-second reply is “about 400″, and only then “408”.
Beliefs are procedural, you don’t need them all written out explicitly. This allows to hold infinite number of beliefs, each of them equipped with a specific level of certainty. I never before thought about the question of what the value of 385+23 is, but I still have a belief that 385+23=408 and also that 385+23 is not 409.
I reservedly agree. Taken to extremes your position implies logical omniscience—that I already have a belief one way or the other about the truth of the Riemann hypothesis because I know the basic axioms of complex mathematics, for example.
On the other hand, if I have a random number generator about to spit out a number between 1 and 10^12 I do assign an implicit probability 10^-12 to each number in that range, even though I (couldn’t possibly) explicitly list them out.
The way beliefs are “procedural” includes the requirement that you must be able to instantiate them, but permitting this bounded step vastly increases the number of possible beliefs. Beliefs are answers to questions, and epistemic mind is a question-answering engine. Without logical omniscience, the process of computation increases information about statements over time (even without learning new facts from environment). When first confronted with a question of what 385+23 is, the one-second reply is “about 400″, and only then “408”.
I believe that would still be a contentious position in epistemology, but I agree.