axiomatic systems, this peculiar feature holds. With K and N (the Distribution Rule and the Knowledge Generalization Rule, respectively), which are axioms that are minimally true of all normal modal logics, we can prove that we know all the logical consequences of our beliefs. If is a logical consequence of (i.e. we have the tautology ), then we can derive with N, and using a conditional proof with the axiom K, we can then derive with K'''. When we translate this into epistemic terms, this says that if is a logical consequence of , then a knows that it is, and if a knows , a knows . That is to say, a knows all the logical consequences of every proposition. This is necessarily true of all classical modal logics. But then, for example, if a knows that prime numbers are divisible only by themselves and the number one, then a knows that 8683317618811886495518194401279999999 is prime (since this number is only divisible by itself and the number one). That is to say, under the modal interpretation of knowledge, when a knows the definition of a prime number, a knows that this number is prime. This generalizes to any provable theorem in any axiomatic theory (i.e. if a knows all the axioms in a theory, then a knows all the provable theorems in that theory). It should be clear at this point that a is not human (otherwise there would not be any unsolved conjectures in mathematics, like P versus NP problem or Goldbach's conjecture). This shows that epistemic modal logic is an idealized account of knowledge, and explains objective, rather than subjective knowledge (if anything). Epistemic fallacy (masked-man fallacy) In philosophical logic, the masked-man fallacy (also known as the intensional fallacy or epistemic fallacy) is committed when one makes an illicit use of Leibniz's law in an argument. The fallacy is "epistemic" because it posits an immediate identity between a subject's knowledge of an object with the object itself, failing to recognize that Leibniz's Law is not capable of accounting for intensional contexts. Examples The name of the fallacy comes from the example: Premise 1: I know who Bob is. Premise 2: I do not know who the masked man is Conclusion: Therefore, Bob is not the masked man. The premises may be true and the conclusion false if Bob is the masked man and the speaker does not know