> the real problem was not the assumption being implicit/explicit but rather that one doesn't want to rely on it at all. Which again is an extra-logical issue.

> the real problem was not the assumption being implicit/explicit but rather that one doesn't want to rely on it at all. Which again is an extra-logical issue. In a strict sense, yes, the problem with Bloom's proof was due to an implicit unjustified assumption. However, the reason that this assumption was implicitly introduced, was because Bloom accidentally overlooked certain dependencies between the bits - the "real problem" in this sense is the fact that when reasoning about random algorithms, it is hard to keep track of all the various dependencies involved and this can lead to incorrect proofs. This problem of tracking dependencies is a logical issue and one that is solved by proving the bound in a proof assistant.