In my last post, I mentioned the doctrine of internal relations as implying the necessity of an eternally omniscient being. I've written about this necessity before (most comprehensively, here). The doctrine of internal relations is the theory that everything is related to everything else. "Everything," however, may be unnecessarily ambiguous, so let's qualify it to specifically apply to propositions. Are all propositions related, or can a proposition be known to be true in isolation from all others?
By definition, one who isn't omniscient doesn't know at least one proposition: A.
For such a person to claim to know proposition B is false if B is predicated on A.
For him to know that B is not predicated on A presupposes a method C according to which he is able to determine such.
The question, then, becomes: from whom did he learn C, or did he himself claim to discover it?
If one learned C from another, from whom did that person learn C, did that person claim to discover C, or is that person omniscient?
If that person in turn learned C, we merely repeat the same question such that it is evident one has discovered C himself or has ultimately learned C either from one who is not omniscient and claimed to have discovered it or from one who claims to be omniscient.
Here is the kicker: if either of the former is the case - if a non-omniscient source claimed to discover C - by what method D did said source discover that C is not itself predicated on A? By what method E did said source discover that D is not itself predicated on A? Etc.
It is apparent that one who is not omniscient cannot both claim to know a proposition in isolation and avoid begging the question. Note that this is not intended to question the right of a person to appeal to an epistemic source. It is rather a question of determining preconditions for [the means of] knowledge and whether or not a particular epistemic source satisfies them. This post, like the one cited at the top, is intended to establish the unviability of an epistemology which has no recourse to an omniscient source of knowledge. The point is that just as no epistemology can stand without logic, no epistemology can stand without an omniscient being - more precisely, an eternally omniscient being, if the argument in my other post is sound. I'll leave that aside for now, however, as I want to emphasize that I believe this is a strong argument against secular rationalists who believe logic alone is a sufficient condition for knowledge. It's the best one I know, anyway, in terms of its breadth of application.