But isn't this necessarily self-defeating? For I am not omniscient. Is it not possible, then, that the truth value of the proposition in which I assert what the omniscient source is to which I have access is one which could be predicated on the truth value of an unknown proposition?
No. For it is possible for an omniscient source to be self-authenticating. In fact, given that we are not omniscient, it is necessary in order to avoid skepticism. What this means is that while an omniscient source is necessary, it is also necessary that for those who are not omniscient to know anything, the proposition that "it is possible the truth value of any proposition is predicated on the truth value of an unknown proposition" is false.
But since this proposition is false, does that mean an omniscient source is unnecessary after all? Again, no. There is a mutual dependency among the preconditions for knowledge. For example, logic and language are preconditions for knowledge. You can't have one without the other. You can't know what logic is without using language, and you can't know what language is without using logic.
Similarly, I am saying it logically follows that you can't know that an omniscient source is necessary if that source isn't self-authenticating, and you can't know a source is self-authenticating if you did not deduce that from an omniscient source. And you can't know either of these if the alleged source is illogical or doesn't communicate. Etc.
To assert "source x is self-authenticating" without having recourse to an omniscient source which states or implies such falls prey to the possibility (within that worldview) that "the truth value of any proposition is predicated on the truth value of an unknown proposition." Rejection of this too as a possibility falls prey to the same possibility that "the truth value of any proposition is predicated on the truth value of an unknown proposition." These rejections are propositions, after all.
Rather, what saves the possibility of knowledge at this point is precisely having recourse to an omniscient source which, since the source knows all, knows that "the truth value of any proposition is predicated on the truth value of an unknown proposition" isn't, in fact, a possibility. Furthermore, the source is able to communicate such information to men, able because the communication is, among other things, self-authenticating. The need for self-authentication strictly pertains to the need for the possibility of communication from an omniscient source; it doesn't erase the need for an omniscient source.
[I have tried to be as neutral as possible in describing the nature of this "source," though it must be the God of Scripture. For why I would write my post in this way, see the last five paragraphs here.]