Justification for Foundational Belief

[Angrboda]

First, the non-contradiction thing, I don't fully understand that, but am not at this point willing to investigate the matter further, so I'll just have to accept that I don't know whether or not proposition P is foundational or not, nor whether that criterion of foundationalism is valid or not. As noted in my OP, that's work I have yet to do.

However, you keep raising objections of the sort that say, "well here is another way in which proposition P may not be 'true'". Unless you can gerrymander the logical landscape to an almost unheard of extent, foundationalism entails proposition P under most any conceivable "epistemology" (any conceivable epistemology under which foundationalism can be asserted and demonstrated to be true; epistemologies in which it can't be thusly shown are irrelevant, as foundationalism is about what is true — any other result is the end of [that] foundationalism). If there exists a demonstrable foundational axiom, then proposition P is true under most any useful concept of entailment and membership conceivable. If the existence of a single axiom isn't demonstrably true, then foundationalism is not true, or at least not demonstrably true, which amounts to the same thing. Therefore finding yet another way proposition P may not be demonstrably true does not in any way criticize my argument; if anything, it strengthens it by adding more ways that foundationalism can fail. Moreover, if you're not defending foundationalism.... well I guess that does explains the lack of cogency and logical force of your objections. Anyway, I don't need any additional arguments for why proposition P may not true, and therefore foundationalism is not true. But hey, thanks anyway!

Anyway, this has wandered off into a situation in which a person who earlier confessed his ignorance of contemporary epistemology is making hand-waving arguments about what "alternative epistemologies" might show. I think you're simply wandering among the brambles in hopes of finding gold. Lotsa luck with that. I've given my twin argument, the only real gap remaining (besides the additional clauses you've provided which yield the same conclusion) is the rather foundational question of what makes a foundational axiom foundational and whether proposition P is foundational (or its equivalent). However that's one of the limbs of my counter-argument, that if you have to justify a foundational axiom, then that axiom isn't properly foundational; and despite all your talk about epistemology, you never once challenged that point.

Anyway, I'm leaving this discussion. Primarily to devote attention to more interesting matters, but whatever.