@Adam Sharpe -- Do you have any links or references for foundational externalism? And any discussion, either form yourself, or someone else, on how it resolves the Trilemma?
4 hours later…
12:42
I've lost the plot slightly here. My point has been that the rules for Aristotle's system do not allow exceptions to the LNC. This is because a dialectical proposition obeys it a priori. It is part of the definition of 'dialectical proposition', as defined by Aristotle. For this reason I cannot imagine how a true contradiction could exist and would deny the possibility. This point is not grasped by dialethists but it is logic 101.
8 hours later…
20:13
There's a very general introduction to the idea of externalist foundationalism here on the IEP. Two specific theories that I've read about are Goldman's reliabilism and Plantinga's proper functionalism. There's also virtue epistemology which I think is a kind of externalism, but I honestly don't know too much about it.
I first learned about Plantinga's epistemology from his Knowledge and Christian Belief where he uses it to argue that the rationality of religious belief depends crucially on how those beliefs are formed. But the epistemological theory itself can be accepted/rejected independently of his religious conclusions (I believe some secular epistemologists do endorse proper functionalism).
As for externalism and how it avoids the trilemma, I posted this question a few months ago. I was sure that externalism avoids the trilemma, but wanted to verify it. Externalism isn't without its critics, but I've never heard trilemma-like arguments brought against it, and avoiding skepticism is one of very motivations for externalism. The trilemma just doesn't apply, since non-beliefs can justify beliefs without themselves being justified.
I didn't really get an answer; Conifold's first comment says it does, but it re-emerges at the meta-level. But, externalists reject the KK thesis, so they'd say that meta-knowledge isn't required for knowledge. Since posting that question, I've found good articles like this that discuss externalism and its "solution" to skepticism.
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