Ideally this would involve a somewhat mathematical treatment of the subject. A good contemporary textbook would also be welcome. I just want to avoid heavy metaphysics and stay firmly in the realm or justifying inferences and interpreting statistics. I haven't read enough epistemology to give specific examples of what I'm looking for, but I can give examples of what I'm NOT looking for. The Critique or Pure Reason is exactly the kind of thing which I'm not looking for. Quine's "Epistemology Naturalized" is closer but still too focused on metaphysics. Hume's major epistemological works are also too metaphysically focused, and I'd prefer something a little more contemporary.

Interested in both the more theoretical/mathematical side and empirical/psychological side of this


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"Infinite Cycles and the Graphical Approach to Epistemic Justification" and "Coherentism via Graphs" are good introductions (if partly in media res, so to speak) to the evolution of the Agrippan/Münchhausen trilemma into a heptad of sublemmas. See also the work of Susan Haack, e.g. "Double-Aspect Foundherentism", for more from the implicit heptad.

Two SEP articles worth a look: the one on epistemic logic overall as well as on the dynamic versions of that.

It's a bit of a shame that you want to avoid Kant: modern cognitive science owes much to him, and owns this debt squarely, so you might want to rethink your eschewal of his work. Or you can at least look into cognitive science itself, anyway, for some on-the-borderlines-of-psychology epistemological studies. The SEP article on social epistemology should be a decent curative for any overbearing infection with individualistic-psychologism about knowledge, though.

Something of a heavy outlier in the field might be Reinhardt's "Epistemic Set Theory":

It is the purpose of this paper to formulate axioms for Gödel's modal operator B for provability (see [3], [8]) in the context of set theory. This provides a framework for consideration of the Post-Turing thesis which is more adequate than arithmetic with B, where the thesis can only be expressed as a schema. The framework also provides a new perspective on ordinal notations.

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