Epistemic justification I am an Aristotelian.
1. I reject the correspondence view of truth.
a. While it works in many cases, it is flawed. Nothing corresponds to universal ideas or negations. There is no one-to-one mapping between what we think and reality. Reality is much more coomplex than our limited experience and abstractions reveal.
b. The definition of Isaac ben Israel, adopted by Aquinas is much better: Truth is the adequacy of intellect and reality. Adequacy is a relative concept. What is adequate to one requirement need not be adequate to another. It is not lying to teach Newtonian physics to civil engineers, even though it is woefully inadequate in quantum and relativistic contexts. This means that truth is an analogous concept -- partly the same and partly different depending on context. What is adequate for physics may be inadequate for metaphysics.
2. I think knowledge is not a species of belief.
a. I define knowledge as awareness of present reality. Reality is present by acting on us, My knowledge of my keyboard is due to it acting on my sensory system, and my awareness of some of the effects it has wrought. Things can be cognitively present directly (by acting on me) or indirectly (by having acted on others, who act on me).
b. A belief is completely different. It does not require awareness of the presence of the object of belief. Instead it is a commitment to the truth of a proposition which is the object of belief. So, while knowing is an act of intellect (our capacity to be aware), believing, as a commitment, is an act of will. So, while Descartes knew he was in his chamber (because it acted on him via his senses), he chose (for methodological reasons) not to believe he was in his chamber. This act of will (Cartesian doubt) was completely orthogonal to his knowledge, and so, no reason to question what he knew.
3. As Aristotle pointed out, not all propositions can be proven. Some must be accepted without proof, i.e., as fundamental.
a. Fundamental propositions are knowable. Although we cannot prove them, we can know them experientially. For example "This apple is red." We know from experience that the phantasm (bound contents) that evokes the concept <this apple> is the identical phantasm that evokes the concept <red>. As the proposition's truth is based on identity of origin, the copula "is" denotes identity -- not of concepts, but of foundation in reality.
b. Once we have a population of fundamental, experiential propositions, we begin a constructive movement we can call "modeling." It adds to our experienced content new notes of intelligibility to "fill in the gaps." These constructive elements or gap fillers, are not known, but are believed. That does not make them unimportant, or even unreliable, as we test them in daily living. E.g., we expect objects to persist, even when we don't experience them. Many of these gap-filling beliefs are so reliable, that we are willing to say we "know" them -- even though we can't derive them from experience.
c. Considering Eddington's two tables, for example, we think of the table of everyday experience as continuous and not atomic because the construct of continuity is adequate to our everyday needs. Our dishes, knives and forks do not fall through it, onto the floor. We don't think it's continuous as a result of direct experience of its microstructure. So, while the notion of macroscopic continuity is experiential, adequate to our usual needs, and so true; that of microscopic continuity is a gap filler, and unreliable when consider the table's microstructure.
4. If our knowledge were merely a self-consistent set of beliefs, we would have no reason to think they would be applicable to reality. Why?
a. In order to apply our knowledge to reality, we need to recognize that we're dealing with an instance of something we know. For example, to apply "Coral snakes are dangerous," we must recognize that we are facing a coral snake. If the animal before us could not evoke the concept <coral snake>, we could never recognize it as one. But if sensing it can evoke the concept, then our knowledge is not merely a self-consistent web, but linked to reality.
b. Again, if our knowledge were merely a self-consistent web, experimental data could never change our knowledge. First, we would not know the results, because that requires experiential input, and second, what was self-consistent before would not become inconsistent. The only inconsistency is between what we used to think and the new, experiential data.