Uncertain knowledge and reflective epistemology

Our knowledge forms a highly interconnected and dynamically changing body of propositions. One obviously important way that knowledge changes is via rational inference, based either upon new insight into the content of what we already know or upon new knowledge provided by the senses. The most obvious codification of the acceptability of inference driven knowledge growth is the so-called known entailment closure principle, the principle that if S knows that p and knows that p implies q then S knows that q, or, more formally.
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