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There is a long tradition trying to approach knowledge as a true and justified belief (The Tripartite Analysis of Knowledge . Recently, Gettier(1963) just showed that we need more than those 3 conditions, and if we follow Zagzebski (1994), it seems we can always deduce some counterexamples to one or another version of the tripartite analysis of knowledge. A different approach could be:

S knows that p, if and only if, S does NOT ignore p

This way, we could just look for an adequate theory of ignorance.

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    I think some detail should be added to this post - otherwise, it is clear that one ignores many things that one otherwise would know- I ignore the fact that I am currently wearing clothes, that the less fortunate are hungry, etc....
    – emesupap
    Jul 27, 2022 at 17:09
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    If at first you can't define knowledge, define ignorance instead. Ok, take a swing at it. Buddhism actually has a lot to say about avidya (not seeing / knowing). Maybe the work has already been done?
    – Scott Rowe
    Jul 27, 2022 at 17:20
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    If one simply does not ignore all propositions there are in the sense of 2nd order universal quantification, then by your definition of knowledge one immediately knows every proposition p. Knowledge as defined by JTB is basically certain positive belief while ignore is just its corresponding negative belief, your definition just manipulates like defining necessity in terms of possibility...
    – Double Knot
    Jul 28, 2022 at 1:03
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    Thank you @DoubleKnot for noticing the interdefinability between "know" and "ignore". More than a complete definition, I'm suggesting the global form and trying to motivate, why not?, an adequate theory of ignorance, with all it's necessary and sufficient conditions. Also, what you mention (in the sense of 2nd order UQ) seems to me a plausible inference, I mean, consider this case: S knows all p's that T knows IFF S doesn't ignore all p's that T knows, in other terms, S knows all p's that T knows IFF S doesn't ignore all p's that T doesn't ignore. The spectrum of inference is pretty wide.
    – Felipe Viveros
    Aug 8, 2022 at 14:24

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