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Knowledge/Counterfactual Conditional/co.co./Nozick: E.g. I know that a pair of scissors is now in my drawer. - But it is not correct to say that if there is one there, that I would know then. - ((S) So something can be true, even if the counterfactual conditional is false - namely, because the method can be crucial). - ((S) So the counterfactual conditional must mention the method.).
Gettier/Nozick: Gettier - examples conclude a truth often from a (justified believed) falsehood. - condition
(3) if not-p> not- (S believes that p)
excludes that often.
Knowledge/belief/Nozick: through senile stubborness knowledge becomes belief. - Similar: E.g. knowledge of future brainwashing, then we try to "cement" belief.
Knowledge/belief/local/global/Nozick: condition (3) should be better (indexicality, "now", "here") a local belief than a global one. - Otherwise danger of stubbornness.
Need/possibility/knowledge/Nozick: if ~ p> ~ (S believes that p) necessary condition for knowledge, then possibility of skepticism shows that no knowledge exists.
II 204 f
Knowledge/non-seclusion/NozickVsskepticism: Knowledge is not completed under known logical implication (VsSkepticism - Skepticism: knowledge is complete: that is the (skeptical) principle of seclusion of knowledge: K (p >> q) & Kp> Kq: I should know allegedly the implied by the known? - Nozick: but that would be merely belief, not knowledge.
The situation where q is wrong, could be quite different from the one where p is false. - E.g. that you were born in a certain city, implies that you were born on Earth, but not vice versa.
Non-seclusion of knowledge: means, that knowledge will vary with the facts, because it is in connection with them. - (> Covariance) - notation: K = knowledge, operator "somebody knows".
Knowledge/belief/closeness/Nozick: merely true belief is complete under known logical implication. - Because knowledge is more true belief, we need an additional condition that is not-complete under implication. - Belief is only knowledge when it covaries with facts. - But that is not enough - it depends on what happens if p is false. - Problem: a co-varying belief with facts is not complete. - Punchline: because knowledge involves belief, it is not completed. - VsSkepticism: his argument needs the fact that knowledge needs covariance.
Knowledge/induction/connection/Nozick: knowledge is based on facts that would otherwise have been different - Nozick: In the past. - Therefore, the relevant non-p-world is not a possible world, which is so far identical with the real world (the actual world), and diverges from now on immediately. - It is probably logically possible that it begins to diverge in a moment. - ((S) elsewhere Lewis like Nozick: in the past there would have had to be a change, if I now suddenly act differently). - We have connections to the facts in the past that determine our predictions. -> Covariance.
Knowing that (x)Px is unequal knowledge that every single thing is P: the all-quantification has different truth conditions as the all-removal. - "(x)Px" could be wrong, although "Pa" true.
Philosophical Explanations Oxford 1981
The Nature of Rationality 1994