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Virtually all epistemologists agree that truth is a necessary condition for knowledge. Assuming that our three-dimensional world is nested within a higher-dimensional space, I use multidimensional geometry to present a type of case which undermines this fundamental principle of epistemology. I further argue that we would be unlikely to revise our epistemic practices in light of new discoveries even if our world turned out to be substantially different and many of our beliefs turned out to be false.

The skeptical puzzle consists of three allegedly incompatible claims: S knows that O, S doesn’t know that ~U, and the claim that knowledge is closed under the known entailment. I consider several famous instances of the puzzle and conclude that in all of those cases the presupposition that O entails ~U is false. I also consider two possible ways for trying to make it true and argue that both strategies ultimate fail. I conclude that this result at least completely discredits any solution that denies the principle of epistemic closure. At most, denying that O entails ~U can itself be seen as a novel solution to the puzzle, preferred to any other solution: it accommodates both non-skeptical and skeptical intuitions but does not require us to give up the principle of closure, embrace contextualism or subject-sensitive invariantism, or deny any commonly accepted principle of epistemology or logic.