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This chapter discusses the view, associated with David Hume and Saul Kripke, that the supposed epistemic vice of dogmatism can play a positive role in protecting our knowledge. It discusses Kripke’s dogmatism paradox and Kuhn’s view that dogmatism can play a positive role in normal science. This chapter argues that the supposed epistemic benefits of dogmatism have been greatly exaggerated and its epistemic drawbacks underestimated. The appropriate response to the claims of Holocaust deniers and other conspiracy theorists is not to avoid or ignore them but to rebut them. Knowers have responsibilities, including the responsibility not to dismiss challenges to their beliefs without good reason.

A definition of fallibility shows that agents are fallible about necessary truths. It is shown that fallibility of agents implies a denial of parity reasoning. Moorean paradoxes appear to undercut fallibility, but they are due entirely to the factivity of “know.” Kripke’s dogmatism paradox is explained: the key is recognizing that knowledge fallibility applies to the knowledge that all evidence against something one knows is misleading. That we do not know we will lose a lottery is denied. Fallibility shows this. And that people argue over this also indicates this. Knowledge closure fails because of fallibility; so does aggregation of assumptions. Vagueness shows why debates about whether we know outcomes of lotteries before winning tickets are drawn are irresolvable. Irrational penny reasoning is analyzed; it applies to nonfactive attitudes such as being really really sure. Preface paradoxes are explained. That it is sometimes rational to believe contradictory propositions is explained.

This chapter analyses Saul Kripke's dogmatism paradox. It argues that, in order to address properly that puzzle, one needs a notion of epistemic negligence that fits naturally within a virtue-theoretic framework. Kripke's puzzle concerns a prospective intention to close one's mind. A second puzzle is closely related. Instead of the prospective intention, it concerns an antecedent belief: namely, that any further evidence will be misleading if negative. Once you attain knowledge, you virtually know that any contrary evidence will be misleading and is best ignored. When negative evidence does come forth at some later time, scholars wonder whether a person should ignore it in accordance with what they already know. This problem is resolved by noting that knowledge can be lost with a change of evidence.