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1 Knowledge and Conclusive Evidence David Hemp In ‘‘Conclusive Reasons,’’ Fred Dretske argues that when knowledge is based on evidence, this evidence must be conclusive.1 The present essay uses recent work on epistemic contextualism2 to defend a version of Dretske ’s claim. Advocates of epistemic contextualism usually defend it by arguing that it can solve certain puzzles about knowledge.3 In what follows, I will argue (1) that there are parallel puzzles about conclusive evidence and (2) that, by appealing to similarities between the two sets of puzzles, we can defend a version of Dretske’s claim. Sections 1 to 4 describe three puzzles that motivate epistemic contextualism and some ways of solving them. Sections 5 and 6 argue that there are exactly parallel puzzles about conclusive evidence and that solutions to these puzzles run parallel to the solutions described in sections 1 to 4. Section 7 uses similarities between the two sets of puzzles to defend a version of Dretske’s claim. The gist of the defense is that, by endorsing the claim, both contextualists and their opponents can significantly improve their solutions to the puzzles described in sections 1 to 4. 1 A Puzzle about Importance One puzzle about knowledge that contextualists can solve is generated by pairs of cases4 like the following: Case A: A couple, Mary and John, have just woken to discover that their son, Joe, is ill. They have no reason to think he is seriously ill, but they decide to take his temperature anyway. When they do, they get a reading that says that his temperature is normal. The thermometer that they are using has always been reliable in the past, and they have no reason to think it is malfunctioning now, so when Mary gets this reading, she says ‘‘We know, on the basis of this reading, that Joe’s temperature is normal.’’ Case B: Mary and John have once again woken to discover that Joe is ill. But this time, it is possible that the illness is serious: there is a child at Joe’s school who has measles. As before, they take his temperature with a thermometer which has always been reliable in the past, and as before, they get a normal reading. But this time, Mary is not satisfied. This time, she says ‘‘We don’t know, on the basis of this reading, that Joe’s temperature is normal. The thermometer could be malfunctioning. We ought to check with another one.’’ On the assumption that Joe’s temperature is normal in cases A and B, and that there are no unusual features of either case that are not mentioned in the above descriptions, it is natural to say that the knowledge-claims that Mary makes in the two cases are both true. The fact that it is natural to say this is puzzling. For the thermometer reading seems to provide just as much evidence for Joe’s temperature being normal in case A as it does in case B. Why is it natural to say that this evidence is sufficient for knowledge in A, and natural to say that it is not sufficient for knowledge in B? Contextualists can explain this by saying that the standards for knowledge are higher in B than they are in A. More exactly, they can say that the standards that a piece of evidence must meet, in order to be sufficient for knowledge, are higher in B than in A. A natural way for them to explain this shift in standards is to say that it is more important for Mary to be right about Joe’s temperature in B. They can flesh out this explanation by appealing to a version of the relevant alternatives theory of knowledge.5 According to the relevant alternatives theory, S’s evidence for P is strong enough for knowledge only if it rules out all relevant alternatives to P. Subject-sensitive versions of the theory say that the range of relevant alternatives to P varies with the context of the subject, S, who is said to know P; speaker-sensitive versions say that it varies with the context of the speaker who says that S knows P.6 By appealing to an appropriately formulated speaker-sensitive version of the theory, contextualists can give a more detailed account of why the standards for knowledge are higher in case B than in A. To see this, consider a speaker-sensitive version of the theory on which the range...

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