David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophy of Science 38 (2):216-220 (1971)
Though one believes that P is true, one can have reasons for thinking it false. Yet, it seems that one cannot know that P is true and (still) have reasons for thinking it false. Why is this so? What feature of knowledge (or of reasons) precludes having reasons or evidence to believe (true) what you know to be false? If the connection between reasons (evidence) and what one believes is expressible as a probability relation, it would seem that the only satisfactory explanation of this fact is that when one knows that P is true, the reasons or evidence one has in support of P are such as to confer upon P the probability of 1. It is shown by an application of Bayes' Theorem that any value smaller than 1 would permit having reasons to believe what one knows to be false. Hence, it would seem that knowledge requires conclusive reasons to believe (if reasons or evidence is required at all)
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Peter J. Graham (1997). What is Testimony? Philosophical Quarterly 47 (187):227-232.
Anthony Peressini (2003). Proof, Reliability, and Mathematical Knowledge. Theoria 69 (3):211-232.
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