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Reasons, Knowledge, and Probability

Published online by Cambridge University Press:  14 March 2022

Fred I. Dretske
Fred I. Dretske*
Affiliation:
University of Wisconsin
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Abstract

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).

Type
Research Article
Information
Philosophy of Science , Volume 38 , Issue 2 , June 1971 , pp. 216 - 220
Copyright
Copyright © 1971 by The Philosophy of Science Association

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References

1 This is not strictly true since in the event that Pr(R : P) = 0 it is clear that Pr(R, F: P) cannot be made smaller than Pr(R: P); yet, since this is equivalent to Pr(R: not-P) = 1 we might wish to say that even though the probability of not-P (relative to R) was 1 we could still acquire additional (albeit superfluous) reasons in favor of not-P. In what follows I shall ignore this special case. I am interested in those situations in which P remains a possible, a more or less probable, alternative. That is, I am interested in those situations in which Pr(R : P) > 0 and, more particularly, I am interested in those situations in which Pr(R : P) > .5.

2 There are, of course, other reasons for representing knowledge by a probability of 1. For example, if we should say that S knows that P (on the basis of R) was to be represented by Pr(R : P) ≥ .9, then we should encounter the situation in which S knew that P on the basis of R (Pr(R : P) = .9), knew that Q on the basis of M (Pr(M: Q) = .9), but did not know that P and Q were the case on the basis of R and M since, generally speaking, Pr(R,M: P and Q) < .9.