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Coherence and Epistemic Rationality

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Coherence and Epistemic Rationality

This paper addresses the question of whether probabilistic coherence is a requirement of rationality. The concept of probabilistic coherence is examined and compared with the familiar notion of consistency for simple beliefs. Several reasons are given for thinking rationality does not require coherence. Finally, it is argued that incoherence does not necessarily involve fallacious reasoning.

Most work in epistemology treats epistemic attitudes as bivalent. It is assumed that a person either believes that there is an apple on the table, or that there is not, and that such beliefs must be either warranted or unwarranted. However, a little reflection suggests that it is reasonable to have degrees of confidence in a proposition when the available evidence is not conclusive. The rationality of such judgments, formed in response to evidence, will be my concern here.

Degrees of confidence have mainly been discussed by Bayesians as part of a general theory of rational belief and decision. Bayesians claim that rational degrees of confidence satisfy the standard Kolmogorov axioms of probability:

1. Pr(A) = 0

2. If A is a tautology, then Pr(A) =1

3. If A and B are mutually exclusive, then Pr(A v B) = Pr (A) + Pr(B).

It should be observed that people do not generally assign point values to propositions, which is required if their degrees of confidence are to conform to the axioms. Moreover, it is doubtful that an assignment of point values to propositions is usually reasonable, since it seems that our evidence rarely justifies such precision. Such vague degrees of confidence can be treated somewhat more realistically, as interval valued, by associating them with sets of probability functions. For simplicity, I will take degrees of belief here as point valued in my discussion here.

The claim that degrees of confidence should satisfy the probability axioms is most often defended by appealing to the so-called Dutch Book argument, which was first presented by Ramsey in his famous paper "Truth and Probability". The idea is that degrees of belief that do not satisfy the probability axioms (commonly termed incoherent) are associated with betting quotients that can be exploited by a clever bookie to produce a sure loss. Ramsey held that an agent's degrees of belief can be measured roughly by the bets that she is willing to accept. If they are incoherent, there will be a series of bets, each of which she will be willing to accept, but which are certain to result in a net loss for her.
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