By Prasanta S. Bandyopadhyay, Gordon Brittan Jr., Mark L. Taper
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Additional resources for Belief, Evidence, and Uncertainty: Problems of Epistemic Inference
1961). Probability and the logic of rational belief. Wesleyan, CT: Wesleyan University Press. Lele, S. (2004). Evidence Function and the Optimality of the Law of Likelihood. In (Taper and Lele, 2004). Levi, I. (1967). Probability Kinematics. British Journal for the Philosophy of Science, 18, 200– 205. Lewis, D. (1980). A Subjectivist’s Guide to Objective Chance. In R. C. ), Studies in inductive logic and probability (Vol. 11). Berkeley: University of California Press. Lindsay, B. (2004). Statistical Distances as Loss Functions in Assessing Model Adequacy.
One ﬁnal preliminary. We have assumed for the sake of clarity and convenience that the hypotheses in our schematic examples are simple and not complex. 22 The issues involved are technical, and for that reason we have put our discussion of them in an Appendix to this chapter. Sufﬁce it to say here that this objection can be met. The Evidential Condition Now back to our characterization of evidence. It is made precise in the following equation:23 D is evidence for H1 &B as against H2 &B if and only if LR1;2 !
Moreover, there is a coherence condition on conﬁrmation that need not be satisﬁed by our account of evidence: if H1 entails H2, then the probability of H1 cannot exceed the probability of H2, In addition, the notion of justiﬁcation is agent-sensitive; it depends on a distribution of prior probabilities on hypotheses, and relates, like belief generally, to what is in one’s head. The notion of evidence is agent-independent; it depends on a ratio of likelihoods already determined, and to this extent has to do with how things stand in the world, independent of the agent’s belief or knowledge.
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