Philose Koshy

In this paper, I critically analyse two strands of Bayesian solution to the paradox: the standard Bayesian solution and the attempts to refute Nicod’s criterion. I argue that the standard Bayesian solution evades the exact challenge of the paradox. I hold that though the NC or instance confirmation is imprecisely formulated, it cannot be ruled out as an invalid form of confirmation. I formulate three conditions of instance confirmation which sufficiently captures our intuitive notion of instance confirmation. Finally on the basis of the conditions of instance confirmation, I show that paradoxical contrapositive instances like white shoe are not contrapositive instances of the raven hypothesis.

This paper discusses an aspect of the problem of old evidence which I call here the general problem of old evidence. The probability of old evidence is one or close to one, because background information K entails the evidence E or K consists of propositions which make E probable. In the literature, K is considered as a proposition relevant to E. Based on examples, I argue that K does not support the truth of E; instead, K supports the evidential status of E. I define background information as a set of propositions necessary and sufficient to consider E as the evidence of hypothesis H. Background information is relevant to the bearing of E on H, but not to the truth of E itself. My definition of background information implies that background information of E is probabilistically independent of E; that is, in the case of old evidence, neither P = 1, nor P ≈ 1.