The Bayesians and the Raven Paradox

Abstract

We are all familiar with the traditional genesis of the raven paradox. The law that all ravens are black is logically equivalent to all nonblack things are non-ravens. By Nicod's criterion, where (Fa & Ga is a positive instance of (x) (FxD Gx)), a white shoe ends up serving as evidence for 'All ravens are black.' Since Hempel's discovery of this paradox of confirmation, philosophers have attempted to dispose of it in a variety of ways, usually by denying one of the above premisses. While the Bayesians concentrate their efforts on denying that a positive instance always confirms, others have attempted to solve the paradox by denying the equivalence condition. For example, Rom Harre does this in The Principles of Scientific Thinking. While I argue below that a law relating ravens and black feathers is not logically equivalent to one dealing with shoes and shoe color, I don't think that denying the equivalence condition bars the paradoxical result of a white shoe serving as evidence for the raven law. This is so because there is another way to generate the paradox, and in such a way that it goes through even without the equivalence condition. It seems that the Bayesian's think they have a knock-down solution to the raven paradox. According to their interpretation of the problem, the paradox rests on two premisses: first, that any data confirming an hypothesis confirms' its equivalent; and, secondly, any instance of an hypothesis lends support to it. Now, Bayesians such as I. J. Good and Roger Rosenkrantz home in on the second premiss, insisting that it is a mistake, according to Bayesian principles, to hold that an instance of an hypothesis always lends a degree of confirmation to it. Not only that, they go even further to main-