Innnitely Many Resolutions of Hempel's Paradox

What man is so mad as wil say the swan is black: or that the raven is in couloure white, when the matter is otherwise to be judged by commonsense? {Cardanus ca. 1576 Abstract. What sorts of observations could connrm the universal hypothesis that all ravens are black? Carl Hempel proposed a number of simple and plausible principles which had the odd (\paradoxical") result that not only do observations of black ravens connrm that hypothesis, but so too do observations of yellow suns, green seas and white shoes. Hempel's response to his own paradox was to call it a psychological illusion|i.e., white shoes do indeed connrm that all ravens are black. Karl Popper on the other hand needed no response: he claimed that no observation can connrm any general statement|there is no such thing as connrmation theory. Instead, we should be looking for severe tests of our theories, strong attempts to falsify them. Bayesian philosophers have (in a loose sense) followed the Popperian analysis of Hempel's paradox (while retaining connrmation theory): they have usually judged that observing a white shoe in a shoe store does not qualify as a severe test of the hypothesis and so, while providing Bayesian connrmation, does so to only a minute degree. This rationalizes our common intuition of non-connrmation. All of these responses to the paradox are demonstrably wrong|granting an ordinary Bayesian measure of connrmation. A proper Bayesian analysis reveals that observations of white shoes may provide the raven hypothesis any degree of connrmation whatsoever.