Confirming Inexact Generalizations

I suppose that 'ravens are black' is an inexact generalization having a degree of truth measured by the proportion of ravens that are black, and a probability measured by its expected degree of truth in different 'possible worlds.' Given this, 'ravens are black' differs in truth, probability, and confirmation from 'non-black things are not ravens', and this suggests a new approach to Hempel's Paradox as well as to other aspects of confirmation. Basic concepts of a formal theory developing this approach are described, and some of its fundamental laws are given, together with sketches of applications.
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