disconfirms the contrary statement that all ravens are not black, i.e. satisfies its denial. A black raven, in other words, satisfies the hypothesis that all ravens are black rather than not: it thus selectively confirms that all ravens are black. Selective confirmation violates the equivalence condition since a black raven selectively confirms "All ravens are black" but not "All non-black things are non-ravens". Probabilistic or non-probabilistic induction Scheffler and Goodman's concept of selective confirmation is an example of an interpretation of "provides evidence in favor of..." which does not coincide with "increase the probability of..." This must be a general feature of all resolutions that reject the equivalence condition, since logically equivalent propositions must always have the same probability. It is impossible for the observation of a black raven to increase the probability of the proposition "All ravens are black" without causing exactly the same change to the probability that "All non-black things are non-ravens". If an observation inductively supports the former but not the latter, then "inductively support" must refer to something other than changes in the probabilities of propositions. A possible loophole is to interpret "All" as "Nearly all" – "Nearly all ravens are black" is not equivalent to "Nearly all non-black things are non-ravens", and these propositions can have very different probabilities. This raises the broader question of the relation of probability theory to inductive reasoning. Karl Popper argued that probability theory alone cannot account for induction. His argument involves splitting a hypothesis, , into a part that is deductively entailed by the evidence, , and another part. This can be done in two ways. First, consider the splitting: where , and are probabilistically independent: and so on. The condition that is necessary for such a splitting of H and E to be possible is , that is, that is probabilistically supported by . Popper's observation is that the part, , of that receives support from actually follows deductively from , while the part of that does not follow deductively from receives no support at all from – that is, . Second, the splitting: separates into , which as Popper says, "is the logically strongest part of (or of the content of ) that follows [deductively] from ", and , which, he says, "contains all of that goes beyond ". He continues: Does , in this case, provide any support for the factor , which in the