confirmation an evidential relation between evidence and any statement (especially a scientific hypothesis) that this evidence supports. It is essential to distinguish two distinct, and fundamentally different, meanings of the term: (1) the incremental sense, in which a piece of evidence contributes at least some degree of support to the hypothesis in question – e.g., finding a fingerprint of the suspect at the scene of the crime lends some weight to the hypothesis that the suspect is guilty; and (2) the absolute sense, in which a body of evidence provides strong support for the hypothesis in question – e.g., a case presented by a prosecutor making it practically certain that the suspect is guilty. If one thinks of confirmation in terms of probability, then evidence that increases the probability of a hypothesis confirms it incrementally, whereas evidence that renders a hypothesis highly probable confirms it absolutely. In each of the two foregoing senses one can distinguish three types of confirmation: (i) qualitative, (ii) quantitative, and (iii) comparative. (i) Both examples in the preceding paragraph illustrate qualitative confirmation, for no numerical values of the degree of confirmation were mentioned. (ii) If a gambler, upon learning that an opponent holds a certain card, asserts that her chance of winning has increased from 2/3 to ¾, the claim is an instance of quantitative incremental confirmation. If a physician states that, on the basis of an X-ray, the probability that the patient has tuberculosis i.95, that claim exemplifies quantitative absolute confirmation. In the incremental sense, any case of quantitative confirmation involves a difference between two probability values; in the absolute sense, any case of quantitative confirmation involves only one probability value. (iii) Comparative confirmation in the incremental sense would be illustrated if an investigator said that possession of the murder weapon weighs more heavily against the suspect than does the fingerprint found at the scene of the crime. Comparative confirmation in the absolute sense would occur if a prosecutor claimed to have strong cases against two suspects thought to be involved in a crime, but that the case against one is stronger than that against the other.
Even given recognition of the foregoing six varieties of confirmation, there is still considerable controversy regarding its analysis. Some authors claim that quantitative confirmation does not exist; only qualitative and/or comparative confirmation are possible. Some authors maintain that confirmation has nothing to do with probability, whereas others – known as Bayesians – analyze confirmation explicitly in terms of Bayes’s theorem in the mathematical calculus of probability. Among those who offer probabilistic analyses there are differences as to which interpretation of probability is suitable in this context. Popper advocates a concept of corroboration that differs fundamentally from confirmation.
Many (real or apparent) paradoxes of confirmation have been posed; the most famous is the paradox of the ravens. It is plausible to suppose that ‘All ravens are black’ can be incrementally confirmed by the observation of one of its instances, namely, a black crow. However, ‘All ravens are black’ is logically equivalent to ‘All non-black things are non-ravens.’ By parity of reasoning, an instance of this statement, namely, any nonblack non-raven (e.g., a white shoe), should incrementally confirm it. Moreover, the equivalence condition – whatever confirms a hypothesis must equally confirm any statement logically equivalent to it – seems eminently reasonable. The result appears to facilitate indoor ornithology, for the observation of a white shoe would seem to confirm incrementally the hypothesis that all ravens are black. Many attempted resolutions of this paradox can be found in the literature.
See also TESTABILITY, VERIFICATIONIS. W.C.S.