Reprinted in Readings in Uncertain Reasoning, G. Shafer and J. Pearl, eds., pp. 259-273, San Mateo, CA: Morgan Kaufmann Publishers, Inc., 1990.

… quantifying confirmation and then manipulating the numbers as though they were probabilities quickly leads to apparent inconsistencies or paradoxes. Carl Hempel presented an early analysis of confirmation (Hempel, 1965), pointing out as we have that C[h,e] is a very different concept from P(hle ). His famous Paradox of the Ravens was presented early in his discussion of the logic of confirmation. Let hl be the statement that "all ravens are black" and h2 the statement that "all nonblack things are nonravens." Clearly hi is logically equivalent to h,2. If one were to draw an analogy with conditional probability, it might at first seem valid, therefore, to assert that C[hl,e] = C[h2,e] for all e. However, it appears counterintuitive to state that the observation of a green vase supports hi, even though the observation does seem to support h,2. C[h,e] is therefore different from P(hle) for it seems somehow wrong that an observation of a vase could logically support an assertion about ravens.

Another characteristic of a quantitative approach to confirmation that distinguishes the concept from probability was well-recognized by Carnap (1950) and discussed by Barker (1957) and Harrd (1970). They note it is counterintuitive to suggest that the confirmation of the negation of a hypothesis is equal to one minus the confirmation of the hypothesis, i.e., C[h,e] is not 1 - C[-qh,e]. The streptococcal decision rule asserted that a gram-positive coccus growing in chains is a Streptococcus with a measure of support specified as 7 out of 10. This translates to C[h,e]=0.7 where h is "the organism is a Streptococcus" and e is the information that "the organism is a gram-positive coccus growing in chains." As discussed above, an expert does not necessarily believe that C[mh,e] = 0.3. The evidence is said to be supportive of the contention that the organism is a Streptococcus and can therefore hardly also support the contention that the organism is not a Streptococcus.