The Raven’s Paradox has been the subject of much discussion among philosophers of science. Some of this discussion has concluded that seemingly absurd types of evidence (not-Black + notRaven confirms R⇒B) are nevertheless valid, but most arguments have centered on the intrinsic weakness of the confirmation process. In contrast, I see the tests of the Raven’s Paradox, like all scientific evidence, in terms of information value. Observations of non-ravens do help confirm the hypothesis that ‘All ravens are black,’ but the information value or evidential power of each observation of a non-raven is miniscule. Even thousands of such observations are less useful than a single observation of a raven’s color. Were this not so, we could use the concept of logical equivalence to ‘confirm’ more outrageous hypotheses such as ‘All dragons are fierce.’
Like the example in Chapter 3 of the ‘cause’ of Archimedes’ death, many inferences form a pattern: X1⇒X2⇒X3⇒X4. All elements of the pattern are essential; all elements are not of equal interest. Familiar relationships warrant only peripheral mention. The pattern link of greatest scientific interest is the link that has the maximum information value: the most unusual segment of the pattern.
Scientific research is intimately concerned with the power of evidence. Inefficient scientists are transient scientists. The demand for efficiency requires that each researcher seek out the most powerful types of evidence, not the most readily available data. In the case of the Raven’s Paradox, this emphasis on experimental power means first that only ravens will be examined. Furthermore, a single instance of a non-black raven is much more important than many instances of black ravens, so the efficient scientist might design an experiment to optimize the chance of finding a non-black raven. For example, the hypothesis ‘All dogs have hair’ could be tested by visiting several nearby kennels, but a single visit to a Mexican kennel, after some background research, might reveal several examples of Mexican hairless dogs.
To the logician, a single non-black raven disproves ‘All ravens are black’, and a single Mexican hairless disproves ‘All dogs have hair.’ The scientist accepts this deductive conclusion but also considers the total amount of information value. If exceptions to the hypothesis are rare, then the scientist may still consider the hypothesis to be useful and may modify it: ‘99.9% of ravens are black and 0.1% have non-black stains on some feathers,’ and ‘All dogs except Mexican hairlesses have hair.’
Hypothesis Modification
The distinction between scientists’ and logicians’ approaches does not, of course, mean that the scientist is illogical. Confirmation and refutation of hypotheses are essential to both groups. They usually do not, however, lead simply to approval or discarding of scientific hypotheses. In part, this outcome is progressive: the hypothesis as originally stated may be discarded, but the scientific companion of refutation is modification. In many cases, simple acceptance or rejection is not possible, because hypotheses are usually imperfect.
Confirmation or falsification of a hypothesis, like the ‘diagnostic experiment’, can be difficult to achieve, for several reasons:
• Many hypotheses have inherent ambiguities that prevent simple confirmation or falsification. An experiment may favor one interpretation of a hypothesis, but the door is left open for other interpretations.
