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 theory, the value of a piece of information is proportional to the improbability of that information.

The most powerful and therefore most useful experiment depends on the situation: it may be the experiment most likely to confirm, or to refute, a hypothesis. The fate of most novel, sweeping hypotheses is a quick death, so their refutation has little impact on science. Confirmation of such a hypothesis, on the other hand, does have substantial information value. Similarly, many hypotheses are only incremental modifications of previous theories and so their confirmations are expected to be pro forma. Refutation of such a hypothesis may force us to rethink and revise our core assumptions. Well established theories are not normally tested directly, but when such a theory is found to be irreconcilable with an apparently rigorous experiment, this powerful and informative anomaly fosters intensive analysis and experimentation.

Ronald Giere [e.g., 1983] is one of the leading proponents of the ‘testing paradigm’, more popularly known as the diagnostic experiment. A diagnostic experiment avoids the ambiguity of weak true/false tests such as those of justificationism and falsificationism, and it avoids qualitative value judgments. The diagnostic test is the key test, the scalpel that cuts to the heart of a hypothesis and yields a result of ‘true’ if the prediction is confirmed, and ‘false’ if the prediction is refuted.

For normal science, the diagnostic experiment is generally a myth -- an ideal to be sought but seldom achieved. The diagnostic experiment is, nevertheless, a worthy goal, for it is far better to fall short of the perfectly diagnostic experiment than to fire random volleys of experiments in the general direction of an hypothesis. Jonas Salk [1990] has the ideal of a diagnostic experiment in mind when he says: “Solutions come through evolution. It comes from asking the right question. The solution preexists. It is the question that we have to discover.”

Clausewitz [1830] gives analogous advice to military planners: “A certain center of gravity, a center of power and movement, will form itself, on which everything depends. . . We may, therefore, establish it as a principle, that if we can conquer all our enemies by conquering one of them, the defeat of that one must be the aim of the War, because in that one we hit the common center of gravity of the whole War.”

The Raven’s Paradox [e.g., Lambert and Brittan, 1970; Mannoia, 1980] is an inductive problem that provides a surprising and useful perspective on the power of evidence. Suppose we wish to test this hypothesis: ‘All ravens are black.’ Symbolically, we can express this hypothesis as R⇒B (Raven implies Black) or ‘R, ∴B’ (Raven, therefore Black). Any example of a raven that is black provides confirmatory evidence for the validity of the hypothesis. Even one instance of a raven that is not black proves that the hypothesis is wrong.

The paradox arises when we consider the implications of the following rule of logic: each statement has logically equivalent statements (Chapter 4), and if a statement is true, its logically equivalent statement must also be true. A logical equivalent of the hypothesis ‘All ravens are black’ is ‘All non-black things are not ravens.’ Caution (or practice) is needed to be certain that one is correctly stating the logical equivalent. ‘All non-ravens are not black’ superficially sounds equivalent to ‘All ravens are black,’ but it is not.

The Raven’s Paradox is this: anything that is both not black and not a raven helps confirm the statement that all ravens are black. Without ever seeing a raven, we can gather massive amounts of evidence that all ravens are black.