On novel confirmation

Abstract
Evidence that confirms a scientific hypothesis is said to be ‘novel’ if it is not discovered until after the hypothesis isconstructed. The philosophical issues surrounding novel confirmation have been well summarized by Campbell and Vinci [1983]. They write that philosophers of science generally agree that when observational evidence supports a theory, the confirmation is much stronger when the evidence is ‘novel’. . . There are, nevertheless, reasons to be skeptical of this tradition . . . The notion of novel confirmation is beset with a theoretical puzzle about how the degree of confirmation can change without any change in the evidence, hypothesis, or auxiliary assumptions . . . There have not yet appeared any obviously satisfactory solutions to these problems Much of the literature on novel confirmation relies on the Bayesian analysis of conditional probabilities. Let H represent a hypothesis, E an event that confirms the hypothesis, and B some relevant background information. Denote by Pr(x | y) the conditional probability of x given y. There are various plausible measures of the degree of support that E lends to H. Among these are: Degree of support = Pr(H|E) Degree of support = Pr(H|E & B) – Pr(H|B) Degree of support = Pr(H|B & B) – Pr(H|B – {E}) Degree of support = Pr(H|B & knowledge that H E) – Pt(H|B) In the work cited, Campbell and Vinci offer a somewhat more involved Bayesian interpretation. Formula (1) is discussed by Gardner [1981] who points out that under this formulation there can be no role for novelty. 'The function Pr(H|E) contains no third slot in which to insert a temporal relation between the invention of H and the inventor's learning E. Obviously, then, this relation could not possibly affect E's support of H.' Formula (2), on the other hand, suggests a role for novelty. Bayes's Theorem allows us to rewrite the formula as (2') Degree of support = Pr(H|B) x [Pr(E|H&B) – 1] We can use 1/Pr(E|B) as a measure of the novelty of E. Then (2') shows that the degree of support increases with novelty of E. In the paper already cited, Campbell and Vinci discuss shortcomings of this analysis. Formula (3) expresses an alternative offered by Howson [1984]. In that formula, Pr(H/B – {E}) represents the probability of H assuming (counterfactually) that only B – {E} is known. This allows for the possibility of non-novel facts generating support for hypotheses. Niiniluoto [1984] argues for a variant along the lines of (4), in which we account for the possibility that the theorist was unaware that his hypothesis entails E. One problem in deciding among these approaches is that the choice of a definition for the degree of support appears arbitrary. What kind of argument could justify the choice of one definition over another? It is our position that there can be no basis for addressing this question in the absence of an explicit model of the process by which hypotheses are generated. Only in the presence of such a model can the various conditional probabilities be given meaningful interpretations. We provide such models in Sections 1, 2 and 4. The simple model of Section 1, incorporating strong assumptions, yields the conclusion that novelty is irrelevant. When these assumptions are relaxed in the later sections, novelty becomes relevant for a variety of reasons. It is at least potentially the case that scientists have more information about their own abilities than is publicly available, and this information might influence their decisions about whether even to attempt novel prediction. If this is so, then it should be incorporated into the model of hypothesis generation. This requires an explicit discussion of how scientists respond to incentives and how the incentives themselves evolve, which in turn takes us into the realm of economic theory. We have addressed these issues in another paper, written for an audience of economists. The results of this research are summarized in Section 3.
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    Arthur M. Diamond (1996). The Economics of Science. Knowledge and Policy 9 (2-3):6-49.
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