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Unformatted text preview: Notes for Week 6 of Confirmation 10/10/07 Branden Fitelson 1 Hempel’s (Rather Odd) Reconstruction of Nicod We’ll discuss Hempel’s theory of confirmation in more depth next week. But, it was clearly inspired by some of Nicod’s earlier, inchoate remarks about instantial confirmation (which we saw last week), such as: Consider the formula or the law: A entails B . How can a particular proposition, [ i.e. ] a fact, affect its probability? If this fact consists of the presence of B in a case of A , it is favourable to the law . . . on the contrary, if it consists of the absence of B in a case of A , it is unfavourable to this law. While Nicod is not very clear on the logical details of his logical-probability-raising account of instantial confirmation, three aspects of Nicod’s conception of confirmation are apparent here: • Instantial confirmation is a relation between singular and general propositions/statements (or, if you will, between “facts” and “laws”). • Confirmation consists in positive probabilistic relevance , and disconfirmation consists in negative prob- abilistic relevance (where the salient probabilities are “inductive” or “logical”, as discussed last week). • Universal generalizations are confirmed by their positive instances and disconfirmed by their negative instances (indeed, Nicod also endorses an asymmetry here, as we discussed last week). Hempel offers a precise, logical reconstruction of Nicod’s naïve instantial account. There are several peculiar features of Hempel’s reconstruction of Nicod. I will focus presently on two such features. First, Hempel’s reconstruction is completely non-probabilistic (we’ll return to that unfortunate decision on Hempel’s part later). Second, Hempel’s reconstruction takes the relata of Nicod’s confirmation relation to be objects and universal statements, as opposed to singular statements and universal statements. In modern (first-order) parlance, Hempel’s reconstruction of Nicod seems to be something like the following principle: (NC ) For all objects x (with names x ), and for all predicate expressions φ and ψ : x confirms [ ( ∀ y)(φy ⊃ ψy) \ iff [ φ x & ψ x \ is true, and x disconfirms [ ( ∀ y)(φy ⊃ ψy) \ iff [ φ x & ∼ ψ x \ is true. As Hempel explains, (NC ) has some rather unfortunate consequences. For one thing, (NC ) leads to a theory of confirmation that violates the hypothetical equivalence condition : (EQC H ) If x confirms H , then x confirms anything logically equivalent to H . To see this, note that — according to (NC ) — both of the following obtain: • a confirms “ ( ∀ y)(Fy ⊃ Gy) ,” provided a is such that Fa & Ga ....
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- Fall '06
- Logic, Qualitative Research