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Unformatted text preview: Confirmation Theory Patrick Maher Department of Philosophy, University of Illinois at Urbana-Champaign Predictions about the future and unrestricted universal generaliza- tions are never logically implied by our observational evidence, which is limited to particular facts in the present and past. Nevertheless, propositions of these and other kinds are often said to be confirmed by observational evidence. A natural place to begin the study of confirma- tion theory is to consider what it means to say that some evidence E confirms a hypothesis H . Incremental and absolute confirmation Let us say that E raises the probability of H if the probability of H given E is higher than the probability of H not given E . According to many confirmation theorists, E confirms H means that E raises the probability of H . This conception of confirmation will be called incremental confirmation . Let us say that H is probable given E if the probability of H given E is above some threshold. (This threshold remains to be specified but is assumed to be at least one half.) According to some confirmation theorists, E confirms H means that H is probable given E . This conception of confirmation will be called absolute confirmation . Confirmation theorists have sometimes failed to distinguish these two concepts. For example, Carl Hempel in his classic Studies in the Logic of Confirmation endorsed the following principles: (1) A generalization of the form All F are G is confirmed by the evidence that there is an individual that is both F and G . (2) A generalization of that form is also confirmed by the evidence that there is an individual that is neither F nor G . (3) The hypotheses confirmed by a piece of evidence are consistent with one another. (4) If E confirms H then E confirms every logical consequence of H . Principles (1) and (2) are not true of absolute confirmation. Obser- vation of a single thing that is F and G cannot in general make it probable that all F are G ; likewise for an individual that is neither Published in The Encyclopedia of Philosophy 2nd ed., ed. Donald M. Borchert, Macmillan 2005. ctk.tex; 23/07/2006; 8:46; p.1 2 F nor G . On the other hand, there is some plausibility to the idea that an observation of something that is both F and G would raise the probability that all F are G . Hempel argued that the same is true of an individual that is neither F nor G . Thus Hempel apparently had incremental confirmation in mind when he endorsed (1) and (2). Principle (3) is true of absolute confirmation but not of incremental confirmation. It is true of absolute confirmation because if one hypoth- esis has a probability greater than 1/2 then any hypothesis inconsistent with it has a probability less than 1/2. To see that (3) is not true of incremental confirmation, suppose that a fair coin will be tossed twice, let H 1 be that the first toss lands heads and the second toss lands tails, and let H 2 be that both tosses land heads. Thenbe that both tosses land heads....
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This note was uploaded on 08/01/2008 for the course PHIL 290 taught by Professor Fitelson during the Fall '06 term at University of California, Berkeley.
- Fall '06