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Unformatted text preview: Notes for Week 5 of Confirmation 09/26/07 Branden Fitelson 1 Preliminary Remarks About Nicod, Probability, and Inductive Logic While Nicod intends to be carrying forward the work of Keynes on universal induction, there is a noticeable shift from Keynes to Nicod. Keynes was primarily talking about induction as an epistemological problem. Nicod, on the other hand, seems to prefer to think of induction in “ logical ” terms. [Historical note: the word “confirmation” is used for the first time here by Nicod in connection with a “logical” conception of induction. This sets the stage for the subsequent work of Hempel, Carnap, and others.] Unfortunately, Nicod makes several significant logical errors during the course of setting up his essay on “the logical problem of induction”. As a result, several of his main lines of argument are frustrated, and various confusions arise. Before delving into some of the details of Nicod’s essay, I want to discuss a few of these confusions. First, an important distinction that arises (in rather inchoate/confused form) in Nicod’s discussion is that between probability logic (PL) and probabilistic inductive logic (PIL). (PL) is deductive : it involves deductive entailment relations between certain kinds of probability statements, and it is typically used to provide a theoretical account of how uncertainty in the premises of various sorts of arguments “propagate through” to their con- clusions. (PIL), on the other hand, is inductive : it involves genuine probabilistic relations between premises and conclusions, where these relations are themselves logical in nature (they are analogous to deductive relations). When Nicod sets up the framework of his discussion, he begins with a sort of “preamble”: We first regard inference as the perception of a connection between the premises and conclusion which asserts that the conclusion is true if the premises are true. This connection is implication, and we shall say that an inference grounded in it is a certain inference . But there are weaker connections which are also the basis of inferences. They have not until recently received any universal name. Let us call them with Mr. Keynes relations of probability . The presence of one of these relations among the group A of propositions and the proposition B indicates that in the absence of any other information, if A is true, B is probable to a degree p . A is still a group of premises, B is still a conclusion, and the perception of such a relation between A and B is still an inference: let us call this second kind of inference probable inference . Here, Nicod is postulating logical probability relations (analogous to entailments), the “perception” of which constitute inductive inference (presumably, an epistemological relation). He seems to think this is what Keynes has in mind. I don’t think so. As I explained last week, I think Keynes’s probabilities are (all) epistemic , not logical....
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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 Berkeley.
- Fall '06