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Unformatted text preview: Notes for Week 4 of Confirmation 09/19/07 Branden Fitelson 1 Some Background Issues in the Keynes Readings 1.1 Keynesian Conditional Probabilities There is an ambiguity in Keynes’s discussions involving probability. Sometimes he talks about agents know- ing (or believing) that some objective probability statement (sometimes having a logical flavor, but usually having an epistemic flavor) is true, and sometimes he talks about a rational agent’s degrees of belief (or credences ) having certain properties. These, of course, are different. An agent φ can know (or reasonably believe) that a claim Pr (p | q) = r is true, where Pr is some kind of objective probability, and at the same time have reasonable degrees of belief which are such that Pr φ (p | q) ≠ r . Indeed, for all Keynes tells us, it can even be the case that an agent φ falsely (but reasonably) believes that Pr φ (p | q) = r . Some have defended “bridge principles” or “direct inference” principles which connect certain sorts of objective prob- abilities with rational degrees of belief, in certain contexts. But, this is not an issue that Keynes takes up in any detail. That’s why his discussion is often ambiguous in this way. I will assume that he is trying to characterize (or give constraints on) Pr φ (p | q) itself, and not giving condtions under which it would be reasonable to believe that some class of objective probability statements are true. 1 Later, when we discuss Carnap, we will take the opposite stance, since it is clear that Carnap is talking about logical probabilities, and he realizes that substantive epistemological principles are need to connect them to credences. Keynes makes it clear that he doesn’t think Pr φ (p | q) always has a precise numerical value (or, at least, that we may not always be able to determine such values, either in the first or third person). But, since he is most concerned (in the chapters we’re reading) with relations of probabilistic relevance , it will be comparative claims such as Pr φ (p | q & K > ) > Pr φ (p | K > ) that are most important for us. 2 Keynes thinks that some such comparative claims can be true (or, at least, plausible), even if we cannot determine precise numerical values for Pr φ (p | K > ) or Pr φ (p | q & K > ) . I am using K > to denote an “a priori” background corpus — it is supposed to express/summarize certain “background propositions” that can be known a priori by φ , or, at least, those which are known prior to observing some “foreground” evidence that’s being considered. As such, Pr φ (p | K > ) can be thought of as an 3 epistemically rational “a priori” probability of p . Relative to such “a priori” background(s), some propositions will be favorable to ( i.e. , positively correlated with) p and some will be unfavorable to ( i.e. , negatively correlated with) p . This is an early rendition of an (epistemic) “a priori” probabilistic relevance conception of confirmation/disconfirmation...
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- Fall '06
- Inductive Reasoning, Keynes