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Unformatted text preview: Notes for Week 11 of Confirmation 11/21/07 Branden Fitelson 1 Two Reflections on Our Discussions from the Past Few Weeks 1.1 Reflections on Maher on (NC) As you’ll recall, Maher’s “counterexample” to (NC) was based on intuitions about what raises the probability of what, relative to “what we (actually) know” ( K α ). As I pointed out, this is unfortunate, since he needs an ex ample that holds, relative to no background knowledge (or empty / a priori background knowledge K > ). Sim ilarly, Maher’s argument for the existence of inductive probabilities only establishes the existence of (some) inductive probabilities, relative to substantive , empirical background conditions [Pr (p  K α ) ]. Again, this is unfortunate, since his main applications of inductive probability to confirmation theory involve principles like (NC) which are explicitly to be interpreted as involving inductive probabilities, relative to no/empty/ a priori background evidence [Pr (p  K > ) ]. Apparently, he seems to think that some sort of analogical argu ment will allow us to go from facts about Pr (p  K α ) to facts about Pr (p  K > ) . But, the analogical argument will also have to (somehow) establish the existence of Pr (p  K > ) from the existence of Pr (p  K α ) . Moreover, the analogical argument will also have to (somehow) tell us something about the values (or ranges of values) of Pr (p  K > ) , for some p ’s. For instance, Maher needs certain p ’s to have low Pr (p  K > ) values, in order for his “counterexample” to (NC) to have any force. [This adds up to some very heavy lifting for an analogical argument!] This is all review from what I said in my notes a few weeks back. Now, I want to point out another problematic fact about Maher’s discussions on inductive probability and confirmation. Let’s think about Maher’s explicatum for Pr (p  K > ) . Maher’s λ / γcontinuum has adjustable parameters γ F and γ G , which correspond to Pr (Fa  K > ) and Pr (Ga  K > ) , repsectively, for an L 2 , 2 with two predicates F and G and a constant a , which (let’s assume) appears in some evidence statement E of interest. Maher tells us that: The choice of γ F and γ G will depend on what the predicates ‘ F ’ and ‘ G ’ mean and may require careful deliberation. For example, if ‘ F ’ means ‘raven’ then, since this is a very specific property and there are vast numbers of alternative properties that seem equally likely to be exemplified a priori, γ F should be very small, surely less than 1/1000. A reasoned choice of a precise value would require careful consideration of what exactly is meant by ‘raven’ and what the alternatives are....
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 Fall '06
 FITELSON
 Logic, Probability, Inductive Reasoning, Logical positivism, N. Goodman, Case Studies fitelson.org

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