peter - Problems with Objective Probability for...

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Problems with Objective Probability for Conditionals What Bennett Means by Objective Probability Objective probability is any sort of probability which demands inter- subjective agreement. Bennett distinguishes two types of objective probability. Absolute objective probability: This is the sort of probability which assigns all true facts 1 and all false facts 0. Thus the probability booth shot lincoln is either 0 or 1. Only genuinely physically underdetermined future events like “This radioactive molecule will decay in the next 10 minutes” receive non-extreme truth values. Relative objective probability: Gives the amount of probability a particular body of evidence confers on a statement. Interestingly on page 47 Bennett introduces this as a three place relation, R(P,Q,n), between a proposition P, body of evidence Q and a measure of probability n. One can think of this as a Keynesian inductive probability where R(P,Q,n) gives the degree of support evidence Q confers on proposition P according to measure n. What boolean algebra is this probability defined on? Perhaps Bennett thinks that this is built into parameter n (i.e. is just dom(n)) but this is unclear. To be fair perhaps Bennett is holding off identifying the space here because he thinks the best possibility is in terms of possible worlds. In order to be objective in Bennett’s sense n must not depend on the person evaluating the claim. This too is consistent with a Keynesian, or Carnapian inductive probability where n is an inter-subjective truth. Compatibility with Bennett’s other views (Ramsey test and hence conditionalization) requires something like R(P,Q,n)=n(P&Q)/n(Q). In other words the two place function R is equivalent to some ratio of one place functions. Bennett assumes we need to define the objective probability of particular conditionals in terms of relative objective probability, hence his insistence
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we need to include pieces of background evidence. Though he never explicitly considers absolute objective probability it would seem any such notion still fails bennett’s intuitions in cases of false antecedents. In particular since absolute objective probability assigns probability 0 to every false proposition all conditionals with false antecedents fall victim to 0 intolerance. What does an objective probability for a conditional mean? We know Bennett is assuming we start with a relative objective probability function but what we define using this might be something like an absolute objective probability function. If we are defining something like an absolute objective probability function we are essentially just giving a test for the truth of a conditional, although truth in this case can take on non 0-1 values to account for genuinely random future contingents. As above only future events genuinely undetermined by the current
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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.

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peter - Problems with Objective Probability for...

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