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# 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.
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peter - Problems with Objective Probability for...

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