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Problems with Objective Probability for Conditionals
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What Bennett Means by Objective Probability
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Objective probability is any sort of probability which demands inter
subjective agreement. Bennett distinguishes two types of objective
probability.
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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 nonextreme truth values.
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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.
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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.
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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.
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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
intersubjective truth.
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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.
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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.
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In particular since absolute objective probability assigns probability 0
to every false proposition all conditionals with false antecedents fall
victim to 0 intolerance.
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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.
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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 01 values to account for genuinely
random future contingents.
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 Fall '06
 FITELSON
 Logic, Bennett, objective probability, absolute objective probability

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