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{ Kevin T. Kelly, Hanti Lin } Carnegie Mellon University This work was supported by a generous grant by the Templeton Foundation.

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Propositions A C B

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(0, 1, 0) (0, 0, 1) (1, 0, 0) (1/3, 1/3, 1/3) Propositions Probabilities A C B

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(0, 1, 0) (0, 0, 1) (1, 0, 0) (1/3, 1/3, 1/3) Propositions Probabilities A C B ? ?

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(0, 1, 0) (0, 0, 1) (1, 0, 0) (1/3, 1/3, 1/3) Propositions Probabilities A C B Acpt

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You condition on whatever you accept (Kyburg, Levi, etc.) Very serious business! Does it ever happen? Its not Sunday, so lets buy beer at the super market. You would never bet your life against nothing that what you say to yourself in routine planning are true.

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The geometry of probabilities is much richer than the lattice of propositions. Aim: represent Bayesian credences as aptly as possible with propositions.

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The geometry of probabilities is much richer than the lattice of propositions. Aim: represent Bayesian credences as aptly as possible with propositions. A B C Acpt B

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The geometry of probabilities is much richer than the lattice of propositions. Aim: represent Bayesian credences as aptly as possible with propositions. B C Acpt B v C A

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Suppose you accept propositions more probable than 1/2. Consider a 3 ticket lottery. For each ticket, you accept that it loses. That entails that every ticket loses. (Kyburg) -B-C-A 1/2

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High probability is like truth value 1. B CA 1

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(0, 1, 0) (0, 0, 1)(1, 0, 0) (1/3, 1/3, 1/3)

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A BC p(A) = 0.8

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A BC A v B p(A v B) = 0.8

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A BC A v B A v C

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A BC A v B A v C A Closure under conjunction

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A v B A v C A BCB v C

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A v B A v C A BCB v C T

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A v B A v C A BCB v C T 2/3 t

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A v B A v C A B v C T BC 2/3 t

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A v B A v C A B v CBC T 2/3 t

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A v C A C B v C T B A v B A v C A C B v C T B A v B LMUCMU (Levi 1996)

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A v C B v C T A v B A v C A CB v C T B A v B LMUCMU A CB (Levi 1996)

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A v C B v C T A CB LMUCMU A CB A v B (Levi 1996)

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Thats junk! I want a smoother ride! I want tighter handling! consumer designer

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consumer designer Grow up. We can optimize one or the other but not both.

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consumer designer responsive Grow up. We can optimize one or the other but not both. steady LMU CMU

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= Change what you accept only when it is logically refuted. responsive steady LMU CMU = Track probabilistic conditioning exactly.

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Steadiness Responsive -ness responsive steady LMU CMU

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