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Talk by Kevin Kelly: A Happy Marriage Between Propositional and Probabilistic Reasoning (November 10th, 2011)

Talk: A Happy Marriage Between Propositional and Probabilistic Reasoning by Prof. Dr. Kevin Kelly

This talk describes fresh results concerning acceptance of propositions in light of their probabilities. For a long time, it has seemed that sufficiently probable propositions should be accepted, but that idea leads immediately to the familiar lottery paradox (Kyburg 1961), in which one accepts of each lottery ticket that it loses but that some ticket must win. That is just the tip of the iceberg—we introduce a pair of new, diachronic paradoxes that cannot be avoided by insistence on high probability thresholds. The first arises when one accepts a hypothesis and then rejects it after observing what it predicts. The second arises when one refuses to accept a hypothesis that one would accept regardless of the outcome of some experiment until the outcome is seen. We propose an acceptance rule originally discovered by Isaac Levi (1996) that avoids the old and new paradoxes. We also show that propositional revision of accepted propositions can perfectly track probabilistic conditioning followed by acceptance, for any finite number of steps — a pre-established  harmony between probabilistic and propositional reasoning. Furthermore, we show that the familiar AGM approach to propositional belief revision cannot be made to do the same, regardless of the acceptance rule one chooses. Finally we show that the necessary price of these many logical advantages is that acceptance must depend on contextual framing effects. Context-dependence has long been viewed as a concession to irrationality. We suggest, to the contrary, that the logical advantages of our approach provide a novel, normative argument in favor of the dependence of propositional reasoning on contextual framing effects. Our slogan: logic is where you find it.

Date: 10 November, 2011

Place: Gebäude 23.21, Hörsaal 3F

Video recording of Kelly's talk