Modus Ponens and Modus Tollens for Conditional Probabilities, and Updating on Uncertain Evidence

Theory and Decision 66 (2):103 - 148 (2009)
Abstract
There are narrowest bounds for P(h) when P(e) = y and P(h/e) = x, which bounds collapse to x as y goes to 1. A theorem for these bounds -- bounds for probable modus ponens -- entails a principle for updating on possibly uncertain evidence subject to these bounds that is a generalization of the principle for updating by conditioning on certain evidence. This way of updating on possibly uncertain evidence is appropriate when updating by ’probability kinematics’ or ’Jeffrey-conditioning’ is, and apparently in countless other cases as well. A more complicated theorem due to Karl Wagner -- bounds for probable modus tollens -- registers narrowest bounds for P(not h) when P(not e) = y and P(e/h) = x. This theorem serves another principle for updating on possibly uncertain evidence that might be termed ’contraditioning’, though it is for a way of updating that seems in practice to be frequently not appropriate. It is definitely not a way of putting down a theory -- for example, a random-chanc
Keywords sentential probability logic  Jeffrey-conditioning  hyperreal probabilities  fine-tuning
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DOI 10.1007/s11238-007-9072-0
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References found in this work BETA
Probability Kinematics and Commutativity.Carl G. Wagner - 2002 - Philosophy of Science 69 (2):266-278.
Intelligent Design and Probability Reasoning.Elliott Sober - 2002 - International Journal for Philosophy of Religion 52 (2):65-80.
Radical Probabilism and Bayesian Conditioning.Richard Bradley - 2005 - Philosophy of Science 72 (2):342-364.
Self-Doubts and Dutch Strategies.Jordan Howard Sobel - 1987 - Australasian Journal of Philosophy 65 (1):56 – 81.
Is There a Dutch Book Argument for Probability Kinematics?Brad Armendt - 1980 - Philosophy of Science 47 (4):583-588.

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Citations of this work BETA
Hope, Knowledge, and Blindspots.Jordan Dodd - 2017 - Synthese 194 (2):531-543.

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