David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Theory and Decision 66 (2):103 - 148 (2009)
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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References found in this work BETA
Richard C. Jeffrey (2004). Subjective Probability: The Real Thing. Cambridge University Press.
Jordan Howard Sobel (2004). Logic and Theism: Arguments for and Against Beliefs in God. Cambridge University Press.
Carl G. Wagner (2002). Probability Kinematics and Commutativity. Philosophy of Science 69 (2):266-278.
Elliott Sober (2002). Intelligent Design and Probability Reasoning. International Journal for Philosophy of Religion 52 (2):65-80.
Richard Bradley (2005). Radical Probabilism and Bayesian Conditioning. Philosophy of Science 72 (2):342-364.
Citations of this work BETA
Jordan Dodd (forthcoming). Hope, Knowledge, and Blindspots. Synthese:1-13.
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