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 | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,709 |
| External links | This entry has no external links. Add one. |
| Through your library | Configure |
Similar books and articlesCarl G. Wagner (2004). Modus Tollens Probabilized. British Journal for the Philosophy of Science 55 (4):747-753.
James Hawthorne (2004). Three Models of Sequential Belief Updating on Uncertain Evidence. Journal of Philosophical Logic 33 (1):89-123.
Paul A. Klaczynski & David B. Daniel (2005). Individual Differences in Conditional Reasoning: A Dual-Process Account. Thinking and Reasoning 11 (4):305 – 325.
Seth Yalcin (2012). A Counterexample to Modus Tollens. Journal of Philosophical Logic 41 (6):1001-1024.
Colin Howson (2009). Sorites is No Threat to Modus Ponens: A Reply to Kochan. International Studies in the Philosophy of Science 23 (2):209-212.
Niki Pfeifer & G. D. Kleiter (2007). Human Reasoning with Imprecise Probabilities: Modus Ponens and Denying the Antecedent. In Proceedings of the 5 T H International Symposium on Imprecise Probability: Theories and Applications.
Susanne Bobzien (2002). The Development of Modus Ponens in Antiquity: From Aristotle to the 2nd Century AD. Phronesis 47 (4):359-394.
Susanne Bobzien (2002). The Development of Modus Ponens in Antiquity : From Aristotle to the 2nd Century AD. Phronesis 47 (4):359-394.
Sieghard Beller & Gregory Kuhnm (2007). What Causal Conditional Reasoning Tells Us About People's Understanding of Causality. Thinking and Reasoning 13 (4):426 – 460.
Paul D. Thorn (forthcoming). Defeasible Conditionalization. Journal of Philosophical Logic:1-20.
Daniel Osherson & Jiaying Zhao (2011). Updating Beliefs in Light of Uncertain Evidence: Descriptive Assessment of Jeffrey's Rule. Thinking and Reasoning 16 (4):288-307.
Joshua Schechter & David Enoch (2006). Meaning and Justification: The Case of Modus Ponens. Noûs 40 (4):687 - 715.
Analytics
Monthly downloads
Sorry, there are not enough data points to plot this chart.
|
Added to index2012-06-17Total downloads0Recent downloads (6 months)0How can I increase my downloads? |
My notes
Discussion
