That idea is subject to the celebrated lottery paradox: given a sufficiently large lottery, one would believe of each ticket that it loses and one would also believe that some ticket wins. How do the two relate? A standard view is that uncertain, qualitative beliefs pass a sufficiently high probability threshold. Bayesians speak quantitatively of degrees of belief in propositions. In traditional epistemology, semantics, epistemic logic, artificial intelligence planning, non-monotonic reasoning, and belief revision theory, one speaks qualitatively of belief in a propostion. Qualitative belief and the lottery paradox ![]() "A Close Shave with Realism: Ockham's Razor Derived from Efficient Convergence", completed manuscript."Efficient Convergence Implies Ockham's Razor", Proceedings of the 2002 International Workshop on Computational Models of Scientific Reasoning and Applications, Las Vegas, USA, June 24-27, 2002."Why Probability Does Not Capture the Logic of Scientific Justification", in Christopher Hitchcock, ed., Contemporary Debates in the Philosophy of Science, London: Blackwell, 2004."Justification as Truth-finding Efficiency: How Ockham's Razor Works", Minds and Machines 14:pp."How Simplicity Helps You Find the Truth Without Pointing at it", in Philosophy of Mathematics and Induction, V."Simplicity, Truth, and the Unending Game of Science", in Infinite Games: Foundations of the Formal Sciences V."Ockham’s Razor, Empirical Complexity, and Truth-finding Efficiency", Theoretical Computer Science, 383: 270-289, 2007."Ockham’s Razor, Truth, and Information", in Handbook of the Philosophy of Information, J."Review of Reliable Reasoning: Induction and Statistical Learning theory" by Gilbert Harman and Sanjeev Kulkarni,, 2008.Bandyopadhyay and Malcolm Forster eds., Dordrecht: Elsevier. "Simplicity, Truth, and Probability", in Handbook for the Philosophy of Statistics, Prasanta S.(with Conor Mayo-Wilson) "Ockham Efficiency Theorem for Random Empirical Methods", Journal of Philosophical Logic. ![]() (with Conor Mayo-Wilson), "Causal Conclusions that Flip Repeatedly and their Justification", Proceedings of the 26th Conference on Uncertainty and Artificial Intelligence,Peter Gruenewald and P.This paper presents new logical relations connecting three topics pertaining to inductive inference: (I) synchronic norms of theory choice, like the preferences for simpler and more falsifiable theories, (II) diachronic norms of theory change familiar from belief revision and AGM theory, and (III) the justification of such norms by truth-conduciveness, or learning performance. Learning, Theory Choice, and Belief Revision. ![]() The underlying mathematical framework is point set topology.This ongoing work is currently supported by a three year grant from the John Templeton Foundation. ![]() But what is empirical simplicity and how could a systematic bias toward it help one find the truth without invoking the (circular) assumption that the truth is simple? I propose that simplicity reflects the ability of nature to force a truth-conducive scientist through successive revisions of her theory and that Ockham's razor minimizes those revisions in the worst case. When faced with several theories compatible with the data, scientists tend to prefer the simplest and cite Ockham's razor as the justification. Research Areas Ockham's razor and realism
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