Abstract
(I) Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. (II) Diachronic norms of theory change, as studied in belief revision, restrict how one should change one’s current beliefs in light of new information. (III) Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning (III), we explicate inductive truth conduciveness in terms of optimally direct convergence to the truth, where optimal directness is explicated in terms of reversals and cycles of opinion prior to convergence. Concerning (I), we explicate Ockham’s razor and related principles of choice in terms of the information topology of the empirical problem context and show that the principles are necessary for reversal or cycle optimal convergence to the truth. Concerning (II), we weaken the standard principles of agm belief revision theory in intuitive ways that are also necessary (and in some cases, sufficient) for reversal or cycle optimal convergence. Then we show that some of our weakened principles of change entail corresponding principles of choice, completing the triangle of relations between (I), (II), and (III).
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Acknowledgements
In Spring 2000, John Case suggested to the second author to consider the consequences of U-shaped learning for Ockham’s razor. We are indebted to Thomas Icard for suggesting connections between our topological conception of simplicity and related work in the semantics of provability logic, which proved to be very fruitful. We are indebted to Hanti Lin for the Maxwell example. We are indebted to Alexandru Baltag, Nina Gierasimczuk, and Sonja Smets, for comments and discussions, for informing us of related work by Debrecht and Yamamoto [8], and for sharing their related results with us, particularly Proposition 10.2.
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Presented by Jacek Malinowski
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Genin, K., Kelly, K.T. Theory Choice, Theory Change, and Inductive Truth-Conduciveness. Stud Logica 107, 949–989 (2019). https://doi.org/10.1007/s11225-018-9809-5
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DOI: https://doi.org/10.1007/s11225-018-9809-5