Imaging is Alpha + Aizerman (Jessica Collins)

The Logic and Metaphysics Workshop will meet on April 15th from 4:15-6:15 in-person at the Graduate Center (Room 7395) for a talk by Jessica Collins (Columbia).

Title: Imaging is Alpha + Aizerman

Abstract: I give a non-probabilistic account of the imaging revision process. Most familiar in its various probabilistic forms, imaging was introduced by David Lewis (1976) as the form of belief revision appropriate for supposing subjunctively that a hypothesis be true. It has played a central role in the semantics of subjunctive conditionals, in causal decision theory, and, less well known to philosophers, in the computational theory of information retrieval. In the economics literature, non-probabilistic imaging functions have been called “pseudo-rationalizable choice functions”. I show that the imaging functions are precisely those which satisfy both Sen’s Alpha Principle (aka “Chernoff’s Axiom”) and the Aizerman Axiom. This result allows us to see very clearly the formal relationship between non-probabilistic imaging and AGM revision (which is Alpha + Beta).

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