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Free choice impossibilty results
Goldstein, Simon
Goldstein, Simon
Author
Abstract
Free Choice is the principle that possibly p or q implies and is implied by possibly p and possibly q. A variety of recent attempts to validate Free Choice rely on a nonclassical semantics for disjunction, where the meaning of p or q is not a set of possible worlds. This paper begins with a battery of impossibility results, showing that some kind of nonclassical semantics for disjunction is required in order to validate Free Choice. The paper then provides a positive account of Free Choice, by identifying a family of dynamic semantics for disjunction that can validate the inference. On all such theories, the meaning of p or q has two parts. First, p or q requires that our information is consistent with each of p and q. Second, p or q narrows down our information by eliminating some worlds. It turns out that this second component of or is well behaved: there is a strongest such meaning that p or q can express, consistent with validating Free Choice. The strongest such meaning is the classical one, on which p or q eliminates any world where both p and q are false. In this way, the classical meaning of disjunction turns out to be intimately related to the validity of Free Choice.
Keywords
semantics, free choice, dynamic semantics, impossibility results
Date
2020
Type
Journal article
Journal
Journal of Philosophical Logic
Book
Volume
49
Issue
2
Page Range
249-282
Article Number
ACU Department
Dianoia Institute of Philosophy
Faculty of Theology and Philosophy
Faculty of Theology and Philosophy
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Open Access Status
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Controlled