The logic of the future in quantum theory

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JournalSynthese
DateAccepted/In press - 7 Jun 2016
DateE-pub ahead of print - 8 Jul 2016
DatePublished (current) - Nov 2017
Issue number11
Volume194
Number of pages25
Pages (from-to)4429–4453
Early online date8/07/16
Original languageEnglish

Abstract

According to quantum mechanics, statements about the future made by sentient beings like us are, in general, neither true nor false; they must satisfy a many-valued logic. I propose that the truth value of such a statement should be identified with the probability that the event it describes will occur. After reviewing the history of related ideas in logic, I argue that it gives an understanding of probability which is particularly satisfactory for use in quantum mechanics. I construct a lattice of future-tense propositions, with truth values in the interval $[0,1]$, and derive logical properties of these truth values given by the usual quantum-mechanical formula for the probability of a history.

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