The logic of the future in quantum theory

Anthony Sudbery

doi:10.1007/s11229-016-1142-9

The logic of the future in quantum theory

Anthony Sudbery

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	4429–4453
Number of pages	25
Journal	Synthese
Volume	194
Issue number	11
Early online date	8 Jul 2016
DOIs	https://doi.org/10.1007/s11229-016-1142-9
Publication status	Published - Nov 2017

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10.1007/s11229-016-1142-9

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Cite this

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