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The logic of the future in quantum theory
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| Journal | Synthese |
|---|---|
| Date | Accepted/In press - 7 Jun 2016 |
| Date | E-pub ahead of print - 8 Jul 2016 |
| Date | Published (current) - Nov 2017 |
| Issue number | 11 |
| Volume | 194 |
| Number of pages | 25 |
| Pages (from-to) | 4429–4453 |
| Early online date | 8/07/16 |
| Original language | English |
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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