The logic of the future in quantum theory

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.

• Publication year

  2014

• Venue

  Synthese

• Publication date

  2014-09-02

• Fields of study

  Mathematics, Physics, Computer Science, Philosophy

• Identifiers
  DOI 10.1007/s11229-016-1142-9arXiv 1409.0755
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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