nLab possible worlds semantics

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Contents

Contents

Idea

In the context of modal logic, by possible world semantics one means the interpretation of the possibility and necessity modalities as existential quantification and universal quantification over a context of “possible worlds”. Such a model is sometimes referred to as a Kripke frame.

For formalization of this in terms of hyperdoctrines/dependent type theory see at necessity and possibility – In first-order logic and dependent type theory.

Under categorical semantics such a context interprets as an object of some category whose interpretation is similar to that of a probability space in measure theory – which is one sensible formalization of possible worlds (e.g. Toronto-McCarthy 10, slide 23).

References

General

The original articles:

Modern exposition:

In general see the reference at modal logic, such as:

and more philosophically (“modal realism”):

See also:

Possible-worlds vs. Many-worlds

References which consider, in one way or another, the notions of

in relation to each other:

  • Mario Bunge, Possibility and Probability, in: Foundations of Probability Theory, Statistical Interference, and Statistical Theories of Science, Reidel (1976) 17-34 [[doi:10.1007/978-94-010-1438-0_2]]

  • Brian Skyrms, Part III of: Possible Worlds, Physics and Metaphysics, Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition 30 5 (1976) 323-332 [[jstor:4319099]]

  • Paul Tappenden, p. 101 (4 of 17) in: Identity and Probability in Everett’s Multiverse, The British Journal for the Philosophy of Science, 51 1 (2000) 99-114 [[jstor:3541750]]

  • Daniel Nolan, p. 22 of: Topics in the Philosophy of Possible Worlds, Routledge (2002) [[ISBN:9780415516303]]

  • Rod Girle, Ch. 8 of: Possible Worlds, McGill-Queen’s University Press (2003) [[jstor:j.cttq48cx]]

  • Simon Saunders, p. 196 in: Chance in the Everett Interpretation, in: Many Worlds?, Oxford University Press (2010) 181–205 [[doi:10.1093/acprof:oso/9780199560561.003.0008]]

  • Nuriya Nurgalieva, Lídia del Rio, Inadequacy of Modal Logic in Quantum Settings, EPTCS 287 (2019) 267-297 [[arXiv:1804.01106, doi:10.4204/EPTCS.287.16]]

  • Alastair Wilson, p. 20 of: Modal Metaphysics and the Everett Interpretation (2006) [[philsci:2635, pdf]]

  • Vladislav Terekhovich, Modal Approaches in Metaphysics and Quantum Mechanics [[arXiv:1909.10046]]

  • Alastair Wilson, The Nature of Contingency: Quantum Physics as Modal Realism, Oxford University Press (2020) [[ISBN:9780198846215]]

  • Raoni W. Arroyo, Jonnas R. B. Arenhart, Whence deep realism for Everettian quantum mechanics?, Foundations of Physics 52 121 (2022) [arXiv:2210.16713, doi:10.1007/s10701-022-00643-0]

Beware that there is also

  • Bas C. van Fraassen, Modal interpretation of repeated measurement, Philosophy of Science 64 4 (1997) 669-676 [[doi:10.1086/392577, SEP review]]

which, even if some vocabulary is superficially alike, does not refer either to modal logic nor to the many-worlds interpretation.

Last revised on August 1, 2023 at 14:21:02. See the history of this page for a list of all contributions to it.