Newtonian determinism to branching space-times indeterminism in two moves
“Branching space-times” (BST) is intended as a representation of objective, event-based indeterminism. As such, BST exhibits both a spatio-temporal aspect and an indeterministic “modal” aspect of alternative possible historical courses of events. An essential feature of BST is that it can also represent spatial or space-like relationships as part of its (more or less) relativistic theory of spatio-temporal relations; this ability is essential for the representation of local (in contrast with “global”) indeterminism. This essay indicates how BST might be seen to grow out of Newton’s deterministic and non-relativistic theory by two independent moves: (1) Taking account of indeterminism, and (2) attending to spatio-temporal relationships in a spirit derived from Einstein’s theory of special relativity. Since (1) and (2) are independent, one can see that there is room for four theories: Newtonian determinism, branching time indeterminism, relativistic determinism, and (finally) branching space-times indeterminism.
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- Belnap, N. (1992). Branching space-time. Synthese, 92, 385–434. A postprint containing a number of additional explanations and a little restructuring is archived at http://philsci-archive.pitt.edu.
- Belnap N. (2002a) Double time references: Speech-act reports as modalities in an indeterminist setting. In: Wolter F., Wansing H., de Rijke M., Zakharyaschev M. (eds) Advances in modal logic, (Vol. 3, pp. 37–58). World Scientific, SingaporeGoogle Scholar
- Belnap, N. (2003). No-common-cause EPR-like funny business in branching space-times. Philosophical studies, 114, 199–221. A preprint may be obtained from http://philsci-archive.pitt.edu.
- Belnap, N. (2005b). A theory of causation: Causae causantes (originating causes) as inus conditions in branching space-times. British journal for the philosophy of science, 56, 221–253. A preprint of this essay may be obtained from http://philsci-archive.pitt.edu.
- Belnap N. (2007a) In: Müller T., Newen A. (eds) Logik, Begriffe, Prinzipien des Handeln (Logic, concepts, principles of action). Mentis Verlag, Paderborn, pp 13–31Google Scholar
- Belnap, N. (2007b). Probabilities and propensities. Studies in the history and philosophy of modern physics, 38, 593–625. doi:10.1016/j.hpdb.2006.09.003. This essay contains a number of calculational errors. See Belnap 2010 for a corrected version.
- Belnap, N. (2010). Probabilities and propensities (revised). This postprint may be obtained as number 144x from www.pitt.edu/~belnap.
- Belnap N., Perloff M., Xu M. (2001) Facing the future: Agents and choices in our indeterminist World. Oxford University Press, OxfordGoogle Scholar
- Einstein, A., Lorentz, H. A., Weyl, H., & Minkowski, H. (1924). The principle of relativity. New York: Dover Publications Inc. A collection.Google Scholar
- James, W. (1884). The dilemma of determinism. In The will to believe. New York: Dover.Google Scholar
- Laplace, P. S. (1812–1820). Theorie analytique de probabilitiés: Introduction, VII, Oeuvres. Translation of passage taken from The Columbia world of quotations. New York: Columbia University Press (1996)Google Scholar
- Lewis D. (1986) On the plurality of worlds. Basil Blackwell, Oxford and New YorkGoogle Scholar
- Mackie J. L. (1974) The cement of the universe. Oxford University Press, OxfordGoogle Scholar
- Müller, T. (2009). Eliminating modality from the determinism debate? Models vs. equations of physical theories. In A. Hieke, & H. Leitgeb (Eds.), Reduction, abstraction, analysis. Proceedings of the 31th international Ludwig Wittgenstein symposium in Kirchberg (pp. 47–62). Frankfurt: Ontos Verlag.Google Scholar
- Øhrstrøm P., Hasle P. (1995) Temporal logic: From ancient ideas to artificial intelligence. Kluwer Academic Publishers, DordrechtGoogle Scholar
- Placek T. (2000) Is nature deterministic?. Jagiellonian University Press, KrakówGoogle Scholar
- Placek T. (2010) Possibilities without possible worlds/histories. Journal of Philosophical Logic 40: 1–29Google Scholar
- Placek, T., & Belnap, N. (2010). Indeterminism is a modal notion: branching spacetimes, and Earman’s pruning. Synthese, forthcoming.Google Scholar
- Thomson J. J. (1977) Acts and other events. Cornell University Press, IthacaGoogle Scholar