Indeterminism is a modal notion: branching spacetimes and Earman's pruning
نویسندگان
چکیده
The paper defends an Aristotelian notion of indeterminism, as rigorously formulated in the framework of branching space-times (BST) of Belnap (1992), against criticism by Earman (2008) based on a model-theoretic characterization of indeterminism. It delineates BST branching against the background provided by Earman’s (2008) distinction between individual vs. ensemble branching. Partly in order to motivate our responses to Earman, it describes a construction of physically-motivated BST models, in which histories are isomorphic to Minkowski spacetime. Finally it responds to Earman’s criticisms leveled against BST by addressing a topological issue, the question of an actual future, the past/future asymmetry, and some semantical questions. In current debates two different concepts of (in)determinism have been used, each having a different historical origin and each being applied in different fields. On the one hand, there is an everyday natural notion of (in)determinism, discussed first by Aristotle, and illustrated by alternative possible futures, one with a sea battle and the other without. On the other hand, there is a tradition started by Laplace, of characterizing (in)determinism in terms of laws and predictions. This latter concept was rigorously analyzed by the logician, R. Montague, in terms of models of a theory that are alike up to a certain time, and then diverge. By replacing “models of a theory” by “possible worlds”, D. Lewis later adapted Montague’s analysis to general philosophy; in turn, philosophers of physics, especially J. Earman, have used Lewis-inspired concepts of (in)determinism. “Branching space-times” is a rigorous attempt to analyze the natural (Aristotelian) notion of indeterminism. The theory appeared in Belnap (1992) (henceforth BST92 for the publication, and BST for the theory), and has since been developed by several philosophers in a variety of directions. For relevant publications, see items in the list of references by Belnap et al, by Müller et al, and by Placek et al. BST92 built on earlier work on the “branching times” (henceforth BT) representation of indeterminism that goes back to a passing suggestion in an unpublished letter from S. Kripke to 1We are indebted to Bryan Roberts and Balázs Gyenis for timely readings of our manuscript and for their comments and corrections. We would also like to thank one referee of this journal for their substantive and detailed comments. TP gratefully acknowledges the support of the Jagiellonian University WRBW2010 grant and of the MNiSW research grant K/PMN/000034.
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عنوان ژورنال:
- Synthese
دوره 187 شماره
صفحات -
تاریخ انتشار 2012