Indeterminism is a modal notion: branching spacetimes and Earman’s pruning

Abstract

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's (2008) based on a model-theoretic characterization of indeterminism. It delineates BST branching against the background provided by Earman's (2008) distinction between individual versus 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.Keywords Indeterminism/determinism · Spacetimes · Branching space-times · TensesIn 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

On A- and B-theoretic elements of branching spacetimes

“…Müller (2009) and Placek and Belnap (2010) each contrast the modal concept of inde-terminism associated with BST with the model-theoretic analyses of Montague (1974) and Earman (1986) in terms of physical theories, and contend that the concept of (in)determinism is inherently modal. Müller, in particular, is critical of model-theoretic analyses for relegating indeterminism to a property of theories rather than of the world: "first and foremost, determinism and indeterminism are based on real possibility" (p. 49), where "real" possibility refers to in-the-world possibility.…”

“…There is something of a consensus in the recent BST literature that the discrepancy between modal indeterminism and theory (model-theoretic) indeterminism means that the concept of indeterminism as usually understood by philosophers of physics is incommensurable with that of the indeterminism of BST. This point, in different forms, is made by Belnap et al (2001), Müller (2009), and Placek and Belnap (2010), to dismiss criticisms of BST's modeling of indeterminism coming from considerations of physical theories. For instance, Placek and Belnap (2010) make this point in response to criticisms of BST by Earman (2008).…”

“…This point, in different forms, is made by Belnap et al (2001), Müller (2009), and Placek and Belnap (2010), to dismiss criticisms of BST's modeling of indeterminism coming from considerations of physical theories. For instance, Placek and Belnap (2010) make this point in response to criticisms of BST by Earman (2008). However, I think this is too quick; consideration of current physical theories does raise genuine problems for the future-only indeterminism of BST.…”

“…Although Müller (2009) and Placek and Belnap (2010) emphasise that indeterminism is to be understood as a modal notion, the kind of modal indeterminism that they endorse-BST indeterminism-is importantly an ontic notion of indeterminism, in that indeterminism pertains to the modal status of particular existing events. It is this that distinguishes it from Physical Indeterminism, which is a nomic account-it locates modality in the laws of temporal evolution.…”

“…Belnap et al (2001) and Placek and Belnap (2010) also make the point that the issue of intervention (e.g. by an experimenter when preparing a system, performing a measurement, etc.)…”