Tomasz Placek

Counterfactuals and Historical Possibility

We show that truth conditions for counterfactuals need not always be given in terms of a vague notion of similarity. To this end, we single out the important class of historical counterfactuals and give formally rigorous truth conditions for these counterfactuals, employing a partial ordering relation called “comparative closeness” that is defined in the framework of branching space-times. Among other applications, we provide a detailed analysis of counterfactuals uttered in the context of lost bets. In an appendix we compare our theory with the branching space-times based reading of counterfactuals recently proposed by Belnap.

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

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.

Possibilities without possible worlds/histories

The paper puts forward a theory of historical modalities that is framed in terms of possible continuations rather than possible worlds or histories. The proposal is tested as a semantic theory for a language with historical modalities, tenses, and indexicals.

On infinite EPR-like correlations

The paper investigates, in the framework of branching space–times, whether an infinite EPR-like correlation which does not involve finite EPR-like correlations is possible.

Partial Indeterminism is Enough: A Branching Analysis of Bell-Type Inequalities

The central message of this paper is that indeterminism in measurement events and experimenters’ free choice are enough to explain violations of Bell-type inequalities. To discuss the issue, I develop algebraic branching models that permit a unified discussion of modal, spatiotemporal, and probabilistic features. Some realizations of these models are given by branching structures of Minkowski space-times to which states are assigned. I draw a distinction between correlations produced by events from one history and correlations brought about by events that do not belong to one history. I prove that any finite number of the first kind of correlations can always be explained by a common cause, whereas for some correlations of the second kind, a single local common cause cannot be posited. I argue that the non-existence of common cause local models of the Bell- Aspect experiment derive from indeterminism in measurement events.

On Belnap’s Branching Space-Times

I compare two theories of branching space-times (BST): Belnap’s (1992) theory and the Kowalski-Placek (1999) theory. I show that Belnap’s postulates imply Kowalski-Placek’s postulates. I also show that many notions of one theory are translatable into notions of the other theory.

Branching for general relativists

The paper develops a theory of branching spatiotemporal histories that accommodates indeterminism and the insights of general relativity. A model of this theory can be viewed as a collection of overlapping histories, where histories are defined as maximal consistent subsets of the models base set. Subsequently, generalized (non-Hausdorff) manifolds are constructed on the theorys models, and the manifold topology is introduced. The set of histories in a model turns out to be identical with the set of maximal subsets of the models base set with respect to being Hausdorff and downward closed (in the manifold topology). Further postulates ensure that the topology is connected, locally Euclidean, and satisfies the countable sub-cover condition.

On Cartwright's models for EPR

Abstract We assess Cartwrights models for probabilistic causality and, in particular, her models for EPR-like experiments of quantum mechanics. Our first objection is that, contrary to econometric linear models, her quasi-linear models do not allow for the unique estimation of parameters. We next argue that although, as Cartwright proves, Reichenbachs screening-off condition has only limited validity, her generalized condition is not empirically applicable. Finally, we show that her models for the EPR are mathematically incorrect and physically implausible.

Laplace’s demon tries on Aristotle’s cloak: on two approaches to determinism

The paper describes two approaches to determinism: one focuses on the features of global objects, such as possible worlds or models of a theory, whereas the other’s concern is the possible behaviour of individual objects. It then gives an outline of an individuals-based analysis of the determinism of theories. Finally, a general relativistic spacetime with non-isometric extensions is described and used to illustrate a conflict between the two approaches: this spacetime is indeterministic by the first approach but deterministic by the second approach.

Causal Probabilities in GRW Quantum Mechanics

The paper constructs modal structures that represent alternative developments of GRW systems. With these modal structures in hand, it shows that GRW probabilities can be read as graded modalities, that is, as numerically specified powers of a system to localize. The construction is intended as offering support for Dorato and Esfeld’s (Stud Hist Philos Mod Phys 41(1):41–49, 2010) project of conceiving GRW theory as an ontology of powers.