The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of properties that dynamical systems can possess. Its five levels are egrodicity, weak mixing, strong mixing, Kolomogorov, and Bernoulli. Although EH is a mathematical theory, its concepts have been widely used in the foundations of statistical physics, accounts of randomness, and discussions about the nature of chaos. We introduce EH and discuss how its applications in these fields.

Decision-making typically requires judgments about causal relations: we need to know the causal effects of our actions and the causal relevance of various environmental factors. We investigate how several individuals' causal judgments can be aggregated into collective causal judgments. First, we consider the aggregation of causal judgments via the aggregation of probabilistic judgments, and identify the limitations of this approach. We then explore the possibility of aggregating causal judgments independently of probabilistic ones. Formally, we introduce the problem of causal-network aggregation. (...) Finally, we revisit the aggregation of probabilistic judgments when this is constrained by prior aggregation of qualitative causal judgments. (shrink)

Several authors have argued that non-extreme probabilities used in special sciences such as chemistry and biology can be objective chances, even if the true microphysical description of the world is deterministic. This article examines an influential version of this argument and shows that it depends on a particular methodology for defining the relationship between coarse-grained and fine-grained events. An alternative methodology for coarse-graining is proposed. This alternative methodology blocks this argument for the existence of emergent chances, and makes better sense (...) of two well-known subjects of philosophical discussion: the Miners Puzzle and Simpson’s Paradox. (shrink)

Our approach aims at accounting for causal claims in terms of how the physical states of the underlying dynamical system evolve with time. Causal claims assert connections between two sets of physicals states—their truth depends on whether the two sets in question are genuinely connected by time evolution such that physical states from one set evolve with time into the states of the other set. We demonstrate the virtues of our approach by showing how it is able to account for (...) typical causes, causally relevant factors, being ‘the’ cause, and cases of overdetermination and causation by absences. (shrink)

Christian List has recently defended what he refers to as a compatibilist-libertarian theory of free will. He attempts to satisfy the libertarian requirement for alternative possibilities without assuming the falsity of physical determinism. To do so, List relies on a multi-level modal theory that he developed with Marcus Pivato. In this theory, List and Pivato demonstrate the compatibility of physical determinism and agential indeterminism. The success of compatibilist-libertarianism essentially hinges upon whether or not List and Pivato’s theory is truly consistent (...) with a non-hypothetical conception of possibility. In this paper, I argue that, despite his attempt to distance himself from a standard compatibilist conception of possibility, List remains committed to such a hypothetical conception. I also argue that List’s theory of agential causation is implausible given his modal interpretation of agency. Therefore, I conclude that compatibilist-libertarianism is an implausible theory of free will. (shrink)

The laws of nature have come a long way since the time of Newton: quantum mechanics and relativity have given us good reasons to take seriously the possibility of laws which may be non-local, atemporal, ‘all-at-once,’ retrocausal, or in some other way not well-suited to the standard dynamical time evolution paradigm. Laws of this kind can be accommodated within a Humean approach to lawhood, but many extant non-Humean approaches face significant challenges when we try to apply them to laws outside (...) the time evolution picture. Thus for proponents of non-Humean approaches to lawhood there is a clear need for a novel non-Humean account which is capable of accommodating these sorts of laws. In this paper we propose such an account, characterizing lawhood in terms of constraints, which are understood as a form of modal structure. We demonstrate that our proposed realist account can indeed accommodate a large variety of laws outside the time evolution paradigm, and describe some possible applications to important philosophical problems. (shrink)