Probability, Chaos and Randomness

Probabilities play an important role both in every-day life and in science. Windsurfers check the probability of wind before taking out their boards, and physicists calculate the probabilities for events like a system being in equilibrium. But what do we mean when we make probabilistic statements about things like having wind or being in equilibrium? In a collaborative project with Carl Hoefer, we develop a Humean interpretation of probability to answer this question:

Humean Chance in Physics, in Carl Hoefer: Chance in the World. A Humean Guide to Objective Chance. New York: Oxford University Press, 2019, 181-213, with Carl Hoefer.

The Best Humean System for Statistical Mechanics, Erkenntnis 80, 2015, 551–574, with Carl Hoefer.

Probabilities also occur in deterministic theories. On the face of it, this seems to be a contradiction because chance and determinism seem to be irreconcilable opposites: either something is chancy or it is deterministic, but not both. One of the advantages of the Humean approach is that it can reconcile chance and determinism:

Chance and Determinism, in Alan Hájek and Christopher Hitchcock (eds): The Oxford Handbook of Probability and Philosophy. Oxford: Oxford University Press, 2016, 460-474.

Determinism and Chance from a Humean Perspective, in Dennis Dieks, Wenceslao Gonzalez, Stephan Hartmann, Marcel Weber, Friedrich Stadler and Thomas Uebel (eds.): The Present Situation in the Philosophy of Science. Berlin and New York: Springer, 2010, 351-372, with Carl Hoefer.

Chaos is an important motivation, or indeed justification, for introducing probabilities into deterministic systems. Chaotic systems also exhibit random behaviour, and the so-called ergodic hierarchy is proffered as a tool to classify levels of randomness in chaotic systems. In a joint paper with Joseph Berkovitz and Fred Kronz we discuss the relation between chaos, randomness, and the ergodic hierarchy:

The Ergodic Hierarchy, Randomness and Hamiltonian ChaosStudies in History and Philosophy of Modern Physics 37, 2006, 661-691, with Joseph Berkovitz and Fred Kronz. (An addendum to this paper can be found here.)

An accessible introduction to these issues can be found in our piece on the ergodic hierarchy in the Stanford Encyclopedia of Philosophy:

The Ergodic Hierarchy, in Edward N. Zalta (ed.): Stanford Encyclopedia of Philosophy (first published April 2011; substantive revision May 2016), with Joseph Berkovitz and Fred Kronz.

The relation between chaos, randomness and the so-called Kolmogorov-Sinai entropy is discussed here:

Chaos and Randomness: An Equivalence Proof of a Generalised Version of the Shannon Entropy and the Kolmogorov-Sinai Entropy for Hamiltonian Dynamical SystemsChaos, Solitons and Fractals 28, 2006, 26-31.

In What Sense Is the Kolmogorov-Sinai Entropy a Measure for Chaotic Behaviour? – Bridging the Gap Between Dynamical Systems Theory and Communication TheoryBritish Journal for the Philosophy of Science 55, 2004, 411-434.

Probabilities lie at the heart not only of statistical mechanics and chaos theory, but also of quantum mechanics. The Humean interpretation of probability can also give a coherent account of probabilities in some versions of quantum mechanics:

Probability in GRW Theory, Studies in History and Philosophy of Modern Physics 38, 2007, 371-389, with Carl Hoefer.

The so-called GRW version of quantum mechanics is discussed further here:

Properties and the Born Rule in GRW Theory, in Shan Gao (ed.): Collapse of the Wave Function: Models, Ontology, Origin, and Implications. Cambridge: Cambridge University Press, 2018, 124-133.

On the Property Structure of Realist Collapse Interpretations of Quantum Mechanics and the So-Called “Counting Anomaly”, International Studies in the Philosophy of Science 17, 2003, 43-57.