Probability and Randomness

Abstract

Random outcomes, in ordinary parlance, are those that occur haphazardly, unpredictably, or by chance. Even without further clarification, these glosses suggest an interesting connection between randomness and probability, in some of its guises.But we need to be more precise, about both probability and randomness, to understand the relationship between the two subjects of our title.It is a commonplace that there are many sorts of probability; and of each, we may ask after its connection with randomness. There is little systematic to say about randomness and credence; even rational degrees of belief may be certain about a random outcome, and uncertain about a non-random one. More of substance can be said about connections between randomness and evidential probability -particularly according to Solomonoff's version of objective Bayesianism, which uses Kolmogorov complexity ( §2.2) to define a privileged prior algorithmic probability (Solomonoff, 1964; see also Li and Vitanyi, 2008;Rathmanner and Hutter, 2011).For reasons both of concision and focus, in the present chapter I set those issues aside, to concentrate on randomness and physical probability, or chance:probability as a physical feature of certain worldly processes.1 A number of philosophers have proposed an intimate connection between randomness and chance, perhaps even amounting to a reduction of one to the other. I explore, with mostly negative results, the prospects for such views; and discuss some weaker but still interesting ways in which randomness bears on chance. I begin by clarifying and distinguishing a number of kinds of randomness.1 For more on the nature of chance, see the entries by Frigg, Gillies, La Caze, and Schwarz in the present volume.

Infinite frequency principles of direct inference

“…Various attempts have been made to create stronger definitions of randomness that do not suffer from the problems of von Mises/Church randomness (see Eagle, 2016). One example is Martin-Löf randomness.…”

“…Such a sequence is far from random. According to some, however, chancy experiments are thought to yield random sequences most of the time (Eagle, 2016). If that is the case, F cannot be chancy.…”