Randomness, as we ordinarily think of it, exists when some outcomes occur haphazardly, unpredictably, or by chance. These latter three notions are all distinct, but all have some kind of close connection to probability. Notoriously, there are many kinds of probability: subjective probabilities (‘degrees of belief’), evidential probabilities, and objective chances, to name a few (Hájek 2012), and we might enquire into the connections between randomness and any of these species of probability. In this entry, we focus on the potential connections between randomness and chance, or physical probability. The ordinary way that the word ‘random’ gets used is more or less interchangeable with ‘chancy’, which suggests this Commonplace Thesis—a useful claim to target in our discussion:

(CT)

Something is random iff it happens by chance.

The Commonplace Thesis, and the close connection between randomness and chance it proposes, appears also to be endorsed in the scientific literature, as in this example from a popular textbook on evolution (which also throws in the notion of unpredictability for good measure):

scientists use chance, or randomness, to mean that when physical causes can result in any of several outcomes, we cannot predict what the outcome will be in any particular case. (Futuyma 2005: 225)

Some philosophers are, no doubt, equally subject to this unthinking elision, but others connect chance and randomness deliberately. Suppes approvingly introduces

the view that the universe is essentially probabilistic in character, or, to put it in more colloquial language, that the world is full of random happenings. (Suppes 1984: 27)

However a number of technical and philosophical advances in our understanding of both chance and randomness open up the possibility that the easy slide between chance and randomness in ordinary and scientific usage—a slide that would be vindicated by the truth of the Commonplace Thesis—is quite misleading. This entry will attempt to spell out these developments and clarify the differences between chance and randomness, as well as the areas in which they overlap in application. It will also aim to clarify the relationship of chance and randomness to other important notions in the vicinity, particularly determinism and predictability (themselves often subject to confusion).

There will be philosophically significant consequences if the Commonplace Thesis is incorrect, and if ordinary usage is misleading. For example, it is intuitively plausible that if an event is truly random it cannot be explained (if it happens for a reason, it isn’t truly random). It might seem then that the possibility of probabilistic explanation is undermined when the probabilities involved are genuine chances. Yet this pessimistic conclusion only follows under the assumption, derived from the Commonplace Thesis, that all chancy outcomes are random. Another interesting case is the role of random sampling in statistical inference. If randomness requires chance, then no statistical inferences on the basis of ‘randomly’ sampling a large population will be valid unless the experimental design involves genuine chance in the selection of subjects. But the rationale for random sampling may not require chance sampling—as long as our sample is representative, those statistical inferences may be reliable. But in that case, we’d be in a curious situation where random sampling wouldn’t have much to do with randomness, and whatever justification for beliefs based on random sampling that randomness is currently thought to provide would need to be replaced by something else.

A final case of considerable philosophical interest is the frequentist approach to objective probability, which claims (roughly) that the chance of an outcome is its frequency in an appropriate series of outcomes (Hájek 2012 §3.4). To avoid classifying perfectly regular recurring outcomes as chancy, frequentists like von Mises (1957) proposed to require that the series of outcomes should be random, without pattern or order. Frequentism may fall with the Commonplace Thesis: if there can be chancy outcomes without randomness, both will fail.

The Commonplace Thesis is central to all three examples. As it is widely accepted that probabilistic explanation is legimitate, that random sampling doesn’t need genuine chance (though it can help), and that frequentism is in serious trouble (Hájek 1997), there is already some some pressure on the Commonplace Thesis. But we must subject it to closer examination to clarify whether these arguments do succeed, and what exactly it means to say of some event or process that it is random or chancy. Though developing further consequences of this kind is not the primary aim of this entry, it is hoped that what is said here may help to untangle these and other vexed issues surrounding chance and randomness.