Determinism and Chance

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Abstract

It is generally thought that objective chances for particular events different from 1 and 0 and determinism are incompatible. However, there are important scientific theories whose laws are deterministic but which also assign non-trivial probabilities to events. The most important of these is statistical mechanics whose probabilities are essential to the explanations of thermodynamic phenomena. These probabilities are often construed as ‘ignorance’ probabilities representing our lack of knowledge concerning the microstate. I argue that this construal is incompatible with the role of probability in explanation and laws. This is the ‘paradox of deterministic probabilities’. After surveying the usual list of accounts of objective chance and finding them inadequate I argue that an account of chance sketched by David Lewis can be modified to solve the paradox of deterministic probabilities and provide an adequate account of the probabilities in deterministic theories like statistical mechanics.

Section snippets

The Paradox of Deterministic Probabilities

It is widely, although perhaps not universally, thought that objective chance and determinism are incompatible. Here are two philosophers voicing this opinion:

Today I can see why so many determinists, and even ex-determinists who believe in the deterministic character of classical physics, seriously believe in a subjectivist interpretation of probability: it is in a way the only reasonable possibility which they can accept: for objective physical probabilities are incompatible with determinism;

Accounts of Chance

There are three questions concerning chance that it is important to distinguish. (1) What facts about the world make it the case that there are chances and that they have particular values? That is, are the truth makers of a statement like the chance that the ice will melt in the next 5 minute is 0.99? The other two questions are (2): Assuming that there are chances how do we know that a particular chance distribution is the correct one?, and (3): What is the explanation, if any, of why a

The Paradox Resolved

None of the accounts so far canvassed come close to resolving the paradox of deterministic probabilities. But there is an account of the nature of objective chance that I think does. This account is due to David Lewis; the same Lewis who claimed that determinism and chance are incompatible. But, as we will see, he is wrong about that.

Lewis's account of chance is closely connected to his account of laws. According to Lewis, laws are, or are expressed by, contingent generalisations that are

References (8)

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    Time and Chance

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  • Jaynes, E. T. (1957) ‘Information Theory and Statistical Mechanics’, Physical Review 106, 620; ‘Information Theory and...
  • Lewis, D. K. (1980) ‘A Subjectivist's Guide to Objective Chance’, in R. C. Jeffrey (ed.), Studies in Inductive Logic...
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