Online research in philosophy

Cause and Chance is a collection of specially written papers by world-class metaphysicians. Its focus is the problems facing the "reductionist" approach to causation: the attempt to cover all types of causation, deterministic and indeterministic, with one basic theory.

On the face of it ‘deterministic chance’ is an oxymoron: either an event is chancy or deterministic, but not both. Nevertheless, the world is rife with events that seem to be exactly that: chancy and deterministic at once. Simple gambling devices like coins and dice are cases in point. On the one hand they are governed by deterministic laws – the laws of classical mechanics – and hence given the initial condition of, say, a coin toss it is determined whether it will land heads or tails.2 On the other hand, we commonly assign probabilities to the different outcomes a coin toss, and doing so has proven successful in guiding our actions. The same dilemma also emerges in less mundane contexts. Classical statistical mechanics (which is still an important part of modern physics) assigns probabilities to the occurrence of certain events – for instance to the spreading of a gas that is originally confined to the left half of a container – but at the same time assumes that the relevant systems are deterministic. How can this apparent conflict be resolved?

There are at least three core principles that define the chance role: (1) the Principal Principle, (2) the Basic Chance Principle, and (3) the Humean Principle. These principles seem mutually incompatible. At least, no extant account of chance meets more than one of them. I offer an account of chance which meets all three: L*-chance. So the good news is that L*-chance meets (1)–(3). The bad news is that L*-chance turns out unlawful and unstable.

Some have argued that chance and determinism are compatible in order to account for the objectivity of probabilities in theories that are compatible with determinism, like Classical Statistical Mechanics (CSM) and Evolutionary Theory (ET). Contrarily, some have argued that chance and determinism are incompatible, and so such probabilities are subjective. In this paper, I argue that both of these positions are unsatisfactory. I argue that the probabilities of theories like CSM and ET are not chances, but also that they are not subjective probabilities either. Rather, they are a third type of probability, which I call counterfactual probability. The main distinguishing feature of counterfactual-probability is the role it plays in conveying important counterfactual information in explanations. This distinguishes counterfactual probability from chance as a second concept of objective probability.

Machine generated contents note: 1. The concept of chance; 2. The classical picture; 3. Ways the world might be; 4. Possibilities of thought; 5. Chance in phase space; 6. Possibilist theories of chance; 7. Actualist theories of chance; 8. Anti-realist theories of chance; 9. Chance in quantum physics; 10. Chance in branching worlds; 11. Time and evidence; 12. Debunking chance.

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.

I argue that there are non-trivial objective chances (that is, objective chances other than 0 and 1) even in deterministic worlds. The argument is straightforward. I observe that there are probabilistic special scientific laws even in deterministic worlds. These laws project non-trivial probabilities for the events that they concern. And these probabilities play the chance role and so should be regarded as chances as opposed, for example, to epistemic probabilities or credences. The supposition of non-trivial deterministic chances might seem to land us in contradiction. The fundamental laws of deterministic worlds project trivial probabilities for the very same events that are assigned non-trivial probabilities by the special scientific laws. I argue that any appearance of tension is dissolved by recognition of the level-relativity of chances. There is therefore no obstacle to accepting non-trivial chance-role-playing deterministic probabilities as genuine chances.

I sketch a new constraint on chance, which connects chance ascriptions closely with ascriptions of ability, and more specifically with ‘can’-claims. This connection between chance and ability has some claim to be a platitude; moreover, it exposes the debate over deterministic chance to the extensive literature on (in)compatibilism about free will. The upshot is that a prima facie case for the tenability of deterministic chance can be made. But the main thrust of the paper is to draw attention to the connection between the truth conditions of sentences involving ‘can’ and ‘chance’, and argue for the context sensitivity of each term. Awareness of this context sensitivity has consequences for the evaluation of particular philosophical arguments for (in)compatibilism when they are presented in particular contexts.

When the physics of Galileo and Newton displaced the physics of Aristotle, scientists tried to explain the world by discovering its deterministic natural laws. When the quantum physics of Bohr and Heisenberg in turn displaced the physics of Galileo and Newton, scientists realized they needed to supplement their deterministic natural laws by taking into account chance processes in their explanations of our universe. Chance and necessity, to use a phrase made famous by Jacques Monod, thus set the boundaries of scientific explanation.

The four case studies on chance in evolution provide a rich source for further philosophical analysis. Among the issues raised are the following: Are there different conceptions of chance at work, or is there a common underlying conception? How can a given concept of chance be distinguished from other chance concepts and from nonchance concepts? How can the occurrence of a given chance process be distinguished empirically from nonchance processes or other chance processes? What role does chance play in evolutionary theory? I argue that in order to answer these questions, a careful distinction between process and outcome must be made; however, the purpose of this essay is not to answer these questions definitively, but rather to elaborate on them and to provide a starting point for further discussion.