Chance and Determinism

Some philosophers maintain that if determinism holds in our world, then there are no objective chances in our world. And often the word ‘chance’ here is taken to be synonymous with 'probability', so these philosophers maintain that there are no non-trivial objective probabilities for events in our world. (The caveat “non-trivial” is added here because on some accounts, under determinism, all future events that actually happen have probability, conditional on past history, equal to 1, and future events that do not happen have probability equal to zero. Non-trivial probabilities are probabilities strictly between zero and one.) Conversely, it is often held, if there are laws of nature that are irreducibly probabilistic, determinism must be false. (Some philosophers would go on to add that such irreducibly probabilistic laws are the basis of whatever genuine objective chances obtain in our world.)
The discussion of quantum mechanics in section 4 shows that it may be difficult to know whether a physical theory postulates genuinely irreducible probabilistic laws or not. If a Bohmian version of QM is correct, then the probabilities dictated by the Born rule are not irreducible. If that is the case, should we say that the probabilities dictated by quantum mechanics are not objective? Or should we say that we need to distinguish ‘chance’ and ‘probabillity’ after all—and hold that not all objective probabilities should be thought of as objective chances? The first option may seem hard to swallow, given the many-decimal-place accuracy with which such probability-based quantities as half-lives and cross-sections can be reliably predicted and verified experimentally with QM.
Whether objective chance and determinism are really incompatible or not may depend on what view of the nature of laws is adopted. On a “pushy explainers” view of laws such as that defended by Maudlin (2007), probabilistic laws are interpreted as irreducible dynamical transition-chances between allowed physical states, and the incompatibility of such laws with determinism is immediate. But what should a defender of a Humean view of laws, such as the BSA theory (section 2.4 above), say about probabilistic laws? The first thing that needs to be done is explain how probabilistic laws can fit into the BSA account at all, and this requires modification or expansion of the view, since as first presented the only candidates for laws of nature are true universal generalizations. If ‘probability’ were a univocal, clearly understood notion then this might be simple: We allow universal generalizations whose logical form is something like: “Whenever conditions Y obtain, Pr(A) = x”. But it is not at all clear how the meaning of ‘Pr’ should be understood in such a generalization; and it is even less clear what features the Humean pattern of actual events must have, for such a generalization to be held true. (See the entry on interpretations of probability and Lewis (1994).)
Humeans about laws believe that what laws there are is a matter of what patterns are there to be discerned in the overall mosaic of events that happen in the history of the world. It seems plausible enough that the patterns to be discerned may include not only strict associations (whenever X, Y), but also stable statistical associations. If the laws of nature can include either sort of association, a natural question to ask seems to be: why can't there be non-probabilistic laws strong enough to ensure determinism, and on top of them, probabilistic laws as well? If a Humean wanted to capture the laws not only of fundamental theories, but also non-fundamental branches of physics such as (classical) statistical mechanics, such a peaceful coexistence of deterministic laws plus further probabilistic laws would seem to be desirable. Loewer (2004) and Frigg & Hoefer (2015) offer forms of this peaceful coexistence that can be achieved within Lewis' version of the BSA account of laws.

6. Determinism and Human Action

In the introduction, we noted the threat that determinism seems to pose to human free agency. It is hard to see how, if the state of the world 1000 years ago fixes everything I do during my life, I can meaningfully say that I am a free agent, the author of my own actions, which I could have freely chosen to perform differently. After all, I have neither the power to change the laws of nature, nor to change the past! So in what sense can I attribute freedom of choice to myself?
Philosophers have not lacked ingenuity in devising answers to this question. There is a long tradition of compatibilists arguing that freedom is fully compatible with physical determinism; a prominent recent defender is John Fischer (1994, 2012). Hume went so far as to argue that determinism is a necessary condition for freedom—or at least, he argued that some causality principle along the lines of “same cause, same effect” is required. There have been equally numerous and vigorous responses by those who are not convinced. Can a clear understanding of what determinism is, and how it tends to succeed or fail in real physical theories, shed any light on the controversy?
Physics, particularly 20th century physics, does have one lesson to impart to the free will debate; a lesson about the relationship between time and determinism. Recall that we noticed that the fundamental theories we are familiar with, if they are deterministic at all, are time-symmetrically deterministic. That is, earlier states of the world can be seen as fixing all later states; but equally, later states can be seen as fixing all earlier states. We tend to focus only on the former relationship, but we are not led to do so by the theories themselves.
Nor does 20th (21st) -century physics countenance the idea that there is anything ontologically special about the past, as opposed to the present and the future. In fact, it fails to use these categories in any respect, and teaches that in some senses they are probably illusory.[9] So there is no support in physics for the idea that the past is “fixed” in some way that the present and future are not, or that it has some ontological power to constrain our actions that the present and future do not have. It is not hard to uncover the reasons why we naturally do tend to think of the past as special, and assume that both physical causation and physical explanation work only in the past present/future direction (see the entry on thermodynamic asymmetry in time). But these pragmatic matters have nothing to do with fundamental determinism. If we shake loose from the tendency to see the past as special, when it comes to the relationships of determination, it may prove possible to think of a deterministic world as one in which each part bears a determining—or partial-determining—relation to other parts, but in which no particular part (region of space-time, event or set of events, ...) has a special, privileged determining role that undercuts the others. Hoefer (2002a) and Ismael (2016) use such considerations to argue in a novel way for the compatiblity of determinism with human free agency.

Chance and Determinism

6. Determinism and Human Action

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Chance and Determinism