# Degrees of Determinism

Degrees of Determinism

People usually talk about determinism and indeterminism as if it were a binary affair. But there are different strengths of determinism and indeterminism, with some more plausible than others. Let me first define the strongest possible kind of determinism: if a cause from the actual world is repeated in a possible world, it will always produce an effect just like the one produced in the actual world. The cause necessitates the effect, in the strongest sense of necessity. Whenever causes recur there cannot be any variation in the effect produced. Duplicate causes produce duplicate effects as a matter of (metaphysical) necessity. We can compare this to the claim that nothing can follow a given number in the number series but the number that actually follows it (e.g. nothing can follow 3 but 4): a given number determines the number that follows it. Similarly, the premises of a valid argument determine the conclusion in the sense that in no possible world does anything else follow from those premises. We use the word “follow” in each of these cases and the determinist claim is that nothing can follow except what doesfollow. This is stronger than saying that in our universe like causes always produce like effects; it says that in every possible universe the sequence of events is the same as in our universe, given identity of causes. If one billiard ball hits another in our universe and brings about a certain effect, then an exactly alike cause in any possible world will produce an effect of the same type. We might call this “full-strength determinism”.

But we can dilute this kind of determinism in different ways. We can replace talk of metaphysical necessity with talk of nomological necessity or we can limit determinism to our own universe while remaining agnostic about other possible universes. We can also introduce the notion of partial determinism understood as follows: the properties of the cause don’t fully determine the properties of the effect, but they do partially determine them. Given the cause, the effect must have a certain subset of the properties it has in other instances—though not all. The effect doesn’t have to be exactly alike in all cases involving the same cause (type not token), but it has to be alike in certain respects. Then we can have degrees of determinism fixed by how many properties have to be invariant across cases: is it most properties or many or a few? And which ones have to be invariant from case to case? For example, the impacting billiard ball might have to produce the same linear motion from case to case, but not the same spin or the same noise or the same displacement of air. Maybe some properties will be selected as always present in the effect while others are optional; or it may be held that no particular set of properties must be present. Thus full determinism is rejected but partial determinism is retained—the weakest kind being that at least some effect has to be produced though it may be very different from case to case (the billiard ball has to do something, but what it does is entirely up for grabs).

Corresponding to degrees of determinism we have degrees of indeterminism. The indeterminist need not be committed to the very strongest form of indeterminism, namely there is no uniformity from case to case. If someone were to claim that nature possesses no uniformity at all, with like causes always producing unlike effects, we would reject that as empirically false: it is simply not the case that billiard ball collisions sometimes cause motion in the struck ball and sometimes cause it to change color and sometimes make it explode and sometimes turn it into an egg. None of this happens, so indeterminism of this kind is obviously false. Still, it is an apparently intelligible view—it might describe a logically possible world. But we can scale back from it as we did with determinism, limiting indeterminism to the possibility that some properties of the effect are not uniform from case to case.  For instance, the exact trajectories of particles may not be determined by the cause, but the cause cannot produce no motion at all or a change of color or an alteration of electric charge. That is, determinism might be partially true but not wholly true; thus indeterminism is only partially true. No one has ever claimed that our universe is subject to full-strength indeterminism; the claim has only been that indeterminism holds in certain limited domains (usually quantum physics and free will). Nor has anyone claimed that there are possible worlds that are subject to indeterminism in every respect: worlds in which identical causes always produce wildly varying effects—from balls moving to balls igniting to balls turning into eggs. I myself find the idea of such a world repugnant to reason—a mere fancy. In any case, it is not what people mean who advocate indeterminism. They typically mean something quite limited, a small breach in the general determinism of nature. They believe in local indeterminism not global indeterminism.

This raises a question that should receive more attention: if extreme indeterminism is out of the question, why is partial indeterminism deemed acceptable? If nature can be non-uniform in one area, why can’t it be non-uniform in all areas? If it makes sense here, why doesn’t it make sense everywhere? People who say that quantum mechanics shows that the world is not deterministic are speaking sloppily, since all they mean is that certainproperties of quantum effects are not always preserved in the presence of the same cause. But many properties arepreserved, so determinism is true with respect to those properties. No one has ever given any reason for supposing that nothing is determined by the cause, so that any kind of effect can follow the same cause; and such a claim is both factually false and dubiously intelligible. To repeat: it is not true that there is radical variation from case to case, with identical causes generating wildly different effects; and if we try to imagine a world like that, we get something that tests credulity. How could a billiard ball turn another billiard ball into an egg or a thought or a singing nun? Such things are impossible! But if they are impossible, why is it not impossible for the same cause to produce a slightly different effect? If they are impossible because determinism is a condition of possibility, then why can there be even minor violations of determinism? It is as if the indeterminist implicitly understands that his startling doctrine can only be pushed so far before it collapses into absurdity, so he declines to consider pushing it further. We end up with the view that only a very limited indeterminism could be true, on pain of leaving all reality behind. It can only occur in small pockets of the universe. Mostly things are deterministic.

To me this suggests that we should do our best to find alternative explanations of observable phenomena, accepting even local indeterminism with great reluctance. In the case of free will, we should not rush to embrace indeterminism without asking ourselves what we would think of more extreme forms of indeterminism; we should work to develop a view of free will that avoids anything like this.  [1] In the case of quantum mechanics, who knows what to say, but we should be cautious about adopting indeterminism even in this restricted domain—given that we would never accept it more globally. No one thinks, for instance, that the unpredictability of the weather is a good reason to accept meteorological indeterminism; and anyone who thinks it is should be asked whether they think the world is subject to indeterminism through and through. How much of an indeterminist are you are you willing to be? I myself am inclined to accept full-strength determinism, as strong as logical and mathematical determinism (though it is hard to see how that position could be proved); but no sane person is willing to accept the correspondingly strong form of indeterminism (nothing is determined). My point has been that local indeterminism is the same kind of thing as the global kind: if it is intelligible in one place, it ought to be intelligible everywhere. And why should it be true of only certain things and not others? Shouldn’t nature be uniformly indeterminist if it is indeterminist at all? It would be strange if nature were only partially governed by laws, with some parts lawful and others lawless: for example, protons fall under laws but electrons don’t. Could cats be law-governed but not dogs? Could particles and people be subject to indeterminism but nothing else? What makes these things so exceptional? And anyway particles and people are somewhat deterministic even according to indeterminist views—so why aren’t they wholly so? Local indeterminism is an anomalous position given that we must accept that determinism is the general rule.  [2]

[1] I think that free will entails determinism, so I have no motivation to invoke indeterminism here. It would be nice to show that quantum mechanics likewise entails determinism (!) and is not merely compatible with it.

[2] The belief in miracles also involves a curious confinement: they happen locally and sporadically, not universally. It is as if people need to believe that nature is not wholly natural—there are pockets of the supernatural in nature. Similarly, the belief in indeterminism is apt to be confined to certain areas, as if the rule of determinism has to have exceptions. The issues are connected inasmuch as miracles will involve breaches of determinism and indeterminism has the look of a miracle (is that the psychological basis of the attraction of indeterminism?). Indeterminism excites our sense of wonder while determinism reminds us of the inescapability of the daily grind.

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