A number of different cosmological arguments — such as the Kalam Cosmological Argument, the contingency argument, Aquinas’s First Mover argument, etc — rely on a sub-argument that attempts to establish that there are no infinite causal chains. Let’s call the principle that there are no infinite causal chains no-infinite-causal-chains. And many cosmological arguments rely on some kind of causal principle, e.g., that nothing begins without an efficient cause. In 1912, Bertrand Russell published an article — ‘On the Notion of Cause’ — wherein Russell argued that causation is incompatible with our most sophisticated understanding of physics. While contemporary philosophers are not convinced by all of Russell’s arguments and typically do not think we should reject causation altogether, Russell’s article has been deeply influential in naturalistic thinking about causation. (See, for example, the articles collected in Price and Corry 2007.) For many years, I’ve thought that Russell’s 1912 article undermines the causal principle required for a number of cosmological arguments.

This morning — in the kind of lightning bolt realization that sometimes happens in the shower — I realized a new way that Russell’s article may put pressure on the combination of no-infinite-causal-chains and the Causal Principle. If I’m right, then Russell’s article provides another, distinct way to reply to some cosmological arguments.

According to one of Russell’s arguments, that time is dense provides us reason to reject causation. When we say that time is dense, we mean that between any two instants of time, there is another instant of time. As Russell is careful to note, for any given causal relation, there are four possibilities:

1. The cause, and not the effect, take non-zero time.
2. The effect, and not the cause, take non-zero time.
3. The cause and the effect take non-zero time.
4. Neither the cause nor the effect take non-zero time.

In cases (1) and (3), where the cause lasts for some non-zero duration of time, the cause acts through some finite interval before producing the effect. Either the cause’s interval involves change or not. If the cause’s interval involves change, then, really, there is a causal chain within the interval during which the cause acts. And then only the end of that causal chain has immediate relevance to the effect. As Russell puts the point,

[…] we are faced with a dilemma: if the cause is a process involving change within itself, we shall require (if causality is universal) causal relations between its earlier and later parts; moreover, it would seem that only the later parts can be relevant to the effect, since the earlier parts are not contiguous to the effect, and therefore (by the definition) cannot influence the effect. Thus we shall be led to diminish the duration of the cause without limit, and however much we may diminish it, there will still remain an earlier part which might be altered without altering the effect, so that the true cause, as defined, will not have been reached […]. If, on the other hand, the cause is purely static, involving no change within itself, then, in the first place, no such cause is to be found in nature, and in the second place, it seems strange — too strange to be accepted, in spite of bare logical possibility — that the cause, after existing placidly for some time, should suddenly explode into the effect, when it might just as well have done so at any earlier time, or have gone on unchanged without producing its effect (Russell, 1912, p. 5).

A parallel argument applies for case (3). Causes and effects must each take zero time to occur, that is, they each must occur at instants. As Russell argues, this suffices for showing that the effect cannot happen immediately after the cause, with no time in between.

That is, if the cause and effect must occur at instants, and do not generally occur at the same instant, the density of time ensures that there will be another member of the causal series between any cause and a subsequent effect. Take two instants of time, t1 and t2, and suppose that there is a cause at t1 and an effect at t2. Since there’s another instant t3 between t1 and t2 (i.e., t1 < t3 < t2), whatever happens at t3 must be an intermediate in the causal chain between t1 and t2. Furthermore, whatever happens at t3 makes a difference to whatever happens at t2. For example, if we throw a brick at t1 and a window breaks at t2, that the brick is traveling through the air unimpeded at t3 is an intermediate in the causal chain between t1 and t2. Since this is true for any cause and any effect, nothing is the immediate cause of anything else. To put the point in more technical language, in Newtonian mechanics, the past domain of dependence of an event at time t is the full collection of space-time points to the past of t; in relativistic physics, the past domain of dependence for an event at some space-time point p is p’s entire past light cone.

We have a strong intuitive sense that causation shouldn’t be anything like that. We ordinarily think that the assassination of the archduke Franz Ferdinand is more the cause of World War 1 than events on Jupiter’s moon Titan. But everything in an event’s past domain of dependence equally determines that event. Furthermore, as Russell would also point out, philosophers have traditionally held that whenever a cause reoccurs, the same effect follows; as Russell shows, once everything in the event’s past domain of dependence is precisely specified, there are no reoccuring cause/effect pairs. And since Russell thought that causation couldn’t be anything like that — it can’t be that everything to the past of an event equally caused the event and it can’t be that there fail to be reoccurrence of cause/effect pairs — Russell held that this provides us good reason to reject causation altogether.

Most philosophers nowadays are not going to find this argument convincing. Russell has made substantive assumptions both about the metaphysics of time and the nature of causation that many philosophers now reject; so, philosophers who reject those assumptions will have good reason to resist Russell’s argument. Nonetheless, their objections are not necessarily available to proponents of no-infinite-causal-chains. Here are two ways philosophers can reject Russell’s argument.

First, philosophers might simply bite the bullet and say that causal series are dense. That is, between any cause and any effect, there is a third, intermediate member of the causal series. Contrary to Russell’s causal intuitions, we’ve just been wrong about the nature of causation. But then causal series will generally include an actually infinite number of members. And hence no-infinite-causal-chains is false. Clearly, this option is not available to proponents of no-infinite-causal-chains.

Second, philosophers might reject the view that time is dense. For example, philosophers can say that time is discrete. While some proponents of cosmological arguments will simply pursue this route and so escape Russell’s argument altogether, not all of them will. For example, William Lane Craig — the Kalam argument’s foremost defender — defends something like a gunky view of time. On Craig’s view, (i) there are no such things as instants, i.e., infinitely thin increments or slices of time and (ii) we can always arbitrarily subdivide intervals of time. As Craig writes, “only intervals of time are real or present and that the present interval (of arbitrarily designated length) may be such that there is no such time as ‘the present’ simpliciter; it is always ‘the present hour’, ‘the present second’, etc. The process of division is potentially infinite and never arrives at instants” (Craig, 1993, p. 260). Elsewhere, Craig tells us, “anything having positive ontological status would seem necessarily to exist for some temporal duration; to say it exists only at a durationless instant is to ascribe reality to a mathematical chimera” (Craig, 1991, p. 499).

So, for Craig, there’s no such thing as the present simpliciter; instead, there are only intervals, of arbitrary duration, that include the present. Crucially, any interval of time, Craig argues, is potentially infinite, in the sense that we can always further mentally subdivide that interval. As Russell argues, anything at the end of a temporal interval will always be separated from anything at the beginning of that interval. In that case, anything in the interval between a cause and an effect can always make a counterfactual difference to the effect. And so, following Russell, there will be an infinite causal series between a cause and an effect. Hence, if time is structured as Craig proposes, then no-infinite-causal-chains is false.

Since proponents of cosmological arguments can simply reject the view that time is dense, there will be many cosmological argument proponents who may feel no dialectical force here whatsoever. Nonetheless, Craig has also argued that, in order for time to have had a beginning, the A-theory of time must be true, and has argued that, for the A-theory of time to be true, something like his gunky view of time must be true. And if all of that is right, then cosmological argument proponents really do face a forceful dilemma: either give up the Causal Principle or else give up no-infinite-causal-series. And on either horn of that dilemma, we ought to reject a wide family of cosmological arguments.

Disclaimer: The posts on the Cosmotherium should never be taken as definitive and I am typically not completely convinced of what I post here. This is my place for working out my views without the pressure or rigor of publication.

References

Craig, William Lane. 1993. “A criticism of the cosmological argument for god’s non-existence”. In William Lane Craig and Quentin Smith (Eds), Theism, Atheism, and Big Bang Cosmology, Oxford University Press, pp. 256-276

Craig, William Lane. 1991. “Theism and big bang cosmology”. Australasian Journal of Philosophy, 69(4), pp. 492–503.

Russell, B. 1912. “On the Notion of Cause”. Proceedings of the Aristotelian Society 13.

Price, Huw and Corry, Richard (Editors). 2007. Causation, Physics, and the Constitution of Reality. Clarendon Press.