Mysticism and Logic, Chapter IX

"On the Notion of Cause," pages 180-208

[Posted on the fiftieth anniversary of Bertrand Russell's death, February 2, 2020.] This chapter addresses some confusions around the notion of “cause” as used by philosophers – confusions that are substantial enough that it would be best if the term were avoided. The misunderstanding of causality leads to other mistaken notions. And though philosophers are confused about the “law of causation,” what does science actually employ in its stead?

Many sciences never talk of causation, even though philosophers assert its fundamental nature to science. But perhaps the lack of talk about causes in physics, for instance, isn’t dereliction of duty, but recognition of the absence of causes. The law of causation is outdated, and survives “like the monarchy, only because it is erroneously believed to do no harm [p. 180].”

Russell examines dictionary definitions of “causality” and related words, leading to the distinction between a propositional function (“x is a number”) and a proposition (3 is a number). Propositions are either true or false, but propositional functions can sometimes be true (for some values of x, say), and sometimes false. This line of reasoning suggests that something is necessary if it is the “predicate” of a propositional function, which means that the statement is true for all possible values of its argument.

Eventually, Russell avers that causality (event e2 is caused by event e1, say) is when, for any event e1 that occurs, within some interval of time τ, event e2 occurs. (Variations of this definition have been provided by John Stuart Mill and by Henri Bergson.) Some alternative definitions suffer from circularity or from not limiting the time between cause and effect.

To examine the definition and explore its applicability or inapplicability to science, Russell puts aside (for now) the problem of multiple causes, to focus instead on the meaning of “event,” and on the length of time separating cause from effect.

If we define an event too narrowly, then we will never again see its exact match in the future, and so the notion of causation would lose all purchase. “An ‘event,’ then, is a universal defined sufficiently widely to admit of many particular occurrences in time being instances of it [p. 187].”

The effect cannot take place at the same instant of time, nor immediately afterwards, thanks to the lack of infinitesimal time intervals – so, there must be some finite passage of time twixt cause and effect. As soon as we allow for such a time lapse, however, it becomes possible that in that interval, an intervening event (a meteorite strikes?) changes conditions sufficiently that the proposed “effect” will not occur. But this in turn means that the proposed cause is not itself sufficient to ensure the effect. Were we to start adding the state of the environment into our cause, we end up draining our cause-and-effect claim of any applicability, through the previously noted problem with excessive narrowness.

Despite our difficulties with explicitly expressing the logic of cause and effect, in our quotidian lives, there are many reliable “regularities of sequence [p. 187].” Some of them may be completely dependable, and even less dependable correlations can spur scientific advances. But science pursues or requires no “law” of cause and effect, it does not assume that there is an invariant causal relationship out there waiting to be discovered. As sciences advance, our old causal claims become more nuanced, with finer partitions of antecedents and consequences. When the antecedents are finely enough delineated that we are certain of the consequences, they are also fine enough that they will not occur again, that there is no predictive value to the causal relationship.

Philosophy has been riddled with misconceptions around causation. One is that causes and effects have to be similar, so that mental processes, for instance, could not arise from inert matter alone. Another [Russell enumerates five – RBR] is connected to free will, the notion that causes cannot make someone do something that they do not desire to do. But these desires themselves might be “caused,” even if there is free will in the sense of only doing what is desired.

What is left when philosophy abandons any putative law of cause and effect? Accept for the nonce the logic of induction, that when we have a long series of cases where a “cause” is followed by an “effect,” then this relationship is quite likely to hold in similar future cases. These series that spark induction, however, speak to likelihoods, not necessary consequences, with respect to future observations. The inductive cause-and-effect might lead us to claim that striking a match causes the match to ignite, but we will find that striking a wet match will still not do so. Nor does the inductive approach suggest that every event has some cause. And it seems to be overly inclusive, supporting the claim that night causes day, but we will not back away from accepting that in the sense we are now discussing, night does cause day. The rules we get from the inductive approach can always fail in the next observation, without violating any scientific law.

As science progresses, we tend to move away from cause and effect claims. Gravity involves rules that masses follow, but we cannot isolate one aspect of gravitational forces as causes and others as effects. The correct formulation is mathematical, a stability in the differential equations that characterize the system. But this is hardly some a priori rule of science, as some philosophers expect from their “law of cause and effect.”

Note also that in physics, the complete state at an instant not only determines the future, but the past. There is no temporal priority that makes earlier things causes of later things, and not the other way around.

While science does not stipulate any law of causality, it does accept, in the background, a certain uniformity of nature. Functions that have characterized relationships in the past are expected (inductively) to hold in the future, and if they do not hold, there is some more general law, capturing both sets of data, that does hold. As with other inductive arguments, this uniformity assertion is only likely, not certain, to hold. And if it prove false with respect to some scientific “law,” the rest of science is not thereby invalidated.

The effects of gravitation within the solar system depend, though minutely, on matter that lies outside of the solar system. As we have little knowledge of that matter, we cannot fully verify gravitational theory. But we can be very confident of our claims about gravity within the solar system anyway, irrespective of what is going on in the rest of the universe. The solar system, with respect to gravitation and over a given time period, is a “‘relatively isolated system [p. 197],’” where it will behave in a uniform manner (approximately) during that time period, no matter what is happening elsewhere. A system is “’practically isolated [p. 198]’” if, though there might be some outside situations that would lead relative isolation to fail, we rightly suspect that those situations do not arise. When it comes to falling bodies, the earth is relatively isolated, but it is not isolated with respect to tides.

It is evidence, not a priori reasoning, that leads us to believe some systems are relatively or practically isolated. “The case where one event A is said to ‘cause’ another event B, which philosophers take as fundamental, is really only the most simplified instance of a practically isolated system [p. 198].” The fact that A is always followed by B is true thanks to the relative unimportance, in this case and for this time, of what is going on in the rest of the universe. The (unknown) laws of the universe could still hold but produce instances where A is not followed by B.

Causality is the reed upon which people make out-of-sample inferences. If these inferences are legitimate, the system is deterministic. A non-deterministic system is capricious (p. 199).

Brains are part of the universe. It seems that there is a one-to-one mapping between states of one person’s brain and states of the universe. Assume also that there is a one-to-one relationship between the state of a mind and the state of the corresponding brain. This leads to the notion that there is a one-to-one mapping between a mind and the state of the universe. Whatever (sub)set of states determines the universe, then, we can find the same number of states of one person’s mind that also “determines” the universe. Those who are concerned that mind is determined by matter (outside of the brain) should recognize that the determination goes both ways. Even if there are multiple states of mind for any state of the brain [Russell, page 203, cites Bergson for this claim], people are not thereby forced (by the world of matter) to take actions that they do not desire to take. A similar point applies to whether or not the universe is goal-directed (teleological); the answer to this query is independent of whether or not the world is mechanical, deterministic given the precise state of matter.

It is believed that our desires cannot alter the past but can alter the future. But this belief is a relic of our memory acting only in the backwards direction (and because generally we only have desires for things unknown to us): we could equally say that the future cannot be altered by our wishes (and were our wishes different the past would have been different).

Most supporters of determinism go beyond claims that whatever may be may be – they regard the world as being determined function-like, a function of earlier data. But with no constraints on the complexity of the function, such determinism is surely the case: at the extreme, the full data themselves can be mapped trivially into “functions” that describe their state at a given time. But what science seeks is the simplest formula consistent with the known facts, from within the infinite set of possible, and so far unfalsified, formulae.

Perhaps what science really seeks is formulae where time (in an absolute sense – as opposed to lapses of time) does not enter as an independent variable, and hence those formulae are uniform in the sense that they hold at any time.

What of free will? Surely the known facts suggest that some of our volitions are determined. But at this point, we cannot be sure that all of our volitions are determined (except in the trivial sense noted above). Nonetheless, our sense of freedom is irrelevant to the scientific question of free will. “The view that it has a bearing rests upon the belief that causes compel their effects, or that nature enforces obedience to its laws as governments do [p. 206].” Our sense of freedom in our volitions is consistent with an appropriate view of determinism.

If our will is determined, is it determined in the mechanical sense, where data concerning material elements are sufficient to generate our will? If our will is so determined, we still need not view this as the triumph of matter over mind: a system with a set of material determinants can also have a set of mental determinants. Nor does a deterministic system require some uncomfortable notion of necessity, where, for instance, we must act against our wishes.

Russell (pages 207-208) offers a one-paragraph summary of this chapter. What philosophers think of as a law of cause and effect is mistaken. Systems can have multiple sets of determinants. Free will may or may not exist, but in any event, it does not have to be in opposition to determinism.