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a. Causality in More Detail

Causality in More Detail

We take it for granted that the universe operates according to the laws of causality. People may disagree on what causes a particular effect, but there is no disagreement on the existence of causality. This is universally accepted. But what is causality? In this and the next few articles I will attempt to explain.

We are well used to thinking in terms of causality, which we understand to mean a cause leading to an effect. However, this apparently simple concept contains much complexity. Firstly, we do not always use the word “cause” when describing causality. For example, rather than saying that a factory causes cars, we say that a factory manufactures them.

Secondly, we normally regard an effect as being the beginning of an event, object, or circumstance. However, it can also be the end, a change of state, or the ongoing event, object, or circumstance in its entirety. Thus, we refer to one event (the cause) as causing another (the effect) to begin, end, alter in state, or be ongoing in its entirety.

Thirdly, although the names cause and effect are singular, both are, in fact, plural collections of events, objects or circumstances of a particular type. Any single member is known as an instance of the cause or effect.

Causality describes the ways in which instances of these two collections can match. The Scottish philosopher David Hume observed that for a causal relationship to exist:

  1. an instance of the effect must always begin after an instance of the cause; and
  2. the instances of the effect and cause must be contiguous in space.

In other words, for a causal relationship to exist, the region of space-time occupied by an instance of the cause must contain the region of space-time occupied by an instance of the effect. The region of space-time occupied by something is the space occupied by it at every point in time during its existence.

Causal rules are derived from the way in which individual pairings of the instances are repeated. Two sets of events are described as being causally related if one of the following conditions apply.

  1. If an instance of the cause is sufficient for an instance of the effect, then the region of space-time occupied by the former always contains the region of space-time occupied by the latter. Fig.1 shows this diagrammatically. In other words, an instance of the effect always takes place in the presence of an instance of the cause. However, it is not necessarily the case that every instance of the effect results from an instance of the cause.
  2. If an instance of the cause is necessary for an instance of the effect, the region of space-time occupied by the latter is always contained by the region of space-time occupied by the former. Fig.2 shows this diagrammatically. In other words, an instance of the effect cannot take place in the absence of an instance of the cause. However, it is not necessarily the case that every instance of the cause leads to an instance of the effect.
Fig.1 A space-time diagram showing instances of a sufficient cause as white ellipses, and instances of the effect as black lines at the beginning of events shown by grey ellipses.
Fig. 2 A space-time diagram showing instances of a necessary cause as white ellipses, and instances of the effect as black lines at the beginning of events shown by grey ellipses.

If an event of a particular type occurs, then these causal rules allow us to deduce, with varying degrees of certainty, what causes have taken place or what effects will take place.

Causality can be complex, with several causes combining to produce an effect. The epidemiologist, Ken Rothman, explained that, for an effect to take place, it is often the case that several necessary causes must combine to create a sufficient cause. The combination of necessary causes of type A, B and C may be sufficient to result in an effect of type D. For example, the presence of gas, oxygen and a spark are each necessary and together sufficient to cause a gas explosion. Fig.3 shows this diagrammatically.

Fig.3 A space-time diagram showing instances of three necessary causes as coloured ellipses, which together comprise sufficient cause, and instances of the effect as black lines at the beginning of events shown by grey ellipses.

One aspect of causality which is often overlooked is the existence of inhibitors. In the same way as a cause and an effect, an inhibitor is a plural collection of physical events, objects, or circumstances of a particular type. However, it is the opposite of a cause in that it prevents an effect from taking place. Depending on its type, the presence of an instance of the inhibitor can prevent an event from beginning, ending, changing state, or occurring in its entirety, irrespective of any causes which might dictate otherwise.

In the same way as causes, inhibitors can be necessary to prevent an event or sufficient to do so. If an inhibitor is necessary but not present, then the effect can occur. However, this does not necessarily mean that it will occur. This depends on what causes are present. On the other hand, if an inhibitor is sufficient and present, then the effect cannot occur. In practice, a sufficient inhibitor can be a combination of several necessary inhibitors. The region of space-time in which the effect is prevented is the overlap between them.

Causality is, of course, a physical process. This process will be described in more detail in the next article.

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