Efficient and Final Causes

 

Aristotle held that there are four distinct kinds of causes or explanations (aitia), namely, material, formal, efficient, and final. The first two - material and formal - refer to what we would call the substance and the description of a thing, respectively, whereas the last two denote concepts closer to what we would consider as “causes” in the modern sense of the word. Efficient causes, according to Aristotle, are prior conditions, entities, or events considered to have caused the thing in question. Final causes are future conditions, entities, or events regarded as the cause of the thing in question. These categories persisted in Western thought until the scientific revolution of the seventeenth century, when philosophers such Spinoza and Descartes rejected final (teleological) causes and argued that efficient causes are necessary and sufficient to account for the workings of the world.

 

Newton’s mathematical approach to natural philosophy is sometimes seen as having shifted the focus of science from causal explanation to pure description. For example, he offered no hypothesis as to the cause of gravitation (in the modern sense of the word “cause”), but simply identified the phenomena of gravity and described them with mathematical precision. In this sense, it might be said that Newton adopted the formal causes of Aristotle as the only true objects of science. However, in the interpretation and application of the laws of motion, Newton and his successors almost invariably thought in terms of efficient causes. For example, although the relation F = ma does not explicitly identify cause and effect, it came to be understood as signifying that a force F applied to a mass m is the efficient cause of an acceleration a = F/m.

 

Thus, beginning in the seventeenth century, the idea of causation became linked with the concept of a temporally asymmetric sequence of events, in which causes invariably precede their effects in time. We might describe this idea by saying that events are invariably pushed from the past into the future. According to this view, the only real causes are efficient causes, and Aristotle’s “final causes” are just fictions or semantic constructions if not outright misunderstandings. The idea that events could be caused by conditions in the future, i.e., that events might be pulled by the future from the past, came to be regarded as non-sensical. The success of Newtonian mechanics seemed to imply that causality acts in only one direction in time, and Aristotle’s notion of teleology was discarded.

 

However, an interesting feature of Newton’s laws of motion - as well as of the laws of electromagnetism developed in the nineteenth century - is that they are inherently symmetrical with respect to time. In fact, all the fundamental processes of physics (with the possible exception of kaon decay, which is not relevant to most phenomena) are temporally symmetrical. Given the positions and velocities of a set of perfectly elastic particles, we can apply the ordinary laws of mechanics to extrapolate from the present conditions into the future, but we can just as well extrapolate from the present conditions into the past. Despite this symmetry, we almost invariably conceive of the flow of causality proceeding from the present into the future, rather than into the past. As Aristotle would say, we think in terms of efficient causes and not in terms of final causes.

 

There is, of course, one very important “law” of classical physics that distinguishes sharply between the two directions of time, namely, the second law of thermodynamics. However, the temporal asymmetry of this “law” is an artifact of the aggregation of many distinct microstates into one macrostate. For example, if all the molecules of a gas are initially clustered in one corner of a box, we expect them to expand (as time advances) to fill up the box, rather than contracting still further. This statement doesn’t distinguish between the many different ways in which the molecules could be initially “clustered in one corner of the box”. It’s true that nearly all the configurations that we would put in this category are such that, when extrapolated forward in time, they will expand, but there are some (very few) microstates in this category that would contract. The sense of paradox comes from confusion between state symmetry and process symmetry.

 

Let s2 = P(s1, Dt) denote the microstate produced by extrapolating from the microstate s1 through a time interval Dt. The temporal symmetry of physical laws implies that s1 = P(s2, -Dt), but of course it does not imply that s1 = P(s2, Dt). In other words, temporal symmetry of the physical laws does not imply that the state should reverse direction in phase space, i.e., we should not expect the microstate to immediately re-trace its steps in the next increment of time. On the other hand, there does exist a microstate s3 in the same macrostate as s2 but such that P(s3, Dt) equals s1. Furthermore, there are microstates in the same macrostate as s2 that extrapolate under an increment Dt to a microstate in the same macrostate as s1. Thus, when we predict how the macrostate of a system will evolve, we are making a statistical prediction based on the distribution of microstates in each of the macrostates. The reason we can predict the macrostates of a gas (for example) so reliably is that the statistics are hugely weighted in a certain direction. It’s possible that a free cloud of gas might spontaneously contract, but the number of microstates of a “free cloud” that lead to contraction is negligibly small compared with the number of microstates that lead to expansion, so when we see an arbitrarily-prepared “free cloud” of gas, it is virtually certain to expand as time increases. To put it simply, there are far more large clouds than small clouds, so a cloud of gas is almost certain to expand.

 

Not withstanding the statistical nature of descriptions of events in terms of macrostates, the fact remains that the fundamental processes of nature – at least in classical physics - are temporally symmetrical, so our choice of a direction for causality is conventional. Indeed Laplace explicitly recognized this when he wrote about determinism within the Newtonian framework, claiming that if the present conditions were known completely and with perfect precision, then the entire history of the universe, both past and future, would be known. According to Laplace’s view, the concept of causality is not even applicable, at least not in the sense of something that flows from the past into the future. Instead, he envisaged a “block universe”, complete and whole for its entire history. He certainly would have denied the necessity of restricting our notions of causality to what Aristotle called efficient causes, but it still seems to have been assumed that efficient causes are sufficient to give a complete and coherent account of physical processes.

 

However, beginning in the 20th century, scientists identified a variety of fundamental processes that seem to defy explanation if we restrict ourselves to just efficient causes. The best known of these processes are those involving quantum entanglement. The results of spacelike-separated measurements on entangled particles exhibit correlations that depend on what measurements are made. It can be shown that no explanation in terms of efficient causes is consistent with the empirical results of such measurements, but the results are quite easy to explain in terms of final causes, i.e., if we allow for the possibility that the emission of a quantum particle may be conditioned to some extent by the circumstances of its absorption. Thus the abandoned notion of “final causes” discussed by Aristotle may turn out to be useful after all. It seems appropriate that the word aitia is a palindrome, since, like the laws of physics, it doesn’t distinguish between the forward and backward directions.

 

Incidentally, we sometimes imagine the advance of science and culture as increasing the level of sophistication and subtlety, giving a fuller recognition of the range of possibilities, and yet there are many example of concepts being winnowed down and categories eliminated (at least temporarily) as science and culture have progressed. The reduction of Aristotle’s four types of causation (aitia) to the single type (efficient) recognized by modern science is an example of this. This was not done by unifying or consolidating the four original types; three of the four were simply discarded. Another example concerns the modes of musical composition, of which during the middle ages there were seven, namely, the Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolien, and Locrian. Today almost all music is written in either the Ionian or the Aeolian modes, which we call Major and Minor keys, respectively. The other five modes have simply been discarded. Still another example is the different ways in which a set of numbers can be represented by a single number, called the mean. The ancient Greeks enunciated ten distinct kinds of means, but of these ten only three (the arithmetic, geometric, and harmonic means) remain in common use.

 

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