Aristotle flourished before the great flowering of Greek mathematics that gave us Euclid, Ptolemy, Apollonius, and Aristarchus. In his day, mathematics amounted to just arithmetic and simple geometry. In spite of the famous Pythagorean theorem that the square constructed from the hypotenuse of a right triangle is equal in area to the sum of the squares constructed from the other two sides, the historic reality of the Pythagorean movement had more to do with number mysticism, other superstitions, and curious injunctions like “don’t eat beans” than it did with real mathematics.

I think Aristotle was entirely right to conclude that arithmetic and simple geometry were of little use for explaining change in the natural world. I’ve characterized his physics as grounded in a kind of semantic inquiry that Aristotle pioneered. We are not used to thinking about science this way, as fundamentally involved with a very human inquiry about the meaning of experience in life, rather than predictive calculation. For Aristotle, the gap between natural science and thoughtful reflection about ordinary experience was much smaller than it is for us.

Aristotle invented the notion of cause as a semantic tool for expressing the reasons why changes occur. Aristotle’s notion is far more abstract than the metaphor of impulse or something pushing on something else that guided early modern mechanism. Even though the notion of cause was originally developed in a text included in Aristotle’s Physics, the “semantic” grounding of Aristotelian physics places it closer to logic than to modern physical inquiries.

I think the discussion of the kinds of causes could equally well have been grouped among his “logical” works. In fact, the form in which we have Aristotle’s works today is the result of the efforts of multiple ancient editors, who sometimes stitched together separate manuscripts, so there is room for a legitimate question whether the discussion of causes was originally a separate treatise. We tend to assume that there must be something inherently “physical” about the discussion of causes, but this is ultimately due to a circular argument from the fact that the more detailed version of it came down to us as part of the Physics (there is another, briefer one that came down to us as part of the Metaphysics).

Since Hume and especially since the later 19th century, many authors have debated about the role of causes in science. Bertrand Russell argued in the early 20th century that modern science does not in fact depend on what I have called the modern notion of cause.

More recently, Robert Brandom has argued that the purpose of logic is “to make explicit the inferential relations that articulate the semantic contents of the concepts expressed by the use of ordinary, nonlogical vocabulary”. I see Aristotelian causes in this light.

I want to recommend a return to a notion of causes in general as explanatory reasons rather than things that exert force. This can include all the mathematics used in modern science, as well as a broader range of reasons relevant to life. (See also Aristotelian Causes; Mechanical Metaphors; Causes: Real, Heuristic?; Effective vs “Driving”; Secondary Causes.)

Russell on Causality

Bertrand Russell (1872-1970) was one of the founders of analytic philosophy. His contributions to mathematical logic, philosophy of mathematics, and philosophy of language were highly influential, and he wrote on a host of other topics as well. In a famous 1912 essay “On the Notion of Cause”, he addressed the common prejudice that I have been referring to vaguely as “causality in the modern sense”, and argued that modern science does not in fact rely on it. I support this conclusion.

According to Russell, “the word ’cause’ is so inextricably bound up with misleading associations as to make its complete extrusion from the philosophical vocabulary desirable” (Mysticism and Logic, p.180). “In spite of these difficulties, it must, of course, be admitted that many fairly dependable regularities of sequence occur in daily life” (p. 187).

The idea of the supposed “law of causality” is that the same causes always produce the same effects. Russell points out that the alleged necessity with which one “event” is said to follow another depends on an abstracted notion of repeatable “events”, but every concrete event implicitly involves such a vast amount of individualizing detail as to be essentially unrepeatable.

“What I deny is that science assumes the existence of invariable uniformities of sequence of this kind, or that it aims at discovering them. All such uniformities, as we saw, depend upon a certain vagueness in the definition of the ‘events’…. In short, every advance in a science takes us farther away from the crude uniformities which are first observed” (p. 188, emphasis added).

Behind such presumptions of uniformity lies the prejudice that a cause somehow compels a particular effect. “What I want to make clear at present is that compulsion is a very complex notion, involving thwarted desire. So long as a person does what he wishes to do, there is no compulsion, however much his wishes may be calculable by the help of earlier events. And where desire does not come in, there can be no question of compulsion. Hence it is, in general, misleading to regard the cause as compelling the effect” (p. 190, emphasis added). “A volition ‘operates’ when what it wills takes place; but nothing can operate except a volition. The belief that causes ‘operate’ results from assimilating them, consciously or unconsciously, to volitions” (p. 191).

“[A]ny causal sequence which we may have observed may at any moment be falsified without a falsification of any laws of the kind that the more advanced sciences aim at establishing” (p. 194). “The uniformity of nature does not assert the trivial principle, ‘same cause, same effect’, but the principle of the permanence of laws” (p. 196). “In all science we have to distinguish two sorts of laws: first, those that are empirically verifiable but probably only approximate; secondly, those that are not verifiable, but may be exact” (p. 197).

“We cannot say that every law which has held hitherto must hold in the future, because past facts which obey one law will also obey others, hitherto indistinguishable but diverging in future. Hence there must, at every moment, be laws hitherto unbroken that are now broken for the first time. What science does, in fact, is to select the simplest formula that will fit the facts. But this, quite obviously, is merely a methodological precept, not a law of Nature” (p. 204, emphasis in original).

“We found first that the law of causality, as usually stated by philosophers, is false, and is not employed in science. We then considered the nature of scientific laws, and found that, instead of stating that one event A is always followed by another event B, they stated functional relations between certain events at certain times, which we called determinants, and other events at earlier or later times or at the same time…. We found that a system with one set of determinants may very likely have other sets of a quite different kind, that, for example, a mechanically determined system may also be teleologically or volitionally determined” (pp. 207-208, emphasis added).

I have suggested that scientific laws expressed in terms of equations are a specific kind of what Aristotle called formal “causes” (or better, formal “reasons why”). They are the kind that is expressible in mathematics. But natural or physical causes are still commonly conceived as efficient causes in the sense that this term acquired in late scholasticism, and it is this prejudice that Russell was addressing here.

The diverse compilation Aristotle’s early editors called Metaphysics (“after the Physics“) includes a summary of the four causes discussed in the Physics. Unlike other parts of the Metaphysics that, for example, discuss the term commonly translated as “substance” in far greater depth than in the Categories, the summary of efficient cause in the Metaphysics is less sophisticated than the discussion in the Physics. Thomistic and late scholastic notions of efficient cause seem to be based on the more simplistic account given in the Metaphysics, where the efficient cause is treated as more narrowly concerned with motion.

The Physics says very explicitly that the art of building, not the carpenter or the carpenter’s action, is most properly the “efficient cause” of the building of a house. The building of a house is implicitly considered as an end, not as a concrete motion. The art of building is the primary means by which this end can be successfully accomplished. This suggests to me that just as the “material cause” in Aristotle is hylomorphically paired with the “formal cause”, the “efficient cause” is related to the “final cause” as means are related to ends. Efficient cause as the means by which an end is realized is quite a bit different than, and more general than, the efficient cause as cause of motion that is the basis of the Thomistic and late scholastic concepts, as well as of the “modern” prejudice addressed by Russell.