Medieval Causality in Modern Chemistry

…whatever happened to the notion of efficient causality on the way from Aquinas’ time to Hume’s, some other things also happened from Hume’s time to ours, which allow us a new perspective on the old idea. For in contemporary natural science it is actually no longer the idea of diachronic event-patterns that is the prevailing idea of causation, although it still is in many philosophical speculations (see “how mental events can cause physical events and vice versa”), but rather it is the idea of the flow of energy and information among systems of various scales and their subsystems. However, that idea is precisely the scholastic idea. Consider Aquinas’ general description of the notion of a cause: “a cause is from the being of which there follows [the being of] something else”. Now, if we add to this that the notion of being for Aquinas is not just the static modern idea of “being an element of the universe of discourse”, but the dynamic notion of being the actuality of all forms, where the notion of actuality is that of being in act, being active, being at work, which in Aristotle’s Greek would be the idea of being in energeia, i.e., in a state of energy, then we should not be surprised at the idea that our modern notions of energy and information will bear some striking resemblances to Aquinas’ dynamic notions of being as act, and of form as that which informs, as that which determines the various ways in which things are, can be, and can be active or receptive, informing others and receiving information from others.
– Gyula Klima, “Whatever Happened to Efficient Causes?”, from Volume 10 (2012) of the Proceedings of the Society for Medieval Logic and Metaphysics, pp. 29-30

 

Recently I’ve been studying the foundations of chemical kinetics and equilibrium, especially about how we can derive the condition of equilibrium. There are two ways to derive the equilibrium constant, which is a number calculated using the concentrations of products and reactants at equilibrium, and which should be the same as long as the same reaction is occurring at the same temperature. One way to derive it involves basic kinetic theory. According to kinetic theory, the rate of a reaction depends on the mathematical product of the concentrations of the reacting chemicals. For a simple reaction that occurs in a single step, such as A + B → AB, the rate of reaction is proportional to the product of the concentrations: forward rate = k[A][B]. For the reverse reaction, AB → A + B, the rate of reaction is proportional to the concentration of AB, reverse rate = k’[AB]. At equilibrium, the forward rate equals the reverse rate, k[A][B] = k’[AB]. Rearranging this to get all the concentrations on one side, we get k/k’ = [AB]/([A][B]), which is the equilibrium constant. This is easy to derive for this reaction, because it only occurs in a single step. But, for any general reaction aA + bB cC + dD, the equilibrium constant is
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To see a derivation from kinetic principles for a general reaction, there is nothing better than Frederick O. Koenig’s article in Volume 42 of the Journal of Chemical Education. This kinetic derivation depends upon the idea of collisions of particles being the condition for a successful reaction. For, the derivation requires the assumption that at least some reactions occur in a single step, i.e., a reaction that “fulfills the following conditions: (1) the reaction occurs through either (a) a collision of two or more particles … or (b) a decomposition of a particle … (2) the particle or particles considered as the reaction products are the immediate result of the collision or decomposition in question” (Koenig, 1965, p. 228). But “This definition suffers from vagueness owing to the terms ‘collision’ and ‘immediate'” (p. 228), which is partly why Koenig says the kinetics derivation of the equilibrium constant requires certain simplifying assumptions. The derivation of the equilibrium constant from thermodynamic principles, meanwhile, is “exact” (p. 227). The thermodynamic derivation only depends on the idea that energy is exchanged in a reversible process, and that the total amount of heat energy absorbed in such a process (at constant temperature) equals zero.

 

In the above quote, Gyula Klima contrasts the 18th-century idea of causation as events following one another with the 13th-and 20th-century idea of causation as “flow of energy and information.” I think this contrast can be seen in the kinetic derivation of the equilibrium constant versus the thermodynamic derivation. The former, it seems, requires thinking of causation as a succession of events, i.e., the cause = the collision event, the effect = the reaction event. The problem here, as Koenig tells us, is that we assume that the collision and reaction are instantaneous, when in fact it may be that, collisions may take time and this may vary depending on the reactants, or that reactions may take time after collisions, and this too may vary, etc. In contrast, the thermodynamic derivation avoids all the problems of involving time and only considers the overall transfer of energy, which is partly why it offers a more exact proof. It seems to me that the thermodynamic approach doesn’t think of causation as a succession of events in time. Rather, it sees reactions happening as energy, contained in one body, flows to another body, which yields changes in substantial form. And by avoiding time, it manages to avoid many complexities.

 

To conclude, I think that the thermodynamic proof offers certain knowledge of the condition of equilibrium, since it only depends upon evident ideas about matter (e.g., that they contain energy, etc.). The kinetic derivation, on the other hand, offers only probable knowledge, since it depends on a certain simplified conception of very complex molecular processes. This is not to say that the kinetic derivation is bad science. After all, Sir Isaac Newton did very much the same with physics, but no one would dare say that he was a bad scientist. Instead, it would seem that making probable assumptions and arguments is a good way to about the issue and helps us achieve more certain knowledge later on. Funny enough, Albert Einstein makes a similar point in his 1919 article “What is the Theory of Relativity?“:

We can distinguish various kinds of theories in physics. Most of them are constructive. They attempt to build up a picture of the more complex phenomena out of the materials of a relatively simple formal scheme from which they start out. Thus the kinetic theory of gases seeks to reduce mechanical, thermal, and diffusional processes to movements of molecules — i.e., to build them up out of the hypothesis of molecular motion. When we say that we have succeeded in understanding a group of natural processes, we invariably mean that a constructive theory has been found which covers the processes in question.

Along with this most important class of theories there exists a second, which I will call “principle-theories.” These employ the analytic, not the synthetic, method. The elements which form their basis and starting-point are not hypothetically constructed but empirically discovered ones, general characteristics of natural processes, principles that give rise to mathematically formulated criteria which the separate processes or the theoretical representations of them have to satisfy. Thus the science of thermodynamics seeks by analytical means to deduce necessary conditions, which separate events have to satisfy, from the universally experienced fact that perpetual motion is impossible.

The advantages of the constructive theory are completeness, adaptability, and clearness, those of the principle theory are logical perfection and security of the foundations.

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