Entropy and Cosmological Proofs

In Nature and Nature’s God I argue that the second law of thermodynamics verifies Aquinas’ claim (SCG I.13) that a sempiternal universe would require God’s sustaining causality. The second law requires that in any isolated system the entropy must increase monotonically over time until it reaches a maximum. If there is no God the universe is an isolated system in the thermodynamic sense. Therefore its entropy must increase monotonically over time. If the universe had no beginning infinite time would have already elapsed, and the entropy density of the universe would have reached a maximum value already. The universe would thus be in a state of heat death with no free energy left, contrary to fact. Thus the universe either came into existence a finite time ago or is not an isolated system, but open to entropy reducing action from outside. Since the universe is the totality of physical beings, there must be a transcendent cause for the universe’s condition that is not physical and thus not subject to the second law of thermodynamics. This is God.

In his comments on my book at the 2023 ACPA meeting, Robert Koons pointed out that it is possible to construct a mathematical function that increases montonically from time equals negative infinity to positive infinity, approaching 0 asymptotically in the negative time direction, and approaching some finite maximum value asymptotically in the positive time direction. For example, the function f(x) = ½ + x/(2|x| + 2). To show that the second law rules out an infinitely old, isolated universe, one must show that the entropy of the universe over time cannot be described by such a function.

Infinitely Increasing Monotonic Function

This can be done. For the entropy value for the universe as a whole is dominated by gravitational entropy. This means that General Relativity is the appropriate context in which to think about the entropy of the universe. In gravitational terms, free energy means the capacity for structure formation and orbital motion. Maximal entropy means either collapse into a black hole, or dispersal in a space undergoing accelerated expansion, in which interaction between bodies becomes impossible due to the finite speed of causal interaction (the speed of light). This speed eventually becomes too slow to traverse the ever expanding distance between bodies.

Albert Einstein’s original application of General Relativity to cosmology attempted to model a steady state universe that could exist in a condition like the universe’s present one for an infinity of time past and future. But it quickly became clear that this was not possible. Such a universe is at a point of unstable equilibrium, and must either begin contracting and collapsing, or begin a runaway expansion at the slightest disturbance.

Applying this to the shape of possible entropy time functions, gravitational entropy cannot increase at an arbitrary slow rate, as an infinitely old universe subject to the second law would require. Entropy has a discrete component, and possibly a continuous one as well. The discrete component is constituted by the quantum states of a system. Entropy is Boltzmann’s constant times the logarithm of possible microstates that could instantiate a given macrostate. (S=k ln W). A minimum of entropy would be zero, representing a single microstate. (log 1=0). The smallest possible increase of entropy would be k ln 2, representing two possible microstates. Thus the entropy would have to increase at a minimal finite rate, which would require only a finite time to reach the present level of entropy.

Currently, however, the energy of a body is accounted for not only by its discrete quantum states, but by its overall translational kinetic energy due to its motion through space. Space and time are not quantized in General Relativity or classical mechanics, and there is no established quantum theory of gravity or space and time. To apply Boltzmann’s entropy formula to this aspect of physical systems, one establishes a measure for the volume of phase space that a system in a given macrostate can occupy. Then the W in S=k ln W is not an integer value of microstates, but a volume in phase space. In principle the entropy value becomes infinitely divisible. (If time, space, and gravity turn out to be quantized and discrete, as many people think, the case for a minimal rate of entropy increase is strengthened. But physicists have been looking for a theory of quantum gravity for a hundred years and have remained unsuccessful. I believe time and space just are fundamentally continuous.)

However, the Heisenberg uncertainty principle should still apply, according to which there is some finite, minimum level of uncertainty in the position and momentum of a physical body or system. This indeterminacy will set a lower limit on how finely-tuned the gravitational system of the universe can be, and thus a lower limit on the rate of collapse/dispersal, and thus a lower limit on the rate of entropy increase for the universe overall.

Thus it is not possible for the entropy of the universe to increase monotonically for an infinity of time past and future. And thus the universe must have been started by God a finite time ago, or be sustained by God in a low entropy condition. Either way, naturalism is false.

Feser on Nature and Nature’s God

Edward Feser has reviewed Nature and Nature’s God in the July 2025 issue of The Thomist. I am grateful for his many kind words. He states that “the analysis in [the] first part, no less than in the second, is detailed and highly illuminating, and the scholarship deployed is impressive throughout. The book is a major achievement, and will contribute mightily to the revival of Aristotelian-Thomistic natural theology and philosophy of nature. Even those who disagree with Shields will learn from, and profit from engaging with, this important work.” “Shields’s analyses not only of inertia and thermodynamics but of gravitation, teleology, and fine-tuning constitute a major contribution to Aristotelian-Thomistic philosophy of nature even apart from any application to natural theology. The book advances both fields, and deserves a wide audience.”

Feser finds the second part of the book—in which I defend Aquinas’ second motion proof from the Summa contra Gentiles in light of modern science and its history—“entirely successful.” Nevertheless, despite his admiration in certain respects, he finds my interpretation of Aquinas’ First Way in the Summa Theologiae in the first part of my book quite implausible overall, and he levels some serious criticisms. This is only fair, since I criticized his reading of the First Way in my book. In fact, his criticisms helped to reveal to me a real weakness in my presentation, namely that I moved too quickly from the First Way in ST to the arguments in Summa contra Gentiles, without sufficiently addressing the immediate context of the First Way itself.

In a spirit of friendly debate, I will respond to Feser’s criticisms here. I have learned a great deal from his many books over the years (including from his characterization of essentially and accidentally ordered causal series, so central to the first three Ways), and we are joined in common cause in defending theism in general and Thomism in particular. But it serves the interests of the community of Thomists if many different interpretations are presented clearly and ably defended by their proponents. Each interpreter will inevitably notice things that others have missed, and the process of disputation will clarify the truth over time.

I begin by noting that I contrast Aquinas’ First Way with the second motion proof in SCG—which for convenience’s sake I call G2 following Kretzmann. The First Way has a quite modest conclusion, not ruling out naturalism all by itself, whereas G2 has a more robust conclusion, demonstrating the existence of a transcendent being. As I read the Summa Theologiae, the Five Ways prove conclusions of increasing strength, but the demonstration of classical theism is not complete until the end of question 3. Feser seems inclined to read the First Way as an abbreviated form of G2. What he says about the second part of my book implies that he appreciates my analysis of G2, which sets the stage for my science-engaged defense of Aquinas’ motion proof, but he is unsympathetic to my analysis of the First Way as a much more modest argument.

Feser’s constructive criticism of part one begins with some clarifications about his own interpretation of the First Way. He calls the First Way metaphysical in his book Aquinas, whereas I see it as belonging to the discipline of natural philosophy. But Feser clarifies that he was using the term metaphysical “in the broad sense common in contemporary academic philosophy (which includes philosophy of nature as part of metaphysics), rather than in the narrower sense in which Thomists often use the term.” Feser also, quite rightly, points out that I was not sensitive to the fact that in his Five Proofs he presents the motion (“Aristotelian”) proof as his own, inspired by Aristotle and Aquinas but not an account of Aquinas’ own proof, so Five Proofs should not have been used as evidence of his own interpretation of the First Way.

Feser makes three further, encouraging clarifications about his own position. First, although he denies “that the First Way need be read in a way that requires any premises from natural science as that is understood today” he does “not deny that it could be read that way.” In other words, he thinks the project of the second part of my book is an important and worthwhile one. Second, he does not want to assimilate the First Way with the De Ente et Essentia proof; they are two separate ways to God. From my perspective, the more proofs for God the better. Third, Feser seems quite open to the non-simultaneity of some essentially ordered causal series, which I argue for in the book and is an important point.

Feser’s criticisms center on my claim that the First Way, by itself, only proves that there is one or more first, unmoved movers, and does not show that any of those movers is not a natural being. “Aquinas tells us the Five Ways are arguments by which ‘the existence of God can be proved.’ And of the first mover he arrives at in the First Way, he says ‘this everyone understands to be God.’ Why say these things if he did not intend the First Way to get us all the way to God?” My response is that Aquinas does not share 21st century philosophy of religion’s understanding of what a proof for God’s existence is. Aquinas tells us himself what he means by the term deus, and thus what it means to demonstrate the existence dei: “This name “god” (hoc nomen deus) is the name of an operation, in regards to the origin of the name. For this name is imposed from universal providence over things, for all who speak about god intend by “god” to name that which has universal providence over things.” (ST I, q. 13, a. 8, c.). He says, further, that

There is a certain common and confused knowledge of god (dei cognitio) which almost everyone has. . . . For human beings, seeing that natural things run according to a certain order, perceive for the most part that there is some regulator (ordinatorem) of the things that we see, since there cannot be order without a regulator. Who, however, or what sort of thing, or whether only one thing is the regulator of nature is not yet immediately grasped by this common consideration. Similarly, when we see that a human being undergoes motion and performs other actions we perceive that there is a certain cause of these operations in him that is not in other things, and we name this cause “the soul,” without yet knowing what the soul is, whether it is a body, or how it effects the aforementioned operations. . . . Certain people have believed that there is no other regulator of the things of the world than the astronomical bodies and so they have said that the astronomical bodies are gods (deos esse). Certain people have even gone farther [and said] that the very elements and those things that are generated out of them [are gods], as if thinking that the motions and natural operations that they have are not due to another regulator, but that other things are ordered by them. Certain people, believing that human acts are not subject to the ordination of anyone other than humans, have said that humans who order others are gods (deos esse). (SCG III, c. 38.)

To prove the existence of god is not to do very much; it is only to prove that there is some one or more ultimate determiners of what goes on in the universe. If the planets or elements really were the ultimate determiners of what goes on, they would be gods; since they are not, they are not gods. Note that Aquinas did not in fact capitalize the word deus/“god,” in the Five Ways; capitalization was only used at section beginnings in medieval manuscripts. The manuscripts of the Five Ways leave deus uncapitalized.The capitalization of Deus in modern Latin editions of the Summa, and of God in English translations, is an implicitly interpretive move. The use of the capital in the Five Ways biases modern readers and scholars towards thinking that Aquinas had something stronger in mind than he actually did. That the word deus/god does not automatically imply incorporeality is clear even from the immediate context of the Five Ways. In objecting to Anselm’s proof in the Proslogion, Aquinas says “Perhaps he who hears the name ‘god’ does not understand it to signify something than which a greater cannot be thought, since certain people have believed that god is a body.” (ST I, q. 2, a. 1, ad 2.) Anselm’s argument is built around the principle of non-contradiction. Aquinas would not have used the fact that certain people believed god to be a body to criticize Anselm if it was a contradiction in terms for god to be a body. Otherwise, he would have been playing into Anselm’s hands.

When Aquinas ends each of the first three ways by saying that “this everyone calls god,” he is not saying that he has just proved the existence of a superlatively divine being, meeting the strictest standards that could be set for the name “god.” He means, rather, that he has just proved the existence of a being that satisfies the lowest common denominator description of “god,” namely the understanding of the term he sets forth in the passages quoted above. This is why he shifts in the Fourth and Fifth Ways to saying “this we call god.” The Fourth and Fifth Ways prove stronger conclusions than the first three Ways, something much more like what Christians conceive God to be. Many people who believed in the existence of god did not believe in something as impressive as the being proved to exist in the last two Ways.

Feser objects that “even if a planet or an emperor counts as a ‘god’ in the thin sense Aquinas allegedly had in mind, an animal soul surely would not.’” But in the book I argue only that if an animal soul were a first, unmoved mover, then it would be the ultimate determiner of some restricted region of the universe, and thus a little god. Of course it is not a first, unmoved mover and so is not a god. Its actions are determined by outside factors in many ways. But the idea that an individual soul could be thought of as a god is not foreign to Aquinas’ intellectual context, as evidence by his comment about human rulers quoted above. Indeed, ancient Greek pagans believed in many minor deities, governing quite restricted domains (such as a single river or grove of trees) within the larger universe. The First Way, by itself, is agnostic as to what sort of thing really fits the bill of a first, unmoved mover. That is why it couches its conclusion with the indefinite adjective aliquod: there exists “some first mover moved by nothing.” All it demonstrates is that there is some one or more first unmoved movers, so some one or more rulers of the universe exist, and thus a god exists, one way or another.

Feser objects that “Shields himself admits that versions of the argument from motion Aquinas develops in the Summa contra gentiles and the Compendium theologiae do aim to get us beyond a mundane cause to a purely actual first mover. Why, then, not take the First Way to be another version of that line of reasoning, truncated but with the same aim? Shields’s reason for not doing so is that he thinks there is no good indication in the text of the First Way itself that it has the same aim as those other version of the argument from motion.” Feser thinks I am inconsistent in using outside texts to help interpret the Fifth Way and not doing so for the First Way as well. But in fact I do use outside texts in both cases. I point out in the book that there are two motion proofs in Aristotle’s Physics, one in book VII and one in book VIII. Aquinas tells us that the Physics VII proof only shows that there is a first mover while the Physics VIII proof shows what sort of thing a first mover is. Aquinas’ own version of both proofs is presented in SCG, as two separate motion proofs. The First Way has the structure of the Physics VII proof, and thus shows only that there is a first mover, not what sort of thing it is. Thus I use SCG and Aquinas’ Commentary on Aristotle’s Physics to interpret the First Way.In the case of the Fifth Way, the argument has the very same structure as an argument in De Veritate, q. 5, a. 2, c., and so I use that text to help interpret the Fifth Way. (I may have overstated the centrality of biology in specific to the Fifth Way, so I might concede to Feser there. However, beneficial adaptation is central to the Fifth Way on my interpretation and not Feser’s.)

My reading of the First Way is confirmed by the immediately following article of the Summa (q. 3, a. 1). There Aquinas gives three independent arguments that god is not a body. The first appeals to the First Way for the premise that god is an unmoved mover (or “immovable”; the Latin word is ambiguous, but the former reading makes the following argument a more perfect syllogism, and fits the logic of the First Way itself better.) It then adds an additional but simple empirical premise not contained in the First Way: “no body moves except insofar as it is moved by another, as is clear from induction.” Therefore god is not a body. This takes us one small step past the conclusion of the First Way. But Aquinas does not intend even here to show that God is a non-natural being. For in the third argument in the respondeo of q. 3, a. 1, Aquinas uses the Fourth Way to argue that god is not a body because the soul of a body is better than the body, and god is the best being. The conclusion that god is not a body thus leaves open the possibility that god might be the soul of a body. The latter possibility is only ruled out seven articles later (q. 3, a. 8, c.) where Aquinas notes that many pagans thought that god was the soul of the world or of one of the astronomical bodies, and then argues against that view. Thus demonstrating that god is not a body is not the same a demonstrating that he is not part of the natural world. To do that, one needs one of the stronger arguments for god’s existence, such as G2, the Third Way, the Fourth Way, the Fifth Way, or the De Ente argument.

Only here in q. 3, a. 1 does Aquinas draw the conclusion that god is pure act. He then appeals to this article again and again in q. 3 (not to the First Way or to q. 2, a. 3 as Feser states in his review) when arguing for further conclusions on the basis of god’s pure actuality. But to establish the conclusion here that god is pure act he uses as premise the fact that “it has been shown above that god is the first being”; he does not use as a premise the fact that God is immovable, as Feser stated in his review. Aquinas is appealing to the Fourth Way (or perhaps to the Five Ways as a collective whole), not to the First Way. In fact, Aquinas uses the First Way only once in his entire discussion of divine simplicity in question 3, and only as one of three arguments to show that god is not a body. The First Way does very little work in Aquinas’ discussion.

Feser also appeals to the second objection in q. 2, a. 3, where the objector argues that natural causes are sufficient and no god is needed. Certainly Aquinas thinks that the Five Ways taken collectively have rebutted naturalism. But Aquinas responds to the objection in two parts. First, in regards to non-conscious natural phenomena, Aquinas appeals only to the Fifth Way, not to the First. In regards to the conscious actions of humans (and perhaps animals) Aquinas appeals to the Third Way and First Way together (or perhaps just to the Third Way, depending on how one reads the text.) The First Way cannot do the job by itself. I argue in the book that the Third Way is doing in ST the job that G2 does in SCG, warranting the stronger conclusion that naturalism is false.

Feser also argues that “interpreting an argument charitably requires giving it a stronger rather than weaker reading if that is realistic. But the First Way would be a stronger argument for God’s existence if we read it as an abbreviation of the Summa contra Gentiles argument than if we read it Shields’ way.” But giving a stronger reading of an argument means interpreting it in such a way that it is valid rather than invalid, sound rather than unsound. It does not mean giving it a stronger conclusion if that conclusion is unwarranted by the premises and logical structure of the argument. That would be to interpret the First Way uncharitably, because it sets it up for ridicule by its opponents. I contend in the book that by giving it too strong of a conclusion, the First Way’s defenders have made it vulnerable to atheist attacks in ways that it wouldn’t be if it was read as I read it.

Despite our disagreement about the First Way in particular, Feser and I are in broad agreement philosophically. I am encouraged by his praise of my natural philosophical project, and am indebted to him for his engagement with my work.

Dominic Ryan on Nature and Nature’s God

Dominic Ryan has reviewed the first two chapters of my book Nature and Nature’s God for New Blackfriars. In regards to the first chapter, which is devoted to interpreting Aquinas’ principle “omne quod movetur ab alio movetur,” Ryan states that I put “forward two main arguments in support of [my] contention” that this should be translated as “everything in motion is put in motion by another.” Ryan, however, does not attend to the text I allot the most space to, namely that from Aquinas’ commentary on Physics VIII.4 (p. 27-30, 34). That text is crucial to the whole argument.

What Ryan has to say about the text I cited from SCG I, c. 13 unfortunately misses the point. There Aquinas says: “Omne quod movetur ab alio movetur. That some] things are in motion (moveri)-for example, the sun-is evident from sense. Therefore it is movetur by some other mover.” Now we must translate movetur/moveri in such a way as to form a valid syllogism. But the minor premise that appeals to sensation cannot be interpreted as saying “that some things are moved (passively) is evident from sense.” It does not appear to the senses that the sun is moved passively, although it does appear to the senses that the sun is in motion. (Aquinas thought it was absolutely in motion, we might say that it is only in relative motion.) We certainly do not see a chariot pulling the sun, nor an angel pushing it, nor do we see some other massive body pulling it by gravity. (Is gravity a force? Both Aquinas and General Relativity say that it is not, albeit in very different ways. But even if gravity is a force it is invisible to the senses.) So we should translate Aquinas’ argument as follows: “Everything in motion is moved by something else. That some things are in motion-for example, the sun-is evident from sense. Therefore it is moved by some other mover.”

Ryan asks “What would be apparent to the senses were such ‘motion’ [of the sun] to occur? Surely what one would sense was that the sun appeared constantly to be changing place. But if the sun or indeed any other celestial body was constantly changing place would it not have to be moved in order to do so? Motion, after all, is not an end in itself.” But Ryan is saying nothing I disagree with, and nothing that is problematic for my interpretation. I take no issue with the obvious interpretation of the conclusion of Aquinas’ argument from SCG I, c. 13. He is certainly concluding that the sun is being moved by another, and for the reason that Ryan states, namely that motion is not an end in itself (see p. 91-92 of my book, from chapter 3.) My contention concerns the interpretation of the minor premise and thus of the middle term of the syllogism: “that something is in motion-for example the sun-is evident to the senses.” Interpreting the minor premise this way then requires the translation of the major premise I have given: “everything in motion is moved by another.” Otherwise the syllogism is invalid; it would commit the fallacy of having four terms.

Ryan continues: “Further and more fundamentally, it is not clear that sense knowledge alone can solve this problem. . . . motion . . . is, like any common sensible, something about which the senses can be in error.” To settle the question, Ryan tells us, we must use intellectual knowledge. Of course I don’t disagree, but this is besides the point. No one would claim that Aquinas had any doubts that the sun was itself in motion, living as he did long before Copernicus. He accepted the evidence of his senses in the most straightforward way. No one will read Aquinas as asserting “that something is passively moved-for example, the sun-is evident from sense”? Not even Pegis translates the text this way. But having gone on to translate the mover principle as “everything that is moved is moved by another,” Pegis makes Aquinas commit the fallacy of a syllogism in four terms.

Ryan takes issue with my characterization of the form of a natural body as the generator’s instrument by which it moves the body even when it is no longer in contact with it. The most helpful contribution of his review is to point out something that Aquinas holds about instrumental causes. Aquinas holds that instrumental causes have a proper effect in virtue of their own form and an instrumental effect in virtue of the principal agent’s form. (Ryan points to ST III, q. 62, a. 1, ad 2, where Aquinas is discussing the instrumental causality of the Sacraments; the same point is made in parallel texts from other periods of Aquinas’ career.) But Ryan argues that if the form of the element is an instrument in moving the element to its proper place–as I claim–then it will have no proper activity of its own.

Ryan does not want to accept the explicit meaning of Aquinas’ text from De Pot., q. 3, a. 11, ad 5: “An instrument is understood to be moved by a principal agent as long as it retains the power (virtutem) impressed by the principal agent. For this reason an arrow is moved by the projector as long as the force of the impulse of the projector remains. In this way also that which is generated is moved by the generator in regard to heavy and light things as long as it retains the form given to it by the generator. Whence also semen is understood to be moved by the soul of the generator as long as the power (virtus) impressed by the soul remains there, although it be physically divided. It is necessary, however, for the mover and the moved to be together (simul) in regard to the beginning of motion, not, however, in regard to the whole motion, as appears in projectiles.”

The distinction Ryan points to between an instrument’s instrumental activity and its proper activity is brought forward by Aquinas in a discussion concerning instrumental efficient causality. But I argued in the book that the form of a heavy body is not the mover’s instrument as an efficient cause; the form is not a mover. Rather, it exercises instrumental formal causality, and so Aquinas’ point in the text Ryan cites need not apply. The proper effect of the form of the heavy body may be instrumental to the external efficient cause. Aquinas states that the form is not a mover, but that by which (quo) the body is moved. (De Ver., q. 22, a. 3, c.). He also states that “an instrument is compared to the action more as that by which (quo) it is performed than as that which performs it.” (De Ver., q. 27, a. 4, ad 8.)

Furthermore, motion towards the element’s natural place is not actually the most proper effect of the form; rather, the truly proper effect of the form is rest in the natural place. (As Ryan himself says, motion is not an end in itself.) The elemental body only undergoes motion towards its natural place because it is out of its natural place. The form is not responsible for the body being out of its proper place, and thus not fully responsible for its motion towards its proper place.

It is also worth pointing out that whether or not we use the word “instrument” to describe the internal form by which the external mover moves the patient is irrelevant, as long as we accurately understand the picture Aquinas is painting. Nothing Ryan has said casts any doubt on my claim that the mover need not be in contact with the body undergoing motion throughout the entirety of the motion, and that the mover principle should be translated as “everything in motion is put in motion by another.”

In regards to the second chapter where I discuss Aquinas’ case against infinite regresses, Ryan states: “Whether Aquinas had intended this denial [of infinite regresses] to pertain to a moved mover’s being moved or its being a mover is not clear. Shields, however, opts for being a mover and therefore renders the proof from motion a more restricted version of the second way (p. 47). One might question this though.” I do not understand what point Ryan is making in the first sentence, but the second sentence requires a clarification: I claim on p. 47 that the premise in the first way that an infinite regress of movers is impossible is a more restricted version of the premise in the second way that an infinite regress of efficient causes is impossible. I make no claims about whether or not the first way as a whole is a more restricted version of the second way as a whole.

Ryan objects to my claim that in essentially ordered series of causes the secondary causes fail to explain their effect. This is quite strange, as it is standard fare among Thomists. He says I must argue “either that (i) per se causes cannot be essentially ordered, or (ii) that if they can, that they fail to explain their effect.” I have no desire to argue for (i), nor does anything in my text suggest I do. The second is not controversial among Thomists, and I provide an argument in the book for non-Thomists. But since Ryan’s concern is with my interpretation of Aquinas, I will provide an example here from Thomistic physical theory: a child sheep is a per se effect of a parent sheep, but on Aquinas’ view the parent sheep fails to explain the child sheep. The sun is also necessary to explain the effect. But the sheep is also a per se effect of the sun, not an accidental effect. Furthermore, the sun and the parent sheep together fail to explain the child sheep, according to Aquinas. The angel that moves the sun is also necessary to explain the child sheep. But the child sheep is a per se effect of the angel, not an accidental effect. Finally, the angel is not sufficient to explain the effect. God is needed, and the child sheep is a per se effect of God. Thus we have an essentially ordered series of causes, each of which is a per se cause, and none of the secondary causes explain their effect, despite being per se causes.

I thank Ryan for taking the time to review my book.

Patterns in the History of Science: The Question of a Beginningless Universe

At the end of my book Nature and Nature’s God I point out that the history of science provides inductive confirmation of the philosophical truth that motion cannot continue in any meaningful sense on its own without beginning and end. I point to the repeated process in which new developments in sense were taken by some to provide support for beginningless and endless motion, only for further developments in science to clarify that this was impossible. There are many pairs of developments in which this is exemplified. In the book I discuss inertia and the subsequent analysis of collisions as less than perfectly elastic; the conservation of energy and the discovery of the second law of thermodynamics; statistical mechanics and the radiation of energy as photons that then undergo cosmological redshift. Big bang cosmology is another episode, but I did not note in the book another aspect of its development that repeats this pattern.

Einstein was initially excited that general relativity would show that the universe exists in a steady state, without beginning or end. But in his debates with De Sitter it soon became clear that general relativity won’t allow for a beginningless and endless universe. At best the universe can be in an extremely unstable equilibrium; even quantum fluctuations will push it out of equilibrium, and a gravitational runaway effect will cause the universe to eventually collapse or expand without end, diluting its contents into effectively nothing. The fact that GR requires a universe with a beginning is helpful to note. I skipped over this and went right to inflationary cosmology and the BVG theorem.

It is very illuminating to study the history of science and to note this pattern. Those who hope to get a beginningless universe (without divine sustaining action) out of the developments of science have been continually disappointed. They are chasing after a pie in the sky: a perpetual motion machine.

Forthcoming Paper on Formal Causality and Properties

My paper “Formal and Proper: Substantial Form and Essential Accidents in Thomas Aquinas” has been accepted by the American Catholic Philosophical Quarterly. I take the same position about formal causality and essential accidents/properties as David Oderberg does. He does not make a historical case for the position, but I show that our shared view was also that of St. Thomas Aquinas. The abstract is below. If you would like a copy, please email me.

Abstract: Aquinas, following Aristotle, distinguishes between substances and their accidents, that is, between things and their attributes. He also distinguishes between proper accidents (also known as properties in Scholastic terminology) and accidental accidents, that is, between accidents that belong to a substance in virtue of what it is, and accidents that belong to it due to extrinsic factors. Aquinas says that a thing’s proper accidents are caused by the thing’s own principles. John Wippel interprets Aquinas as holding that a substance efficiently causes its own proper accidents. I argue that Aquinas is more plausibly read as holding that a substance formally causes its own proper accidents. Formal causality extends to more than just the informing of matter. Formal causality is a principle of determination: being a certain substance involves the determination of having certain proper accidents.

Two Reviews of Nature and Nature’s God

Two reviews of my book, Nature and Nature’s God, recently appeared, one by Gaven Kerr and the other by Glenn B. Siniscalchi. Siniscalchi (writing in the Journal of Theological Studies) appreciates my approach of bringing Thomistic philosophy together with modern science:

Shields’s nuanced interpretations of Aquinas’s first proof is a bold step forward in contemporary Thomistic studies. It strengthens the reasonableness of classical theistic approaches to the God question. Although Aquinas and the scholastic theologians have been accused of presupposing a dubious scientific view of the world, Shields subtly argues that modern scientific paradigms can enhance the soundness of the medieval proofs. Nature and Nature’s God is highly recommended for graduates students, fundamental theologians, and philosophers with a comprehensive background in Thomistic philosophy and modern physics.

I am grateful for Siniscalchi’s kind words.

I am also grateful for Gaven Kerr’s review in the Heythrop Journal and his kind words about my work. He says that my “book is a worthy addition to the library of any individual who takes the thought of St Thomas Aquinas seriously or who seeks to think seriously about the existence of God.” I am encouraged that Kerr agrees with my claim that essentially ordered causal series need not be simultaneous. He does put forward two criticisms of my claim that the First Way is a natural philosophical proof, rather than a metaphysical one. I wish to respond to these here in a spirit of friendly debate.

Kerr’s first criticism is that I did not address the texts in which, as he and others such as Knasas claim, Aquinas restricts demonstrations of God’s existence to the science of metaphysics. That is not completely true, but I only addressed them briefly in one footnote in the introduction. Here is what I say in footnote 17 on p. 5-6, with the most telling texts now bolded:

This understanding [that the motion proof is natural philosophical, preceding and paving the way for metaphysics] is shared by Fr. Benedict Ashley, O.P., The Way toward Wisdom: An Interdisciplinary and Intercultural Introduction to Metaphysics (Notre Dame: University of Notre Dame Press, 2006). Mark Johnson also shares a similar understanding: “Immateriality and the Domain of Thomistic Natural Philosophy,” The Modern Schoolman 67, no. 4 (1990): 285–304. The primary opponent of the natural philosophical reading of Aquinas’ motion proofs is John F. X. Knasas; see Thomistic Existentialism and Cosmological Reasoning (Washington, DC: The Catholic University of America Press, 2019), ch. 6. Knasas consistently fails to provide a plausible reading of a key text put forward by Johnson (In De Trin., q. 5, a. 2, obj. 3 & ad 3.) The celestial spheres fall squarely within the consideration of natural philosophy, not at its boundary as non-natural principles of natural motion, as Knasas would have it. Moreover, since Physics VIII explicitly proves the existence of a “wholly incorporeal” being and ends with God (In VIII Phys., l. 21, n. 1141 & l. 23, n. 1172), Knasas is forced to read Physics VIII, implausibly, as belonging for Aquinas to the science of metaphysics. Aquinas himself, however, explicitly includes it within natural philosophy (see, e.g., In III Phys., l. 1, n. 275, In VII Phys., l. 1, n. 884; In I Phys., l. 1, n. 1–4; l. 2, n. 12.) Knasas’ own favored texts—which do clearly assign the understanding of immaterial beings to the science of metaphysics—do not count against the natural philosophy reading of Aquinas’ motion proofs. Natural philosophy can only just reach the existence of at least one immaterial being, and it can know very little about it. A true understanding and developed science of God and angels belongs exclusively to metaphysics, and goes far beyond anything found even in Aristotle’s Metaphysics, as Aquinas indicates in In III De An., l. 12, n. 785 (cited by Knasas, Thomistic Existentialism, 182–83.) In speaking of such a science, Aquinas seems to have in mind something like what is found in Proclus’ Elements of Theology, or the Book of Causes. Furthermore, as I explain in this book, metaphysics has its own, alternative demonstrations for God’s existence, and these have a more robust conclusion than the motion proofs, but are correspondingly less accessible and manifest. Examples are the Fourth Way in ST and the proof from the De Ente, which I favor highly.

Given the importance of this issue, perhaps it would have been better to devote a section in the body of the text to developing these points. I will try to make the case briefly here. The central text of Aristotelian natural philosophy is Aristotle’s Physics. Book VIII of the Physics is devoted to a proof of the existence of a first, unmoved mover. At the very end of his commentary on Physics VIII Aquinas writes (my translation):

And so it is manifest that the first mover is indivisible and that it has no parts, as a point is indivisible, and also that it is entirely without magnitude, as if existing outside the genus of magnitudes. And thus the Philosopher terminates the common consideration of natural things in the first principle of the entire natural world, who is God over all, blessed forever. Amen. (In VIII Phys., l. 23, n. 1172 [9])

Thus we see that natural philosophy does contain a proof for God’s existence, and that it is not only the science of metaphysics that demonstrates God’s existence.

What then do we make of those texts which Kerr refers to, which seem to reserve the science about God to metaphysics? The answer is clear from Aquinas In De Trin., q. 5, a. 2, obj. 3 & ad 3:

Objection 3: The first mover is treated of in natural science [natural philosophy], as is clear in Physics VIII. But he is free of all matter. Therefore natural science [natural philosophy] is not only about those things which exist in matter.

Response to objection 3: The first mover is not treated of in natural science as the subject [of the science] or as part of the subject, but as the terminus at which natural science arrives. The terminus, however, is not of the [same] nature [as] the thing whose terminus it is, but rather has some relationship to that thing, as the terminus of a line is not a line but has some relationship to it. Just so the first mover also is of another nature than natural things, but nevertheless has some relationship to them insofar as it pours motion into them. And in this way it falls under the consideration of the natural [philosopher], not, namely, in itself but insofar as it is mover.

There is a difference between a science considering something as the object of its study, and a science considering something tangentially, that is, considering it as having an important effect on the object of study. For human reason to make God an object of study, without the aid of divine revelation, i.e., for reason to develop a science of the divine, it must use the full resources of human reason; it must undertake the study of metaphysics. Thus the science of the divine is part of metaphysics. But that does not preclude natural philosophy, whose object of study is not God but the natural world, from proving the existence of God as the source of the natural world. But natural philosophy can say very little about God. To say much, metaphysics is needed.

Kerr’s second criticism is in response to my claim that the First Way would not be called “the more manifest way” by Aquinas if it was a metaphysical argument based on the act of existence. He says that the same point could be made about the argument as I present it: my book is 328 pages long, and I have to say quite a lot to explicate and defend my understanding of the proof. “More manifest” only means that the proof’s point of departure, motion, is something readily accessible to everyone.

But this is to conflate the simplicity of an argument with the simplicity–or lack thereof–of the objections against it and the replies to those objections. I can explain the natural philosophical argument in short order, in readily accessible terms. Anyone can grasp it. But there is a long history of mistaken interpretations and sophisticated objections to this simple argument, and the length of the book is due to the necessity of responding to and untangling these. By contrast, the metaphysical distinction of essence and existence, as well as the necessity for an efficient cause of the act of existence of things, upon which Kerr bases his interpretation of Aquinas’ First Way, are difficult concepts and require subtle insight. Thus it is the argument itself, as opposed to just the objections and responses, that is less manifest on his interpretation.

Kerr has made many important contributions to philosophy through his analysis of the proof for God’s existence in Aquinas’ De Ente et Essentia, based on the real distinction between essence and existence, as well as his analyses of infinite regress. The view that Aquinas has other unrelated arguments for God’s existence does not detract from the value of that work. Once again, I am grateful for his kind words about my book, including his helpful criticisms.

Estep on Nature and Nature’s God

In his summary of my book Nature and Nature’s God for the Review of Metaphysics, Caleb Estep writes that I hold that in infinite time all possibilities will be realized. This is not quite what I claim. As I explain in the book, what I hold is that all possibilities that approach arbitrarily close to 1 over time will be realized. In infinite time even something with a small probability of occurring, in any given finite duration, may become nearly certain to occur. This will be the case unless the probability of its occurring diminishes continually such that the sum-total of its probability over infinite time (technically the integral of its probability density from t=zero to t=infinity) is still significantly less than one.

For example, if there is a 1/2 probability of getting heads on a first coin flip, then there is only a 1/4 chance of not getting heads at all on two flips. After three flips there is only a 1/8 chance of not getting heads at all, and so on. However, in some cases the odds decrease so rapidly that there is very little chance of ever getting the desired result. For example, if there is a 1/100 chance of getting result X on the first go, and then a 1/10,000 chance of getting it on the next go, and then a 1/1,000,000 chance of getting it on the third go, and so on, then the odds are against ever getting the result.

Further Thoughts on Act and Potency

We would colloquially say about a composite substance that it is “actually water, not potentially water,” yet it contains within itself both the act of water (the substantial form) and the potency for water (prime matter). The prime matter has not lost the potency for being water by having the form, just as I have not lost the power/potency (potentia) to see when I am actually seeing. When I am not asleep I both potentially see and actually see. When I am asleep I only potentially see.

In book 1 of the Physics, (see chapters 7-9, especially 9) Aristotle is at pains to distinguish matter’s being per se a potential principle from its having per accidens the privation of the form. The matter loses its privation of water-form when it changes into water, but it does not lose its potency to be water. Objective potency always involves a privation, involves not being in some condition. In some cases it is merely a privation, as in the objective potency of the universe to exist “before” God makes it out of nothing. In most cases it is a underlying principle together with a privation.

Aquinas’ statement in the First Way that a thing can’t both be in potency and act at the same time and in the same respect concerns objective potency. Aristotle’s definition of motion (the act of the potential insofar as it is potential) has reference to what Aristotle calls “imperfect potency” as opposed to “perfect potency” (Physics III.2; the distinction is elucidated in the Metaphysics and De Anima). The imperfect potency involved in motion implies privation; that is why it is called imperfect. The power of sight is an example of perfect potency. Hence the context of motion explains Aquinas’ statement. The potency to undergo a change is always an objective potency, because a thing can’t undergo a change to a condition once it is in that condition. But it must retain the subjective potency to be in that condition once it has changed to that condition, otherwise it could not be in that condition. The potency required for motion is a potency joined to a privation.

Prime matter is a subjective potency for substantial forms, and it retains the potency for a certain form when it possesses that form, for it is such a potency essentially, and not accidentally. So too essence is a subjective potency for the act of existence; it retains the potency for that existence when it exists. In Thomism there is a real composition of potency and act.

Feser on Potency and Act

In his reply to Graham Oppy’s criticisms of Thomistic cosmological arguments, Ed Feser denies that creatures exist both actually and potentially at the same time. (“Oppy on Thomistic Cosmological Arguments,” Religious Studies 57 [2021], 503–522, at 509.) He states that the constituents of an object such as a cup of water are potentially a cup of water in the abstract, but in the concrete they are only actually a cup of water. The constituents in question, protons, neutrons, and electrons, are, considered in themselves, potentially a cup of water, but as possessing the form of water they are actually a cup of water and no longer potentially a cup of water.

This doesn’t seem right to me. The real distinction of essence and existence makes Aquinas’ position clear. Without existence an essence is precisely nothing, not any kind of potency at all. But in an actually existing finite being the essence is really distinct from its existence, and is related to its existence as potency to act, as Aquinas argues in De Ente et Essentia. Now the essence is in potency to existence, and not in potency to anything else at all. It is in potency to only one kind of substantial existence, and it is not in potency to non-existence. So either the essence has no potency at all, or it bears the potency to exist when it is actually existing through its composition with the act of existence. In other words, essence is what later scholastics called a subjective potency (the kind of potency that is composed with its act and thus coexists with it) rather than an objective potency (the kind of potency that is opposed to act and ceases to be when its act arrives.) Note that “subjective” does not here mean “relative to someone’s perception” but rather “subject, that is, receiver of act.” “Objective” does not mean “real,” but something like “the objective of a productive activity.”

The same must be true of the relationship between prime matter and substantial form. Certainly the case is less clear here: one could be tempted to think that prime matter, as a principle of potency, was only a potency to receive other substantial forms. But this is not the case. Prime matter’s potency does not undergo any change (see Aristotle, Physics I.9, 192a26–29); it is always a potency for all substantial forms. So when it is actualized by the substantial form of water, it retains the subjective potency to the substantial form of water, as well as potencies for all other substantial forms. Water is a composite of potency and act.

On the Word “Art”

In teaching Aristotle and Thomas one often encounters the word “art.” This is generally translating techne in Greek or ars in Latin. I always remark to students that this word is being used more broadly than the way in which the English word “art” is commonly used. It does not just mean the fine arts such as painting, sculpture, music, or poetry, although it does include the latter. The word “art” as used by Thomas and Aristotle should be taken in connection with the English words “artificial,” “artifact,” and “artisan.”

While I think this is true, I’ve realized lately that more must be said; in a way, but only in a way, the word techne is opposed to the word “art” used in reference to the fine arts. For techne or ars means a know-how, a knowledge of how to produce or do something, and it characteristically gives a person the ability to produce or do this thing over and over again. The carpenter, through the art of carpentry, can make many tables with the same characteristics.

But although know-how is certainly present and active in the case of the fine arts, what characterizes them is a kind of moment of genius that is not reproducible or entirely under the control of the artist. Depending on the level of genius, an artist may be able to make many masterpieces, or just one in a lifetime. But in neither case is there a formula or process that can be followed to automatically guarantee the production of a new masterpiece.

What word do the Greeks have for this? One’s first thought is poiesis, the root word for the English word “poetry,” but this can’t be right. Aristotle uses poiein as one of his ten categories, and gives as examples “to lance” and “to cauterize,” definitely not specifically poetic productions. Poiein in philosophical Greek just means “to make or do.” The word one is looking for is mousike, an art in the sense of something metaphorically inspired by the muses. This is what we call “fine art” in English, something that may make use of techne/technique, but which is a non-reproducible product of genius.