Matter, Mathematics, and the Laws of Nature
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Andrew Younan. Matter and Mathematics: An Essentialist Account of Laws of Nature. Foreward by Michael J. Dodds, O.P. Washington, DC: The Catholic University of America Press, 2022. 228pp., hardback; $75.00.
Among the many contributors to the revival of the Aristotelian philosophy of nature in recent decades one must include the work of William Wallace, O.P., Benedict Ashley, O.P., Nancy Cartwright, Robert Koons, William Simpson, Edward Feser, and many others. We can now include Fr. Andrew Younan’s title, Matter and Mathematics. Younan’s work is a refreshing, briskly argued addition to recent debates about the nature of the laws of nature that avoids pointless detours into their details without eschewing their necessary substance.
After an initial division into two parts, the argument is structured by cascades of triads. The first part clears the way by facing various challenges raised by Descartes and Hume to “a broader Aristotelian-Thomistic natural philosophy” (Chapters 1 and 2, respectively), as well as apparent difficulties presented by contemporary science (Chapter 3). The second part defends Younan’s account by treating of mathematical abstraction (Chapter 4) and the nature of necessity in Aristotelian natural philosophy (Chapter 5), which each inform his essentialist definition of the laws of nature (Chapter 6). The book includes a fascinating appendix, “Laws and the Lawgiver,” which would have been better placed as a revised, concluding Chapter 7.
Summary of the Argument
The first chapter compares “the natural science of René Descartes and the developed Aristotelian natural philosophy of St. Thomas Aquinas” and argues that they “need not be seen as antithetical and that the mathematical physics championed by Descartes, despite his own understanding (and despite some modern representatives of Aquinas), can arise out of a broader Aristotelian-Thomistic natural philosophy without contradiction” (25, 26). This is attempted by presenting more nuanced, revised readings of the standard interpretations of these schools on three points: first, their accounts of how we know nature (clear and distinct innate ideas versus abstraction from matter), second, their accounts of bodies and extension, and, third, their accounts of causes in nature (laws and occasionalism versus substances with forms).
The second chapter rebuts Hume’s attack on induction and causality. First, the chapter reviews the Humean case against induction, especially insofar as this informs contemporary Humean accounts of the laws of nature. Second, it presents a threefold refutation of Hume. Third, Younan sketches the Aristotelian alternative account of induction and causality. The criticisms of Hume hit hardest: Younan shows that Hume uncritically accepts deduction as a mode of reasoning (while consistency would demand otherwise), that he ill-advisedly takes imagination as the measure of ontological possibility, and that he approaches the entire issue backwards:
It appears that Hume has reversed the explanandum and the explanans in his argument against causality and induction. The uniformity of nature is an observed fact that is blindingly undeniable and, once seen through the lens of chance, unbelievably unlikely. We can give it many different names—“symmetry” being the most popular among scientists. But this uniformity is the thing that needs to be explained; induction to natural kinds and causality are the attempted explanations. Hume has reversed this by asking how induction and causality are to be explained. To me, this reversal appears to be his central mistake. (61)
The concluding treatment of Aristotelian induction and causality contain a helpful use of the notion of “species neutral universals” and an insightful interpretation of the “battle rout” in Posterior Analytics II.19, on which more below.
In the third chapter, Younan presents an act-potency gloss of the mysteries of quantum mechanics, arguing that “the Aristotelian doctrine of potentiality is one fitting solution to the problem of wave-particle duality” (76). He argues, first, that “subatomic particles exist in a mode of extremely high potentiality and … low actuality,” second, that this helps to “make sense of wave functions as mathematical expressions of potentiality,” and, third, that the “wave function ‘collapse’” in a measurement is an increase in the actuality of the particle.” Making good use of Heisenberg’s observation that the quantum theory reintroduces potentia into scientific discourse, Younan constructs a dialectical “squeeze theorem” of sorts, arguing that the logical place on the scala natura for quantum phenomena is that such particles are “proto-substances,” thus “bridging the gap between Aristotle’s prime matter and the most basic elements” (82–83). Thus, one should interpret “the ‘wave state’ as the ‘potency state’ and the ‘particle state’ as the ‘actualized state’” (89). It is “because the potency-wave is not a complete substance but rather a ‘proto-substance’ with very low actuality, [that] it does not have determinate accidents such as position and momentum” (91). Taking his cue from Richard Hassing’s observation that “of the various senses of the potentially being and its actualization in Aristotle, none fits quantum processes exactly,” (94) Younan proposes that the act of measurement “presents a striking parallel to Aristotle’s notion of the actualization of sensible forms by the act of perception, although it goes further and reveals a similar pattern in the ontological realm” (98). Despite his disagreements with Wolfgang Smith in the footnotes (26n16, 45n91,77 and n7, 89n93), Younan’s proposal parallels Smith’s solution that the act of measurement as “the actualization of a certain potency” (see Wallace, “Thomism and the Quantum Enigma,” 459–60). Indeed, most Aristotelian-Thomistic proposals seem to have some variation of this solution. However, to my knowledge, the precise analogy of the wave function collapse to the actualization of a potentially sensible object is unique to Younan.
The constructive part of the project begins with Chapter 4, a fascinating, close reading of key chapters in Metaphysics, XIII–XIV. This engagement with Platonism places Younan’s view, following Aristotle, between two extremes.
Indeed, underlying [Aristotle’s] explanation of how the Platonist may have formed his impression [that Forms can be causes], we discover Aristotle’s own understanding of what we today might call the mathematical structure of nature, which is neither Platonist nor Nominalist but gathers the strengths of both alternate accounts. The Aristotelian account of mathematics will also have obvious implications for the ontology of the laws of nature. (103)
The chapter first examines Metaphysics, XIII.3, concerning the ontological status of mathematicals, before continuing to consider Aristotle’s rejection of mathematicals as causes in Metaphysics, XIV.5 and, lastly, his qualified acceptance of mathematical forms in Metaphysics, XIV.6. Younan argues that Aristotle takes mathematical forms to “describe true order, symmetry, and definiteness that are realities in nature” (121). Thus, “what this suggests for our understanding of mathematical physics, as well as the philosophy of mathematics, is that the mathematical realities studied in both are neither independent Platonic Forms nor simply Nominalist patterns existing only in the mind. Rather, they are mental abstractions of the symmetries that are truly there in nature” (122).
Yet if these mathematicals are somehow present in nature, how are they causally relevant to the natural philosopher? How would this comport with the “cause of causes,” the final cause? Chapter 5 addresses itself to such topics. Younan first considers the different senses of contingency and necessity in Aristotle, then considers the argument for teleology and how necessity is related to teleology (in Physics II.9), and, lastly, proposes how matter is a source of both necessity and potentiality, and how the mind’s abstraction affects our conception of both. The first part helpful focuses upon the central meaning of necessity in Aristotle, from Metaphysics, Book V, the central meaning of “that which cannot be otherwise.” This informs Younan’s exposition of Physics, II.9, arguing that we ought to call “absolute or simple necessity a modality of matter and hypothetical necessity a modality of teleology” (134). This dyad of necessity is crucial to opposing both a Cartesian or Humean conception of nature as well as Platonic or Humean interpretations of its laws. Younan’s proposal that “the principles of mathematics represent the very boundary conditions for the simple necessity of matter itself” (141–42) keenly articulates the crucial intervention of the Aristotelian approach in the debate.
Having established the existence and nature of what appears to be a necessity in natural things amenable to mathematical expression, Younan turns to his account of the laws of nature in Chapter 6. How can we account for the “unreasonable effectiveness” of mathematics, as Wigner asked? How might one “avoid the Quinean view that all knowledge is nothing more than a ‘web of belief,’ with some beliefs more central to the web than others but all contingent,” while also accounting for “the ‘obviousness’ of logic and mathematics” and that “mathematics is less necessary than logic” (146–45)? Younan takes up the challenge from Marc Lange that essentialists need to explain how some laws are apparently more necessary than others—that there are “strata” of necessity: for instance, conservation laws are more fundamental than dynamical laws. In this chapter, Younan first discusses how absolute necessity is a constraint arising in nature, second, explains how the degrees of abstraction articulate related and ordered conceptions of natural and mathematical necessities, and, lastly, he proposes his definition of the laws of nature.
As for the first, and in contrast to a view such as Brian Ellis (who makes laws too close to essential properties), Younan follows another cue from Richard Hassing, an idea borrowed originally from Fr. Wallace, that modern science analyses natural things by “species-neutral universals” (152–53 and n31). Thus, for example, “mass” or “energy” are abstract universal kinds present univocally across specifically different substances (cats, dogs, human, etc.):
Thus, contrary to Ellis, whatever the laws of nature are, we should not be surprised if they have less to do with essential properties strictly speaking and more to do with quantifiable accidental properties following from matter considered generically. Whether and how accidental properties might be related to essential properties is an entirely different topic requiring its own account, but it is not a question mathematical science can directly address. (153)
The laws of nature, then, subsist in the non-substantial and yet rich realms of the accidents of natural things, especially their relations, actions, undergoings, and motions. Both formal and efficient causality are relevant in this realm if one wishes to transpose the physico-mathematical secular talk of the sciences into an Aristotelian sectarian idiom (153–54).
To further this account, and second, Younan presents a lithe summary of the degrees of abstraction to explain how different strata of necessity arise from nature conceived at different levels of abstraction: “Mathematics is more necessary because it is more abstracted from the contingency of matter” (161). Such higher-order mathematical abstractions can be applied “to lower ones and to concrete beings” (165), thus allowing one to “formulate” the laws of nature (a technical usage that Younan borrows from Pierre Duhem and likens—too briefly and unclearly in my view—to Fr. Wallace’s notion of “modeling”). That is,
What it means to “formulate” nature in this sense, then, is that higher level mathematical or geometrical abstractions are applied in various combinations to understand less abstract, or entirely concrete, realities. Through these combinations we understand abstractly a great deal about the particular objects we observe in the world, although not everything . . . . But the surprising thing about the scientific revolution is just how much we can understand in this way, especially using the powerful tools of analytic geometry and calculus, the brainchildren of Descartes and Newton, respectively. But if mathematics is known through abstraction and not a priori, this simply means that there is a deeply mathematical consistency already there in nature for us to discover. (167)
Younan is now ready to propose his definition. Noting that, historically, the laws of nature were born in the lap of mathematical physics and, epistemically, these express relationships of mathematical-functional equality and makes them generically relations, he defines
a law of nature plainly as a relation of mathematical abstractions describing material things or their motion. This definition can apply to aspects of their formal structure or material reality, such as some conservation laws, or to aspects of their capacities for causing and suffering change, such as dynamical force laws. (168)
Thus, excluded from the definition are mere universal descriptions (168), but not necessarily biological laws (170). The definition itself helpfully takes mathematical laws of nature as a central case, and its use of “abstractions” which “describe” material things or their motions are defended as steering between Platonism and Humeanism and espousing a realistic appraisal of the task of scientific inquiry (169–70). Younan concludes, taking a cue from Aquinas, that law-talk “is a metaphor that can be helpful in understanding the workings of nature, as long as it is understood as a metaphor” (172). His account claims certain “payoff’s”—“(1) the avoidance of “governance” language; (2) the avoidance of a need to assert a priori knowledge; and (3) the assertion that individual things, rather than laws or events, are the fundamental primitives in nature” (174ff)—and suggests certain implications in the philosophy of science, mathematics, and natural theology.
Some Critical Considerations
On the one hand, an overarching strength of the book, especially for an audience sufficiently familiar with the background debates, is Younan’s efficient mode of argument. (Footnotes would help guide newcomers to further resources.) He consistently focuses on the main points at issue in the debate about the nature of the laws of nature, and not the myriads upon myriads of counterpoints. He is also right to return to the original sources of the debate about the laws of nature as found in the paradigmatic thinkers who have defined it.
More particular strengths of the book are its the rebuttal of Hume, the exploration of Aristotle’s qualified acceptance of mathematicals as causes of beauty, goodness, and order in nature in Chapter 4, and how both Chapter 4 and 5 set the stage for seeing the origin of mathematical structure in nature. While it is nice to have more ammunition against Humean fortifications, it is better to have an articulated answer to Wigner’s question about the unreasonable effectiveness of mathematics in the study of nature based upon the central Aristotelian-Thomistic principle of the mind’s abstraction of form from material things in nature.
On the other hand, and first, I found the chapter on Descartes underwhelming. Younan sets out “to show that [the natural philosophies of Descartes and of Aristotle/Aquinas] are not as contradictory as often assumed,” and that “this will take somewhat more than nuance” (26). However, on the first point of contrast (between Descartes’s doctrine of clear and distinct, innate ideas which are fundamental for understanding nature mathematically, on the one hand, and the Aristotelian-Scholastic doctrine of abstraction from matter, on the other hand), he admits that “here we run into a point of total contradiction in which nuance will not come to our aid” (33). The second point of contention between the two (Descartes’s doctrine of body as mere extension versus the Scholastic idea of body as substance with form) likewise results not in a more nuanced reading of Descartes’s position, but rather in the conclusion that Descartes’s arguments for his own view of body are insufficient, that he “fails to produce an argument for the elimination of forms that meets his standards of certainty” (39). This leaves the Scholastic position as the better view which can both incorporate body possessing extension (and thus subject to the methods of mathematical physics) as well as other characteristics. I also find Younan’s use of Schamltz and Hassing convincing on the third point (42–43, that Descartes’s laws of nature and occasionalism are unsustainable). However, this means that there is not so much a reconciliation or compatibility between the two schools of thought, found by some nuanced reading. Rather, the three stages of analysis shows that Descartes’s project fails as a complete proposal in natural philosophy and that its remaining sound points are recoverable by the Aristotelian-Thomistic position.
Second, the use and articulation of an Aristotelian natural philosophical method in the book has a few rough edges and moments of incompleteness. Some of these are minor details: mathematical abstraction retains “intelligible” and not “common” matter in the scholastic technical jargon (31); Jacques Maritain does not teach that natural philosophy provides quia demonstrations only, contrary to what is claimed on 155n35 (see Maritain, Degrees of Knowledge, ch. 2, n. 13, 40–41ff, where “physics” or the philosophy of nature is called a “science of explanation” alongside other knowledges that argue propter quid). Others are less minor.
Younan rightly locates the central image of Aristotelian method as following the “natural way” in our knowledge (also translated as “natural path” or “road”; see Physics, I.1). Younan describes this path correctly, albeit incompletely (see 31 and 63), as proceeding from sense knowledge, what is as better known to us, to knowledge of universals, which are better known by nature. While this is one aspect of the natural path—see Posterior Analytics, II.19—the other and more important aspect of the natural path is that we proceed from more universal conceptions of things to less universal and more specific concepts, as indicated in Physics, I.1 (and see Aquinas’s commentary, nn. 7–8, and cf. ST, Ia, q. 85, a. 3). That is, we proceed both from sense knowledge to intellectual knowledge as well as, within intellectual knowledge, from a vague and generic account of things to a distinct and specific account.
Now, whether or not natural philosophy and the particular natural sciences are different in kind, they are located along different stages of the natural path in our knowledge. At a certain point, our inquiries must begin building artificial roads (using experiments, systems of symbolic representations, and other tools) so as to uncover nature’s causes. To borrow from Younan’s insightful reading of the operative metaphor in Posterior Analytics, II.19: “Science as we know it is obviously not so easy— otherwise, why would Aristotle immediately use the image of the ‘rout in battle,’ which implies that there is something chaotic, even warlike, about reality, and that finding unity in such chaos is like winning a war?” (65)
What was one of these major battles? As Younan describes, it was the invention and application of a new method of describing nature, viz., through algebraic quantities and the infinitesimal calculus, and a new sort of universal: the common features and behaviors of natural things that cuts across natural kinds, species-neutral universality. Another aspect of this battle was the constructions of modern mathematics (see 162–164).
However, the insights of modern mathematics that uncover the real or imaginary number domains are better described as the extension of certain operations or functions—“abstractions” only analogously at best. These involve entia rationis as well as straightforward abstractions (see Maurer’s treatment). Furthermore, the “mathematical abstractions” in the proposed definition of the laws of nature are themselves conceptual unities and not straightforward abstractions. Younan gives Newton’s Second Law as his example of a law of nature: F = ma. Consider one of these terms, “force.” ‘F’ is at the very least a concept made from abstractions in the natural order conjoined to abstractions from the mathematical order. Indeed, the Newton as a unit defined in terms of physically measurable things (kg•m/s•s) is such a conjunct. The unity that characterizes the object of the mathematical-physical sciences is a unity sealed by the mind in close dependence upon reality and prior abstractions from material things.
The medievals located such objects of knowledge in the subalternated sciences; discussion of the logic of subalternated science, however, is at best virtually present in Younan’s argument. Indeed, “it is only by seeing these sciences precisely as intermediary sciences, that is, as combinations of two different levels of intelligibility which arise out of two distinct kinds of abstraction, that we can understand their true nature” (Mullahy, “Subalternation and Mathematical Physics,” 106). Because the laws of nature are found to be relations among natural things by the “net” of physical abstractions subalternated to mathematical ones are we able to formulate such laws. Here, I would recall Younan’s definition of a formulation—where “higher level mathematical or geometrical abstractions are applied in various combinations to understand less abstract, or entirely concrete, realities” (167). It seems to me, then, that a more adequate definition of a law of nature, on Younan’s approach, would be “a relation of mathematical abstractions which formulates material things and their motion.” It is in these formulations that we locate the ever-progressing limits of science’s foray into what is better known in itself, and where we hope to find not merely that things are so in the cosmos but why.
The “Mathematics” of the Fifth Way
To conclude this review, I wish to reflect upon and extend the centerpiece of the book’s argument, the way in which matter bears within itself a necessity that is intelligible through mathematization. This is developed in the fifth chapter.
At the very least, we can say that there are (at least) two distinct senses of matter: one from which necessity follows and another from which contingency follows. But this is simply a restatement of the problem: how can one principle bring about both necessity and contingency? One step toward a solution could be to clarify the distinction between simple and hypothetical necessity, or at least one sense of them. In Physics II.9, matter is described as necessary in the sense that it, unlike form, is nonteleological. Form, which is associated with teleology but also with intelligibility, is necessary in the sense that it is noncontingent—that is, something is more intelligible the more unchanging it is, and therefore the more immaterial it is, since potentiality is a principle of change insofar as a thing is other than itself. These are different distinctions. In the order of intelligibility, which is founded on immutability, form takes the role of necessity and matter takes that of contingency. In the order of intentionality, which is founded on purpose, form takes the role of teleology and matter takes that of necessity—that is, limitation of possibilities. (138)
Younan then develops this Aristotelian-Thomistic line of argument by appeal to the distinction between particular matter, common matter, and intelligible matter. Properly speaking, this distinction between “matters” is a difference in how form is abstracted from matter. Younan writes: “Particular matter in the order of intelligibility is contingent and ever-changing—as opposed to form, which is permanent, knowable, and necessary—but common and intelligible matter in the order of intentionality provides simple necessity—as opposed to form, which provides hypothetical necessity” (141). However, form does not merely provide hypothetical necessity—indeed, it is only matters of certain kinds or under certain forms that are principles of simple necessity. Indeed, it is by synecdoche that we speak of the intelligibility of matter, for its intelligibility is due to form.
So, on the one hand, this leads one to understand the following true conclusion in a different light, namely, that “One might go further and say that the principles of mathematics represent the very boundary conditions for the simple necessity of [formed] matter itself” (141–42). On the other hand, it is not quite true that “the assertion that physical substances act in certain ways under these boundary conditions that we term ‘necessary’ requires no further ontological explanation” (142), and this is because of the priority of the final cause, causa causarum. Now, that these mathematical structures in nature are boundary conditions is not under dispute; rather, they are not for all that aboriginal ground that calls for no further ontological explanation. This is because such matter is teleologically shaped—in the words of Charles De Koninck, “matter is a desire for form, not a desire in the order of exercise, but a desire that is matter itself.” (The Cosmos, 263)
This requires some elaboration. Younan makes good use of the lines of Heisenberg, now familiar to many Aristotelians and Thomists, that “It is no longer the actual happening itself but rather the possibility of its happening—the potentia, to employ a concept from Aristotle’s philosophy—that is subject to strict natural laws” (78). As Younan points out (83–84 and nn25–29), a number of Aristotelians and Thomists have developed this connection between potentiality and act and energy in modern physics (see in particular the work of Thomas McLaughlin here and here). Fr. William Wallace was also one to appeal to this connection made by Heisenberg, doing so in “Elementarity and Reality in Particle Physics.” That paper includes an indirect response by Heisenberg himself (in a letter to physicist Edwin Gora). Heisenberg writes that he “[finds] it extremely instructive to look at these formulations [of Plato or Aristotle], but one should not combine this with an attempt to prove that the philosopher is still right in our times (such a claim would do injustice to the original intent of the philosophers)” (ibid., 259). Gora himself had written (ibid.) that “the Aristotelian concept of ‘[prime matter]’ appears to reflect typically macroscopic modes of thought. A corresponding concept adapted to the modes of thought of modem microphysics is probably nonexistent.”
The apparent contradiction between the microphysical account of material reality and the macroscopic account of “prime matter” is a tension that Younan’s proposal would resolve by his “squeeze theorem”: particulate reality exists at the level of proto-substance. (How this proposal would interact with the “thermal substances” of Robert Koons’s work would be an interesting topic for another time.) Younan also gives a hearing to Steve Barr’s rather sanguine proposal that matter is mathematizable “all the way down” (see 2n7 and 32). Is this possible? In the conclusion to Chapter 3, Younan writes:
Instead of the negative “collapse of the wave function,” perhaps a positive “actualization of a particle” may be a closer reflection of the way nature really works. In this idiom, the emphasis is not so much on the “perturbation” of the system caused by measurement as much as on the (metaphorical) “desire” that matter has for form. Heisenberg is insightful enough to see this: “Energy becomes matter by taking on the form of an elementary particle, by manifesting itself in this form. Here there is an echo of the relation between form and matter that plays such a central role in the philosophy of Aristotle.” . . . Nature is not only an “is” but also a “could be.” Potentiality may be a real principle in nature, one that can be observed and expressed mathematically as a wave function. But it is still potentiality, and requires (as well as, metaphorically, “desires”) form (or, analogously, substances higher up on the formal scale) in order to be complete and actualized. (97, 98)
This expresses in a sounder way the “further ontological explanation” that Younan seems to deny is needed in Chapter 5. This deeper ontological explanation can be made the stronger, however, if we recognize that the “desire” of matter for form (see Physics, I.9) is not a metaphor, but an analogy. As St. Thomas says, “Nor does [Aristotle] use a figure of speech here; rather, he uses an example.” (In Phys., lib. I, lect. 15, n. 138) In another place, Aquinas explains that “the desire for form is not some action of matter but a certain bearing of matter to form, insofar as it is in potency to it” (my translation; De Potentia, q. 4, a. 1, ad. s.c. 2). Because of this, “every subject, even prime matter, which is in potency to what perfection soever, from this very fact that it is in potency, meets the definition of the good” (St. Thomas Aquinas, De Malo, q. 1, a. 2, c.; see also St. Augustine, Against the Manicheans, ch. 18).
This desire—the transcendental relation of matter to form as its perfection and good—shows the primacy of the good as cause at the lowest level of the natural world, the only rung more fundamental than the microphysical. Matter would be mathematizable “all the way down,” then, only if it could adequately and directly capture this relationship. Yet this is not possible, for “mathematicals are abstracted in ratio only, insofar as they are abstracted from motion and matter, and thus abstracted from the ratio of the end.” (ST, Ia, q. 5, a. 3, ad 4; see also SBdT, q. 5, a. 4, ad 7) The metaphysician and natural philosopher, each in his own way, can reintegrate mathematical beings into the order and beauty of the cosmos, because their consideration do not make such abstractions: “For the very being of lines and numbers is good” (De Veritate, q. 21, a. 2, ad 4). However, perhaps mathematics can indirectly and partially capture this rootedness of matter in the good. For such a reason, Younan is right to argue that the Aristotelian-Thomistic position must savor all that it can of the being of mathematics in the natural order.
Younan concludes the book with a fine reconsideration of mathematically knowable order in nature, its origin from the Creator, and Aquinas’s Fifth Way. What the contemporary sciences reveal are the laws of the being and acting of natural things are also the “laws” of their teleology.
The analogy of the arrow and the archer in the text of the Fifth Way must be understood with this teaching in mind. God does not cause motion by pushing creatures around, and teleology does not mean that creatures are billiard balls moving toward the end-pockets that God has in store for them according to some arbitrary decree. Very much to the contrary, God “directs” things to their end by making them to be the kinds of things they are, and they in turn act in accord with the natures they were given at their creation. Because each creature is a particular kind of thing, with a certain arrangement of actuality and potency, form and matter, it is able to act in particular ways and act upon other things, which in turn have their own constitution, and so on until the end of the age. (190)
The natural theological reflections in this appendix sketch the resolution of the Aristotelian-Platonic debate that Younan reviews in Chapter 4. What is ultimately the cause of goodness and necessity in the well-ordered cosmos? “Perhaps only God [according to Aristotle], who is that which all things strive for, is pure telos. On the other hand, he is also pure necessity.” (136) The broadly Thomistic resolution proposed in the Appendix would have made a better concluding chapter.
Indeed, following out the “metaphor” of the laws of nature, Younan closes the Appendix by suggesting a parallelism between Gratian’s definition of law, followed by Aquinas, and the laws of physical nature. To paraphrase: the laws of nature are orders of necessitating mathematical reasons structuring the common good of the cosmos, instituted as the laws of creatures’s natures by God and “promulgated” in divine wisdom and found out in our scientific inquiry (205–207).
Now, if the Fifth Way is drawn “from the governance of things [ex gubernatione rerum],” one might wonder whether the argument for God’s existence from teleology—from the good in nature—has any bearing on the mathematical character of the laws of nature defended in this book. Younan does say that his “account leaves open the question of whether laws of nature are only about fundamental physical particles or about more complex things such as organisms or social structures” (170), and rightly so. As Kant argued:
For it is quite certain that we can never adequately come to know the organized beings and their internal possibility in accordance with merely mechanical principles of nature, let alone explain them; and indeed this is so certain that we can boldly say that it would be absurd for humans even to make such an attempt or to hope that there may yet arise a Newton who could make comprehensible even the generation of a blade of grass according to natural laws that no intention has ordered: rather, we must absolutely deny this insight to human beings. (Critique of Judgment, §75)
That is—pace Kant’s own intentions here—we must deny such an insight to human beings because ateleological explanations of a universe shot through with teleology is simply not there to be found. This suggests is a conclusion at converging lines of thought. It is seems unlikely that the universe is a sort of computer, working out natural processes by algorithmic laws. Furthermore, mathematical structure and function are concretized in nature due to the good of the whole universe, as made clear by Fr. Andrew Younan’s fine book. Even among biological processes robust, nearly law-like convergences can be found, solutions in the fitness landscape of the possibilities of creatures great and small (e.g., in eye evolution). The governance of the world disposes “all things in measure, and number, and weight” (Wis 11:21), a mathematically knowable, teleological cosmos. Perhaps the expression “law of nature” is less of a metaphorical expression, and more of a (distant) proper analogy.