Course in April

As part of the last stages of my postdoctoral project here in Chile, I’m happy to announce a course that I’ll be teaching this April at Universidad Gabriela Mistral: Dios y la Filosofía. The course is an overview of the fundamentals of natural theology, especially in view of modern science, following a classical Thomistic approach to the subject.

Dios y la filosofía

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The Principle of Least Action (Chile)

The following presentation is another entry in my attempts to understand the principle of least action from a Neo-Aristotelian perspective. It was presented at First Chilean Conference on the Philosophy of Physics. In the presentation, I engage the views of Vladislav Terekhovich and Vassilis Livanios, who have both provided keen counterpoints to dispositionalist approaches to this subject. Livanios has also given a most helpful “Challenge” to the dispositionalist by outlining the resources available and the shortcomings of that ontology. The paper presents two lacunae, one of particular interest, which dispositional ontologists of the stronger, Neo-Aristotelian or Thomistic variety much attend to if global laws, conservation principles, or other similar key concepts of modern physics are to be incorporated into a broader Aristotelian-Thomistic philosophy of nature.


The Action and Power of the Universe (Part 2)
The Principle of Least Action and Our Knowledge of Nature

John G. Brungardt
Postdoctoral Fellow, Instituto de Filosofía
Pontificia Universidad Católica de Chile

Introduction

The purpose of this presentation is to outline an interpretation of the principle of least action (or PLA) using dispositional ontology in general and a Neo-Aristotelian approach in particular.1 Dispositional ontologyor an ontology of powers—is opposed to at least two other philosophical schools concerned with the laws of nature: a Humean regularity approach (e.g., David Lewis) and a nomic necessitarian approach (e.g., David Armstrong). To describe it briefly, dispositionalist ontology generally maintains that the ontological “furniture of the world” must include, apart from actualities, properties that are not actualities or manifestations but are themselves “dispositions”—a property of being disposed to, prone to, potent to, or having a power to act or manifest other properties. Hence some versions view are called Neo-Aristotelian, for Aristotle claimed millennia ago that being or what exists is divided into what exists in act and what exists in potency.2 Dispositions or powers are mind-independent realities that are not mere ways of speaking or psychological projections, they exhibit an order to or directedness to their manifestations, and they still exist even when their correlative manifestations do not (unbroken glass is still fragile). This dispositional ontology becomes Neo-Aristotelian when one attempts to incorporate more robust, updated claims about hylomorphism and a four-cause analysis of the natural order, including teleology. So, our question is whether this expanded tool-kit helps or hinders us when discussing physical principles like the PLA.

There is a growing discussion in the philosophical literature about whether dispositional ontology can shed any philosophical light on the PLA. This presentation will focus on two papers in this field: one by Vladislav Terekhovich, the other by Vassilis Livanios. Livanios, who is not in favor of dispositionalism, actually answers several key objections against the dispositionalist himself; however, Livanios also raises an important unanswered difficulty for the dispositionalist. Likewise, the views of Terekhovich also highlight by contrast the demands placed upon a dispositionalist interpretation.

We proceed in three parts. First, I highlight some aspects of the PLA. Second, I consider the views of Terekhovich and then those of Livanios. Finally, I outline a Neo-Aristotelian, dispositionalist ontology of the PLA, taking into consideration the objections raised against it. The PLA, if it is grounded by a disposition, is only grounded by a disposition of a far different sort than is usually considered. Our conclusion: The PLA is a global, bottom-up effect from the perspective of mathematically local, differential dynamics; it is a physically global condition for coordinated interaction when one sees the universe as composed of objects with real power for action and motion.

1. Background for the PLA

First, I highlight certain aspects of the PLA. Mathematically, the PLA is a time-integrated Lagrangian with a stationary value. The integrated Lagrangian yields the physical quantity called “action.” When used with the Euler-Lagrange equations, one can derive the equations of motion of a system. Action as a physical quantity is measured in Joule-seconds, and so a minimized or stationary value with respect to alternative motion paths represents a certain character to the use of energy in the physical system through time. This energy-character is specified by the Lagrangian. The Lagrangian is, therefore, crucial to joining the PLA (as a mathematical tool in the calculus of variations) to physical reality. Similarly, the alternative possible “histories” or motion paths must be understood by looking to this physical tie as a governing factor.

2A. Terekhovich: Leibniz or Aristotle?

We now turn to Terekhovich’s consideration of the PLA. Terekhovich attempts to ground the PLA using a Leibnizian view of modality in lieu of a “possible worlds” view of modality (on this, he and the Neo-Aristotelian dispositionalist agree), and Terekhovich uses his Leibnizian model to reinterpret the dispositionalist’s view of the PLA.3 The Leibnizian metaphysical model has two levels. The first level concerns the reality of possibilia, and the second level proposes how the possibilia become actual.

Regarding the first level, Terekhovich agrees with the dispositionalist in rejecting the reality of possible worlds and distinguishing such worlds from our worlds possibilia.4 He divides the unique, real world in two: the possible modality and the actual modality. The possible modality includes the totality of all “possible events and histories,” which all, as long as they are not self-contradictory and consistent with the laws of physics, “have essences but do not have existence” (i.e., they are not observed) and thus these alternate possibilities “‘occur’ simultaneously in the possible realm of our world. The actual history is naturally consistent with the physical laws of our world and occurs in the only actual realm of our world.”5

The second level of the model explains how the possibilia become actual; here, Terekhovich uses an analogy to Feynman’s path integral formalism: just as quantum histories with the highest probability promote an actual history, so also for all possible histories of motion those with the highest degree of essence lead to the world’s actual history.6 This appeal to a Leibnizian notion of a “highest degree of compossibility”7 as the rule for constituting the actual world from the resources of the possible modality is governed by the PLA:8

Accordingly, in the modal interpretation of the PLA, of the infinite set of the possible histories, only the one with the minimal action can exist as actual because it has the highest degree of essence and combines the greatest number of possibilities at the same time. It appears the more essence a possible history has, the less action there is.

On the basis of this model, Terekhovich proposes that the dispositionalist could adopt his interpretation of the PLA by thinking of the alternative histories in the possible modality as unrealized dispositions: “The dispositions of actualized histories differ by degrees of necessity in being manifested in the actual modality, and the degree of necessity can be measured by the value of the action.”9

However, it is unclear how his view explains rather than stipulates that the PLA is that reason due to which “the maximal number of possible histories” are combined. Indeed, what makes it possible to combine these possible histories in a “maximal” way, besides a brute-fact appeal to the PLA? That is, the possibility to combine possible histories must be a possibility in a different sense than that possessed by the alternate histories and therefore requires its own analysis. Besides, the dispositionalist typically takes a disposition’s being possible to mean that it is realizable or able to be manifested, whereas, on Terekhovich’s approach, there are infinities of so-called “possibilities” that have no such disposition (because it is not possible to combine them into a maximal number of possible histories) and, therefore, they are not “possibilities” in the same sense.

So, we are left with the following results: First, some distinction must be made in the senses of possibility.” Second, what Terekhovich has done, through his laudable focus on the nature of possibility and actuality in a single world, is to highlight the need for dispositional ontology to clarify how dispositions and manifestations are related in the very constitution of the world’s history as a whole.

2B. Livanios: Has the World an Essence?

We now turn to Livanios’s consideration of the PLA. In his 2018 article, Livanios argues on behalf of the dispositionalist to answer three objections against its view of the PLA.10 Recall that, ultimately, Livanios is not a dispositionalist. Indeed, his third point leads to what I will call Livanios’s Challenge.11

The first point concerns the difference in the modality of logical possibility and physical possibility.12 The objector to dispositionalism maintains that the PLA “presupposes that the action of any given physical system could metaphysically have taken different values.”13 That is, the alternative motion paths are really possible. However, this is contrary to a dispositionalist ontology, for a dispositionalist evidently maintains that “there is only one metaphysically possible quantity of action and just one metaphysically possible sequence of states.”14 To this objection, however, Livanios replies on behalf of the dispositionalist—and rightly, to my mind—that one should distinguish between logical possibility and physical possibility. We slightly adapt his reply here: The alternative histories are possible in the logical space of our mathematical imaginations. This logical possibility of alternative histories is a necessary but not a sufficient condition for the application of the PLA and therefore for understanding the meaning of “physically possible.”

The second point concerns the priority of certain types of explanations of physical systems. The objector to dispositionalism points out that actual scientific practice uses the PLA to derive the equations of motion for a system, which equations tell us about the systems’s character. The order of explanation according to the dispositionalist, however, is in the contrary direction. The dispositions of the objects in a system give rise to the laws or equations of motion, and these are codified in general by least action principles.15 To this objection, however, Livanios replies on behalf of the dispositionalist—and rightly, in my view—that we must attend to the nature of the Lagrangian at the heart of the PLA.16 In order for the PLA to provide a physical explanation, one must have found the Lagrangian that is proper to the system being studied. Thus, the Lagrangian stipulates the properties and hence—the dispositionalist is free to claim—the physical dispositions of the system involved. Consequently, physical dispositions can still underwrite the laws of a system’s temporal evolution discovered mathematically using a least-action analysis.

These first two responses distinguishing between logical and physical possibility and the dependence of the Lagrangian upon physical dispositions go a long way to distancing dispositional ontology from Terekhovich’s Leibnizian modal view; the tools of our mathematical physics and the possibilities which they imply in our eidetic variations reveal options beyond what nature in fact exhibits and thus deems “possible” in a physical sense.17 Despite these defenses, however, Livanios notes that under certain conditions there is an “equivalence of the description of motion by differential equations of motion and by integral action principles,” and then he infers: “A potential worry is that the consequences of this equivalence render the whole debate under consideration metaphysically insignificant or redundant.”18 In what follows we will see if the dispositionalist is metaphysically otiose.

The third point Livanios discusses is whether dispositionalism is compatible with grounding both differential and integral explanations of motion.19 Here, the objector points out that dispositional ontology for mathematical physics is entirely local in its claims, i.e., local in the mathematical sense of being restricted to an infinitesimal neighborhood of points.20 Dispositionalism can only ground differential equations of motion through this local ontology. The PLA, however, is a mathematically global and not a local explanation, and is therefore incompatible with dispositionalism.

Livanios proposes that the dispositionalist can meet this charge by reevaluating how the PLA is an explanandum.21 That is, the dispositionalist must reinterpret the PLA so it is no longer a law that flows from the object-level dispositions of physical systems in the way that differential dynamic laws usually do. Rather, the PLA should be deemed a meta-law to which other laws about physical objects must conform. How, then, would dispositional ontology provide an explanation for the PLA as a meta-law?

Here, Livanios raises what he considers the unanswered difficulty facing the dispositionalist. The most plausible way one might provide for a dispositionalist ground of the PLA as a meta-law is by trying “to show that [the PLA] ‘flows’ from the dispositional essences of the world” and thus extending the scope of dispositionalism’s application “from the object-level to the law-level.”22 Some dispositionalists take this route and propose that there exists a dispositional property called “Lagrangianism.” Lagrangianism is “of the essence of all physical systems. It is a truly universal property without which no physical object could be a member of the most general kind of substances existing in the world.”23

Livanios argues that there are two difficulties with such a proposal. First, it is ad hoc—there is no measurable, physical property corresponding to this “Lagrangianism” and, as a sui generis property, its only role is to save face for a dispositional grounding for the PLA. Second, even if the appeal is not ad hoc, it is redundant. The reason a world-disposition like “Lagrangianism” grounding the PLA is redundant is that the Lagrangian itself already relies upon the dispositional properties of the objects composing physical systems. So, what independent role does this world-disposition of “Lagrangianism” play in our explanations over and above an individual object’s dispositions?

The difficulty for the dispositionalist, therefore, can be stated as follows. I will call it Livanios’s Challenge: How can the local origins of dispositional ontology explain a global meta-law like the PLA?

3. The Neo-Aristotelian Proposal

To motivate my dispositionalist interpretation of the PLA, I first propose some distinctions about “local” and “global” at different levels of conceptualization. I will then use these distinctions to answer Livanios’s Challenge.

First, we should briefly consider our talk of “local” and “global.” These terms exhibit a manner of systematic equivocation on three levels: the mathematical, natural-scientific, and ordinary language levels. That is, “local” and “global” are analogous terms.24 The mathematical physicist might trade on similarities between these levels, but we must keep them distinct. What is true about one level of the local vs. global distinction is not necessarily true at another level.

Furthermore, recall that Livanios had reformulated the PLA as a meta-law on behalf of the dispositionalist so as to avoid a conflict with the presumed commitment to grounding differential laws of motion at a local scale first and not the PLA at a global scale. However, this implies—incorrectly—that the dispositionalist favors a sort of pointillisme as an ontology. Jeremy Butterfield defines pointillisme as “the doctrine that a physical theory’s fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there, so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts.”25 However, this is not true. Dispositionalists, especially Neo-Aristotelian ones, are concerned with dispositions that are not mathematically local in this pointilliste sense (e.g., the dispositions of a living organism as a whole or in its parts are not mathematically local). More crucially, a Neo-Aristotelian analysis of physical motion cannot be pointilliste because motion as a dispositional reality is mathematically non-local. The mobile object when actually moving possesses a disposition to later places or states where it can end up. To say this in another way, the Neo-Aristotelian permits the dispositional non-locality of motion, where “non-local” is a denial of “local” in the mathematical sense. This denial that moving objects are “local” in the sense employed by mathematical physics allows the possibility that more-than-mathematically-local realities are fundamental. What is “local” or global” in meanings that are available to the natural sciences or to a natural philosophical or metaphysical analysis can now be brought to bear.26

Now, to answer Livanios’s Challenge: I first deny that a dispositionalist must prioritize a grounding ontology that is “differential” or pointilliste, that is, local in a mathematical sense. The properties involved in physical motion cannot be defined as intrinsic to points but must make reference to extrinsic properties, among which some are dispositional in nature. If we can back out of the commitment to a differential ontology, what do we put in its place? Here, the dispositionalist must say more by elaborating a dispositionalist theory of physical continua, i.e., how dispositions lead to non-pointilliste physical properties (such as velocity, momentum, or energy). However, we must admit that such a theory is currently lacking in dispositionalist literature (at least to our knowledge); this is a first promissory note.

After this denial of pointillisme, we can distinguish how we agree and disagree with Livanios. We agree that, mathematically speaking, the PLA is equivalent to differential derivations of equations of motion. In this way, there is no priority between the local and the global. However, it does not follow from this that the physical universe is itself indifferent to the local or the global in other senses; a broader notion of “local” vs. global” might exhibit explanatory or ontological priority. The dispositionalist therefore needs a more holistic view even of dispositions that are “local” in the restricted mathematical sense.27

If there is such a level of “local” and “global” that escapes what mathematical physics can articulate in differential or integral equations of motion, then at this level the PLA might enter into our overall interpretation of nature in a different way. But there does seem to be such a local and global that escapes mathematical physics, and at two levels (at least, on the dispositionalist’s view). A first level is that even purely physical properties cannot be defined in a pointilliste fashion (e.g., velocity, momentum, energy). The second level brings a higher-order demand. The scales of physics and chemistry must be compatible with the dispositions belonging to life and to mind. On this second level, the PLA might be a condition due to a higher-order demand. Here, however, this Neo-Aristotelian dispositionalist can only offer the mission of a research program (as a second promissory note). That program must bear out the following claim: A universe that exhibits the evolution of living or thinking beings as parts or members requires the behavior of physical matter to exhibit certain characteristics, such as the PLA.

At the first level—that of non-pointillistic physical objects with dispositions for motion—the PLA is a condition for the global interaction of physical objects in the universe, where “global” is meant not a mathematical sense but in the way that the natural sciences, and especially cosmology, speak of “the global” (referring to physical regions and, ultimately, the universe). As a condition at this level, the PLA co-defines the given natural dispositions for motion. To flesh this out, recall that the principle of least action is a time-integrated Lagrangian with a stationary (or a minimum) value. The Lagrangian is an object in mathematical physics, and, as a mathematical object, it must be applied to a physical situation. (This is why, by distinguishing between logical and physical possibility, the “alternatives histories” implied by the PLA’s mathematical formalism are not physical possibilities.) This application involves physical dispositions and measurements; hence, the PLA’s Lagrangian encodes the essential dispositional properties of a system naturally in motion. I call such motion naturalbecause the true path—the one with least or stationary action—is the path observed to exist in nature (or, as Terekhovich would say, in the actual modality). The PLAencodesthis motion because the Lagrangian directly represents certain mathematical relationships defined by the Lagrangian. Because of the application to background dispositions, however, the Lagrangian indirectly represents the dispositions belonging to a physical system that is capable of or disposed to motion. This physical system, however, does not exist in a Leibnizian possible modality or in a pointilliste way, but through real dispositions that are not defined locally but by what global interaction demands—by what the universe demands. This is why we qualify our proposal as Neo-Aristotelian. Natural motions are natural because they are formal parts of a coordinated order of things. By encoding a natural motion through a Lagrangian that indirectly represents dispositions, the PLA shows itself to be a condition for coordinating the interaction of physical objects in the universe.

If the universe’s essence or nature is partly defined by this coordinated physical order among physical objects disposed for various motions, we can answer Livanios’s objection that a dispositionalist ontology for the PLA is explanatorily redundant. Recall that the PLA becomes explanatorily redundant for the dispositionalist because Livanios relocates the dispositions for the PLA from the object-level to the law-level. However, a true “system” of objects, like the universe, needs its own ontological analysis.28 The Neo-Aristotelian locates the universe at the object-level and not the law-level.29 Furthermore, the universe is not in one category (e.g., the universe is not a substance, pace Jonathan Schaffer) but it is a transcategorical reality, a unity of order between categories (e.g., substances, their properties, and relations). Since the universe exists at the object-level but does not exist in a single category, we need not add a single-category property of “Lagrangianism” to the object level to ground the PLA through a global disposition. This allows us to answer Livanios’s objection that proposing a dispositionally grounded essence to the world is ad hoc. If there is an essence to the world, one which we can discover by gathering the empirical results of all the natural sciences into a broad philosophical view, then claiming the existence of “Lagrangianism” or some other such property of global systems is not ad hoc but warranted. However, on our view, “Lagrangianism” would then not be a disposition of the universe as such, but (to use an old scholastic term) an “extrinsic formal cause,” part of the form of the unity of order of physical things apt for motion.

Conclusion

In conclusion, I partially admit Livanioss critique. The PLA is not the disposition of independent objects or individual substances; however, the PLA is still a global condition that defines the dispositions of those objects insofar as they are members of a universe. This condition permits physically global coordination and interaction between its members as a system with physical or biological modes of motion, process, and development at various scales (or it would, if the Neo-Aristotelian can make good on the two promissory notes). The PLA is a global, bottom-up effect from the perspective of mathematically local, differential dynamics; it is a physically global condition for coordinated interaction when one sees the universe as composed of objects with real power for action and motion.


 

1 Among the many persons to whom I owe thanks for ideas and suggestions that went into this paper are, first and foremost, Timothy Kearns and Thomas McLaughlin, with whom I participated in a long-distance collaborative project on this theme. I also thank Roberto Salas, James McCaughan, Ryan Miller, Geoffrey Wollard, Marco Stango, and Andrew Seeley for comments on drafts, to James Franklin for comments on the presented version of Part One of this paper, and José Tomás Alvarado and Fr. Philip Neri Reese, O.P., for their comments on this and related ideas. Finally, I thank John O’Callaghan and Anjan Chakravarrty for their support during a research stay at the University of Notre Dame, where I began the work for this paper. This paper was produced as part of my postdoctoral research, FONDECYT Postdoctorado, Proj. No. 3170446.

2 See Aristotle, Metaphysics, IX.1, 1045b27–1046a4. For Neo-Aristotelian views on the philosophy of science and nature, consider Ruth Groff and John Greco, eds., Powers and Capacities in Philosophy: The New Aristotelianism (New York/London: Routledge, 2013) and William M. R. Simpson, Robert C. Koons, and Nicholas J. Teh, eds., Neo-Aristotelian Perspectives on Contemporary Science (New York: Routledge, 2017).

3 See Vladislav Terekhovich, “Metaphysics of the Principle of Least Action,” Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 62 (2017): 189–201. He claims, ibid., 194, that dispositionalism would provide the following interpretation of the PLA: “The possible history is in our world as unrealised manifestations of possibilities, but the possible history does not exist there. The observed history with the minimal action is the realised manifestation of one of the possible histories and thus it exists in the actual world.”

4 See ibid., 195; his dispositionalist interlocutor is Alexander Bird.

5 Ibid., 195.

6 Note that Terekhovich clarifies the explanatory direction of the analogy, 196: “Despite the analogy with quantum superposition, I do not reduce the metaphysically possible histories to the quantum histories. The FPI does not explain the metaphysical combination model, since the FPI is unlikely to have an independent metaphysical essence. On the contrary, the significance of the FPI lies in one of the effects of the combination model.”

7 See ibid., 197: “Only mutually compatible essences constitute the actual world. Here, I follow Leibniz, who invoked the notion of compossibility, so that «the universe is only a certain collection of compossibles, and the actual universe is the collection of all existing possibles, that is to say, those which form the richest composite»”

8 See also 196, where he offers this qualifying clarification: “Nevertheless, it is not exactly so. As we know, in the integral variational principles, a certain system’s functional (not just the action) is stationary and takes a minimal or maximal value for the actual process among all alternative possible processes. It means that the essence and the action are not exactly the same; the former is not a definition of the latter and vice versa. Rather the metaphysical interpretation of the action (and certain system’s functionals) is one of the physical measures of the essence, which consists of the necessity of each possible history to be realised in actuality.”

9 Ibid., 197.

10 See Vassilis Livanios, “Hamilton’s Principle and Dispositional Essentialism: Friends or Foes?” Journal for General Philosophy of Science 49.1 (2018): 59–71.

11 Note that our first and second point correspond to Livanios’s first and third points. We reorder them for clarity in our response to his views.

12 Ibid., 62–64.

13 Ibid., 62. Note that Livanios, in his article, speaks of “Hamilton’s Principle” as a generalization of the PLA. We do not think any philosophical problems arise by our difference in emphasis.

14 Ibid. See also Benjamin T. H. Smart and Karim P. Y. Thébault, “Dispositions and the Principle of Least Action Revisited,” Analysis 75.3 (July 2015): 388, as well as Joel Katzav, “Dispositions and the Principle of Least Action,” Analysis 64.3 (2004): 210.

15 See Livanios, “Hamilton’s Principle and Dispositional Essentialism,” 66. See Katzav, “Dispositions and the Principle of Least Action,” 211–12.

16 See Livanios, “Hamilton’s Principle and Dispositional Essentialism,” 67.

17 This amounts to a physics-mathematics secularism. That is, just as political secularism claims to eliminate philosophical disputes about ethics from public policy without any detriment, so also physico-mathematical secularism makes old metaphysical questions about the ontological difference between physical and mathematical objects a private philosophical concern, not to be mixed with public scientific practice. This secularism is noted by Richard Hassing, who expresses the issue as a question: “Are mathematical objects different in some fundamental way from physical objects?” The ancient Greeks answered “Clearly, yes,” (think of Aristotle and Plato’s famous disagreement about Forms). However, classical physics adopted a certain physico-mathematical secularism in place of an ontology, agreeing, as it were: “Let us set aside these philosophical disputes, and assume that any difference between mathematical objects and physical objects makes no difference for the conduct of our mathematical physics.” Richard F. Hassing, “Modern Turns in Mathematics and Physics,” in The Modern Turn, ed. by M. Rohlf, 60:131–82, Studies in Philosophy and the History of Philosophy (Washington, DC: Catholic University of America Press, 2017), 169–70.

18 See Livanios, “Hamilton’s Principle and Dispositional Essentialism,” 69–70.

19 Ibid., 64–66.

20 See ibid., 64. Livanios helpfully quotes Jeremy Butterfield, “Against Pointillisme about Mechanics,” The British Journal for the Philosophy of Science 57.4 (2006): 715: “An equation of motion is called ‘local in time’ if it describes the evolution of the state of the system at time t without appealing to any facts that are a finite (though maybe very small) time-interval to the past or future of t.”

21 See Livanios, “Hamilton’s Principle and Dispositional Essentialism,” 66. Livanios also notes one solution whose price is too high for the dispositionalist to pay; see ibid., 65: “In contrast with the ‘differential’ scientific explanation for which DE [dispositional essentialism] does provide a metaphysical ground, no DE-friendly metaphysical account of the [PLA]-based scientific explanation currently exists. So, the problem for the DE-ist can be solved simply by claiming that there could be no metaphysical [PLA]-based explanation.”

22 Ibid., 68.

23 See ibid. He cites Brian Ellis, “Katzav on the Limitations of Dispositionalism,” Analysis 65.1 (2005): 90–92; see also John Bigelow, Brian Ellis, and Caroline Lierse, “The World as One of a Kind: Natural Necessity and Laws of Nature,” The British Journal for the Philosophy of Science 43.3 (1992): 371–88.

24 In common speech, “local” and “global” name aspects of our environment. “Local” is what belongs to this region or neighborhood in which one lives; the “global” refers to what embraces a whole of something, just as the globe includes the terrestrial collection of all locales. From this origin the words were transferred to a mathematical usage: “local” refers to what is true in the neighborhood of a point (or “in the small” at the infinitesimal scale); “global” names what was true of the integrated whole or the entire domain available to a given function; see James Franklin, “Global and Local,” The Mathematical Intelligencer 36, no. 4 (December 1, 2014): 6. Crucially, the mathematical notion relates local to global through a background appeal to the fundamental theorem of calculus. However, there are also natural-scientific uses of “local” and “global” which lie between the looser common usage and the more precise mathematical ones. This is required for senses where one must describe a local habitat in biology or the global conditions of, well, a planet.

25 Butterfield, “Against Pointillisme about Mechanics,” 710.

26 The PLA might not be “contained” on only one level of analysis, but might be a effect or a condition due to a different level of analysis. Or, to put it another way, a “purely isolated physical system” that behaves according to the PLA does not exist in the concrete natural order as such, i.e., an isolated physical system, and thus certain features of the PLA in our isolated analysis might be a clue to what lies beyond the physical system as such. Recent work in emergence and top-down causality seems to bear out this claim. See George F. R. Ellis, How Can Physics Underlie the Mind?: Top-Down Causation in the Human Context (Berlin/Heidelberg: Springer, 2016); also, G. F. R. Ellis, D. Noble, and T. O’Connor, “Top-down Causation: An Integrating Theme within and across the Sciences?” Interface Focus 2.1 (2012): 1–3, an editorial devoted to a special issue on the topic.

27 The key Neo-Aristotelian claim here is that the forms of things, that is, the fundamental, kind-giving actualities and powers of substances, are not causes of objects in local, point-like isolation but are potentially determinable with respect to a global array of properties. That is, an ontology of substances is compatible with both the dependent emergence of and the antecedent priority of certain global properties.

28 This need is difficult to see. In W. Norris Clarke, “System: A New Category of Being?” In The Creative Retrieval of Saint Thomas Aquinas: Essays in Thomistic Philosophy, New and Old (New York: Fordham University Press, 2009), 39–47. While we do not agree with all points of his analysis, the general lesson that Clarke draws is sound. He defines “system,” 40–41, as a “unified immanent order which [links] together groups of individuals in such a way that they form a single objectively existing or recognizable order, a single intelligible network or pattern of relations forming a whole.”

29 Contrary to Livanios (on behalf of dispositionalists) and Brian Ellis. For Ellis, see “Katzav on the Limitations of Dispositionalism,” 91: “At the summit of each hierarchy, I postulate that there is a global natural kind that includes every kind of thing in the corresponding category. The global natural kind in the category of substances is that of the physical system.”


These presentations were produced as part of my postdoctoral research project.
FONDECYT Postdoctorado, Proj. Nº 3170446

Quaestio Quodlibet: Whether God could have made a better universe, or, the existence of radical natural evil

the-center-of-the-milky-way-galaxy

The following is a quodlibetal-type question that I recently received. Such questions are always welcome, just email them to me here.

If God is all knowing and all powerful then does that mean He knew creating this specific universe with its physical laws would inevitably lead to them interacting in such a way as to create unpleasant events (like earthquakes)? While it can be argued these are part of a larger system that is good (e.g., plate tectonics indirectly help sustain us) couldn’t God being all knowing and all powerful have created such fundamentally and radically different laws of physics that creation doesn’t depend indirectly or directly on these conflicting processes to achieve progress?

The point about plate tectonics is fascinating and points to one of the necessary conditions for the existence of life. That is, the destruction of parts of the Earth’s surface and attendant geological upheaval (an ontological evil) is, from another respect, a good.

Not only does Earth lie in the ‘Goldilocks zone’ that allows water to exist in the liquid form that life requires. It is also the only rocky planet we know of that constantly renovates its surface as its tectonic plates dive into the mantle in some places and re-emerge as molten lava in others. Many astrobiologists now think this constant renewal is just as important as liquid water for the flourishing of life as we know it. (Cosmos, 27 Dec 2017)

The question posed is an interesting one for several reasons. First, it generally has to do with God’s wisdom, power, and the problem of evil; so it is speculatively rewarding to consider. Second, it brings to mind the possibility of “alternate universes” in the sense that it seems possible for God to have created the entire universe (from angels to atoms) in a completely different way; this is also a speculatively fascinating topic. Third, the question is posed in a precise way that adds something to its difficulty: the question immediately focuses upon physical processes and not the existence of intelligent, free beings. In this respect, it is a special case of the problem of evil.

To propose an answer to the question, I will need to break the question down into three parts. First, since the question concerns what is possible for God with respect to the object of His creative act, namely, the universe, we must first ask: 1. Could God have created the universe differently? With these principles in mind, we should then ask if there are reasons for the existence of ontological evils in the universe: 2. Why did God create a universe with ontological evils? Finally, we will be in a position to propose an answer to the question: 3. Can a universe exist that does not contain ontological evils? We shall see that this question is closely bound up with the following question: Is a universe possible that does not directly or indirectly depend upon contrariety to achieve the end of the universe?

1. Could God have created the universe differently? (Preliminary clarifications and some definitions)

We can answer this question by considering how St. Thomas answers the following question in In I Sent., d. 44, q. 1, a. 2Utrum Deus potuerit facere universum melius—Whether God could have made a better universe (a translation of this article is at the end of this post). His answer is “In some ways yes, and in other ways no.” However, before diving into this question, we should propose some initial clarifications about certain terms.

The universe, according to St. Thomas, consists in all created substances. The form of the universe is its intrinsic order, namely, the relationships of diverse kinds of beings, their hierarchy, and their causal interactions. This intrinsic order is the common good of the universe and hence the greatest of all created goods, but the whole universe is nonetheless ordered to God as to its ultimate end.

St. Thomas, as many philosophers also do, distinguishes between real possibility and logical possibility. This latter is also called absolute possibility. Something is really possible (and action, an individual being, an event) in virtue of the relationship of that thing to the existing power or potentiality to bring it about. In this sense of possibility, nothing in impossible to God. Real possibility is also rooted in actual being. Logical possibility is rooted in being insofar as being includes what is true. Thus, logical or absolute possibility includes both God and existing creatures in its notion, such that something that is logically impossible is also impossible for God to bring about. Here is how St. Thomas defines this type of possibility/impossibility:

And they are said to be such [impossible] not because of the privation of some potency but because of the opposition existing between the terms in propositions. For since potency is referred to being, then just as being is predicated not only of things that exist in reality but also of the composition of a proposition inasmuch as it contains truth and falsity, in a similar fashion the terms possible and impossible are predicated not only of real potency and incapacity but also of the truth and falsity found in the combining or separating of terms in propositions. Hence the term impossible means that of which the contrary is necessarily true. For example, it is impossible that the diagonal of a square should be commensurable with a side, because such a statement is false whose contrary is not only true but necessarily so, namely, that it is not commensurable. Hence the statement that it is commensurable is necessarily false, and this is impossible. (St. Thomas, In Meta., lib. 5, lect. 14, n. 971)

This allows us to distinguish between the possible that is opposed to the impossible (as above) and the possible which is opposed to the necessary. This latter type of possibility is also called contingency. What is necessary is unable to be otherwise, whereas what is contingent can either be or not be—it is possible for such a being not to be. However, both necessary beings and possible (i.e., contingent) beings are absolutely speaking possible. That is, neither are impossible. These distinctions are important so as to help us think about what it would mean for God to make another universe. For instance, it is absolutely possible for God to make a universe in which I do not exist, but it is impossible for God to make a universe wherein the diagonal of a square is commensurable with its side (or a universe where √2 is a rational number).

Furthermore, this distinction between real and logical possibility helps us to understand, insofar as we are able, God’s power. What is crucial to note is that logical possibility does not follow upon God’s omnipotence considered formally in itself—that is, God’s power does not measure logical possibility. Rather, logical possibility is presupposed to God’s omnipotence, for His power is the power to do all that is able to be done, i.e., all that is possible absolutely. (This notion plays a central role in Pope Benedict XVI’s lecture at Regensburg.) This leads us to a distinction between God’s power considered absolutely and His ordered power. These are not two distinct kinds of power in God, but differ only in our mode of conceiving. His ordered power is God’s power insofar as it acts according to His wisdom—that is, it is divine omnipotency not considered in abstraction from the other Divine attributes. Hence, Pope Benedict XVI can say “Not to act ‘with logos’ is contrary to God’s nature.” God’s absolute power is His power considered in itself and thus formally distinct from the other attributes. St. Thomas states the difference as follows:

The absolute and the conditional are ascribed to the divine power solely from our point of view. To this power considered in itself and which we describe as God’s absolute power, we ascribe something that we do not ascribe to it when we compare it with his ordered wisdom. (St. Thomas, Q. Disp. de Potentia, q. 1, a. 5, ad 5um)

Thus, in notion, these are not coextensive. Something that is possible to God’s absolute power but not to His ordered power is a hypothetical possibility. In the order of creation ad extra, what God has actually done, one Thomistic commentator notes: “Divine omnipotence works only as an ordered power. It produces nothing which is not determined according to the dispositions of His wisdom.” (L. Vachon, “Les preuves naturelles de l’existence des substances separees,” 26)

Now we can answer our first question, namely, is it possible for God to have made the universe differently? By answering the question above—whether God could have made the universe better—at least partly the affirmative, St. Thomas implicitly answers this first question also. God could have made the universe differently. In the body of the article, however, St. Thomas distinguishes various ways in which God could make this universe better, and these are always accidental modes of being. Were God to make the essences of things better by creating more kinds of creatures and “filling in” the hierarchy of being, this would essentially change the universe insofar as a new unity of order, a new form of universe, would obtain. Thus, making a different universe is within God’s absolute power, it is logically possible. The reason why He did not do so much be found by considering His ordered power.

The article in question from the Sentences commentary also echoes the opening quodlibet question. Indeed, St. Thomas virtually answers the quodlibet question in the first sed contra, and does not outright deny the answer in the reply to the sed contra (to qualify its assertion somewhat):

On the contrary: According to the Philosopher, what is whiter is intermingled with less black. So also, what is better is intermingled with less evil. Yet God could have made a universe in which no evil existed. Thus, since many things are evil in this universe, it seems that God could have made the universe better.

Reply to On the Contrary 1: A universe in which there was no evil would not be as good as this universe, because there would not be as many natural goods in such a universe as in this one, in which there are certain natural goods which are not attached to evil and certain ones which are. It is better that both kinds exist than only one of them. (St. Thomas, In I Sent., d. 44, q. 1, a. 2)

That is, while it is absolutely possible for God to have made a universe without evil in it, such a universe would not be better than this universe! The reasoning for this is that those natural good which are adjoined to evils in this universe would not exist in the alternate universe.

This leads us naturally to our second question.

2. Why did God create a universe with ontological evils?

To prepare to answer this question, let us consider—at some length—how St. Thomas answers a similar question in Summa contra Gentiles, Book III, ch. 71Quod divina providentia non excludit totaliter malum a rebus—“That divine providence does not wholly exclude evil from things.” We will look at a few of the arguments from this chapter.

The second argument that St. Thomas gives (out of seven) appeals to the definition of what makes a universe:

Moreover, perfect goodness would not be found in created things unless there were an order of goodness in them, in the sense that some of them are better than others. Otherwise, all possible grades of goodness would not be realized, nor would any creature be like God by virtue of holding a higher place than another. The highest beauty would be taken away from things, too, if the order of distinct and unequal things were removed. And what is more, multiplicity would be taken away from things if inequality of goodness were removed, since through the differences by which things are distinguished from each other one thing stands out as better than another; for instance, the animate in relation to the inanimate, and the rational in regard to the irrational. And so, if complete equality were present in things, there would be but one created good, which clearly disparages the perfection of the creature. Now, it is a higher grade of goodness for a thing to be good because it cannot fall from goodness; lower than that is the thing which can fall from goodness. So, the perfection of the universe requires both grades of goodness. But it pertains to the providence of the governor to preserve perfection in the things governed, and not to decrease it. Therefore, it does not pertain to divine goodness, entirely to exclude from things the power of falling from the good. But evil is the consequence of this power, because what is able to fall does fall at times. And this defection of the good is evil, as we showed above. Therefore, it does not pertain to divine providence to prohibit evil entirely from things. (Ibid., n. 3)

The first part of the argument is ordered to manifesting the various ways in which the universe, in order to be a perfect imitation of the divine goodness (insofar as this is possible), requires an order or hierarchy of diverse kinds of beings. The perfection, beauty, and even multiplicity of things follows from this principle. Then St. Thomas specifies that this hierarchy implies beings that infallibly achieve their good and beings that can fail to achieve their good. The reason that both types of beings make the universe better will be found below: the presence of failure allows for types of goodness that otherwise would not exist.

We should carefully ponder what it required in a being such that it can fail to attain its good, that is, it is defectible. The reason for defectibility is to be found in a quasi-contrariety within the essence of things, namely contingent beings, and in particular in human beings. Charles De Koninck describes this as follows:

An angel cannot by itself fail to attain the end of its person or the common good proper to its nature. But the good of the angelic nature is not the highest good which is God as He is in Himself. But God commanded that the angels should order themselves to this highest good. Since the proper end of the angelic nature bears in this respect the character of an end which is to be ordered to a higher end, which ordering is not assured by the nature of the agent, its will can fail to attain to the higher end, and, by way of consequence, it can fail also to attain its proper end.

If the angel is not per se fallible except in regard to its supernatural end, man on the contrary is able per se to lose even his natural end. “There is this difference between man and  the separated substances, that the same individual has several appetitive powers, of which some are subordinated to others; this does not occur at all in the separated substances, although the separated substances are subordinated one to another. But sin occurs in the will whenever the inferior appetite deviates in any way. Therefore just as sin in separated substances would occur if one deviated from the Divine order, or if an inferior deviated from the order of a superior while the latter remained in the Divine order; thus also in one man there are two ways in which sin may occur. First man may sin when the human will does not order its proper good to God; this way man has in common with the separated substances. In another way man may sin if the good of the inferior appetite is not ruled according to the superior; as when the pleasures of the flesh, which are the object of the concupiscible appetite, are not sought observing the order of reason. This latter kind of sin does not occur in separated substances.” (SCG III.109) Even within man, there is a superiority of the good of the intellect over the good of the senses. The union of intellectual nature and sensible nature makes man subject to a certain contrariety. Sensible nature carries us towards the sensible and private good; intellectual nature has for its object the universal and the good understood according to its very character of goodness, which character is found principally in the common good. The good of the intellect, from which man receives his dignity as man, is not assured by man’s own nature. The sensitive life is first in us; we cannot attain to acts of reason except by passing through the senses which, considered in this way, are a principle. As long as man is not rectified by the cardinal virtues which must be acquired, he is drawn principally towards the private good against the good of the intellect. For man there exists, even in the purely natural order, a liberty of contrariety which makes him fallible per se in relation to the attainment of his end. To achieve his dignity, he must submit his private good to the common good. (Charles De Koninck, The Primacy of the Common Good)

This helps us to understand more deeply the great good that fallibility or defectibility entails, at least per accidens. It also allows us to see that it is logically possible, on God’s absolute power, to make a universe free of evil—as St. Thomas claims in the article from his Sentences commentary. That is, if God were to make a universe consisting entirely of angels, they would by their nature infallibly achieve their natural ends. However, while such a universe is possible, it is not best—thus in God’s ordered power, creating the universe in wisdom, He ordains otherwise.

The third argument appeals to a type of Divine subsidiarity and—like the first argument, which was skipped—appeals also to the notion of secondary causality.

Again, the best thing in any government is to provide for the things governed according to their own mode, for the justice of a regime consists in this. Therefore, as it would be contrary to the rational character of a human regime for men to be prevented by the governor from acting in accord with their own duties—except, perhaps, on occasion, due to the need of the moment—so, too, would it be contrary to the rational character of the divine regime to refuse permission for created things to act according to the mode of their nature. Now, as a result of this fact, that creatures do act in this way, corruption and evil result in things, because, due to the contrariety and incompatibility present in things, one may be a source of corruption for another. Therefore, it does not pertain to divine providence to exclude evil entirely from the things that are governed. (St. Thomas, ScG II.71, n. 4)

This argument makes more explicit what was only implied by the role of defectible creatures in the previous argument: namely, the principle of contrariety and incompatibility in things. This principle will occupy us in what follows. Apart from the quasi-contrariety within human nature, what are examples of the principle of contrariety in the created order? St. Thomas provides examples in the following arguments.

The fourth and fifth arguments should be considered together:

Besides, it is impossible for an agent to do something evil, unless by virtue of the fact that the agent intends something good, as is evident from the foregoing. But to prohibit universally the intending of the good for the individual on the part of created things is not the function of the providence of Him Who is the cause of every good thing. For, in that way, many goods would be taken away from the whole of things. For example, if the inclination to generate its like were taken away from fire (from which inclination there results this particular evil which is the burning up of combustible things), there would also be taken away this particular good which is the generation of fire and the preservation of the same according to its species. Therefore, it is not the function of divine providence totally to exclude evil from things. (Ibid., n. 5)

Furthermore, many goods are present in things which would not occur unless there were evils. For instance, there would not be the patience of the just if there were not the malice of their persecutors; there would not be a place for the justice of vindication if there were no offenses; and in the order of nature, there would not be the generation of one thing unless there were the corruption of another. So, if evil were totally excluded from the whole of things by divine providence, a multitude of good things would have to be diminished. And this is as it should be, for the good is stronger in its goodness than evil is in its malice, as is clear from earlier sections. Therefore, evil should not be totally excluded from things by divine providence. (Ibid., n. 6)

The example in the fourth argument is useful for the quodlibetal question because it uses an example of a natural or ontological evil: fire’s destructive capacity. Likewise, the fifth argument gives the example of the natural evil of corruption, or the ceasing-to-be of an individual substance, which is the condition for the generation or coming-into-being of a new substance. The biological order is replete with examples of this. Thus, in these two paradigmatic examples of physical and chemical forces and biological conditions, St. Thomas swiftly draws our attention to the entire order of what we would now call the operations of the laws of nature.

What is crucial (but unstated) in these examples is the aforementioned principle of contrariety. This principle is present in two ways in the natural order: first, in change itself, and second, in the relationship between agents and patients. Thus, first, in any change, something is first in a state contrary to what it will be in at the end of the change (first it is here, then there, an object is first hot then cold, etc.). This means that any change where one object suffers a change to a worse state (and this is especially evident in living things) implicates the principle of contrariety. Second, apart from contrariety in changes, there is also contrariety in the agent causes bringing about change. An agent must act on a patient, and this is not always a good thing for the patient. Again, this is especially clear in the biosphere—food is only a fruit of death.

This allows us to understand what St. Thomas meant by the “incompatibility” in things in the third argument. Thus, we can hypothesize at this point—and consider more fully when we answer the third question—that a universe without natural evils would be a universe without change and without organic life. It remains to be seen if this hypothesis is true.

Now, the sixth argument takes this principle of contrariety and places it back in the schema of the universe taken as a whole, of which contrary agencies are parts:

Moreover, the good of the whole takes precedence over the good of a part. It is proper for a governor with foresight to neglect some lack of goodness in a part, so that there may be an increase of goodness in the whole. Thus, an artisan bides the foundations beneath earth, so that the whole house may have stability. But, if evil were removed from some parts of the universe, much perfection would perish from the universe, whose beauty arises from an ordered unification of evil and good things. In fact, while evil things originate from good things that are defective, still, certain good things also result from them, as a consequence of the providence of the governor. Thus, even a silent pause makes a hymn appealing. Therefore, evil should not have been excluded from things by divine providence. (Ibid., n. 7)

Note how the principle of defectibility enters into the picture. Evil originates from what defect soever, the old adage goes. Thus, any aesthetic blemish whatsoever, or any physical weakness, or any unfortunate chance event—however minor—are natural evils. What is the root cause of this defectibility?

Here we should note that contrary formal principles (such as the form of fire and the form of combustible materials) are not as such principles of defectibility. As we saw above with De Koninck’s discussion of human nature, opposed principles within one being can cause a failure to achieve that being’s end. However, the general notion of defect includes not only a failure to achieve one’s end but also a falling short what is formally within the notion of a given nature. Thus, we recognize birth defects or injuries as privations or failures of what a given nature ought to be, what could have been but was not realized.

This general note of defect must be resolved to material causality. Because material causes are open to many formal realities, and many of these realities are opposed and even incompossible, it follows that matter is the root of defect insofar as the realization of some nature can be interfered with. The reason is simply that matter is capable of more than one realization—of more than one state or mode of being. Thus, the generation and growth of organisms can be interfered with because the material causes of those processes are potent towards other outcomes. (In the ancient cosmology, the heavenly spheres had no potency apart from their ability to move, and even this was unable to be interrupted by natural causes; their matter was fully realized and thus incorruptible. For this reason, there were no chance events in the ancient heavens. Such is far from the case in our modern account!)

The seventh and final argument focuses in on a particular part in the universe, namely, the human being. However, it can be skipped in our discussion. Let us summarize what St. Thomas has taught us before moving on to our final question, and especially with regard to what was just noted about material causality. First, we noted that a universe free of defectible creatures and thus a universe containing no natural evils would have to be a universe of angels. Second, a universe without natural evils would appear to be a universe without change and without organic life. Third, a universe without natural evils (especially those occurring by chance events) would be a non-material universe. At least, these were our suspicions. However, the question at hand does not regard the current order of things, but an alternate universe.

3. Can a universe exist that does not directly or indirectly depend upon contrariety to achieve the good?

We should first note the precisions which we have been able to introduce into our question. When asking about an alternate physical universe, we are asking about what is absolutely or logically possible within God’s absolute power, not within His ordered power. Thus, we are wondering if there is something intrinsically impossible about a universe whose physical order contains no natural evils. So, we should also note that we are not considering those parts of the universe that are angelic. We are only considering the physical cosmos—or, at least, an alternate version of it.

Thus, our question stands at this: Could God make a physical universe free of such natural evils? However, in light of the above discussion, we should be able to rephrase the question. We should rather ask if a physical universe could exist that does not depend in any way upon the principle of contrariety to achieve the good.

To which we can answer that it would seem impossible for such a universe to exist. In order for the negative answer to be true, it must be the case that an indefectible physical universe is a contradiction in terms. Now, a physical universe is one composed of an order of physical substances (the cosmos), and those substances are themselves composed of matter and form. Thus, on the one hand, a physical universe without the principle of contrariety could not achieve the good through agent-patient relationships that involved generation and destruction of individual substances. On the other hand, a physical universe without the principle of contrariety would not contain substances composed of matter and form, insofar as matter is the principle of defectibility in natural substances (one should note, that the indetermination present in form—its inability to completely master matter—is also a co-principle). That is, an indefectible natural order would not be an order of natures in the same sense.

This idea is expressed by Charles De Koninck in this passage:

From a strictly philosophical point of view, “laws of nature” means either the natures as measured by eternal law [the ratio of things in the Divine Mind], or these same natures as measures of the activity by which natural beings achieve and accomplish their end. It is the latter meaning that occupies us now, one in which the laws of nature are called laws only by analogy—unlike the natural or moral law.

. . . As soon as it is a question of the participated laws in the universe which are identified with natures—and note that nature is not law insofar as intrinsic and thus necessary measure, but as measure of the motion distinct from it and of which it is the principle and cause—it is impossible that they necessitate the activities which spring from the nature without nature ceasing to be nature and the laws becoming contradictory. In fact, if these laws necessitate activities, they would no longer be laws, for necessity considered in itself is above the law—necessitas non subditur legi. If natures could infallibly attain their ends only by means of activities entirely predetermined in their causes, they would be forms and matters entirely determined ad unum, they could not be intrinsic causes of motion—motion being taken here in its proper sense. And entirely determined form is not a nature; a totally actuated matter is contradictory. If future activities were perfectly predetermined in nature, they would no longer be ordinanda [ordainable], but ordinata [ordained]. (Charles De Koninck, “The Problem of Indeterminism”)

That is, De Koninck’s contention is that it is of the essence of nature that it be fallible, and not predetermined, because natures are not entirely determined ad unum, to one effect. A physical universe that contains all events in a determined way would not be a physical universe such as we have it now. This is because the principle of contrariety and defectibility is not to be found within it.

Thus, the root reason for the apparent logical impossibility of God to make a material universe free of natural evils lies, radically, in the nature of matter. This is not because matter itself is evil, but rather because matter is the potentiality for a range of goods, some of which are contrary to each other and in various respects incompatible. In other words, the essence of the physical cosmos consists in an order of substances that are intrinsically composed of parts that of their nature permit contrariety and defect. A physical universe without these principles would really just be a universe full of angels by a different name.

So: do we have a logical impossibility?

We should first qualify this answer somewhat and note that,—and this is implicit in St. Thomas’ principles that answer the question if God could make a better universe—on both the essential and the accidental orders, it is entirely possible that God make a universe in which the physical laws give rise to natural evils of a lesser degree (e.g., fewer diseases could exist, or the ones that exist could be less virulent). However, this is not the same as claiming that a physical universe can exist without the principles of contrariety and defect.

However, we should note a further qualification. Perhaps it were possible that God create the physical universe in a state of achieved perfection. That is, even though the principles of contrariety and defect would still remain, they would not be necessary to achieve further ends or goals. The reason for this would be that the universe would come into being in the state of having achieved the perfection that God intended for such a universe.

Nonetheless, is such a creation also a logical impossibility? As we shall see below, it is not an impossibility that God bring the universe to the state of beatified perfection—this is a proposition of revelation in the Catholic faith. Thus, if it is possible as an end state, why is it impossible for the physical universe to be created in its end-goal state? Why could the universe not begin and always remain an Eden? However, it is at least difficult to conceive how such a logical possibility could be discovered apart from revelation, because it is the essence of a mobile being to begin in its terminus a quo and proceed to its terminus ad quem. A mobile being that does not move—and analogously, a universe that does not undergo a series of motions in its cosmic history to achieve its goal—seems to be contrary to the nature of being a mobile, changing being.

Still—it must be logically possible if it is possible as an end. What can exist as a goal cannot be intrinsically impossible in itself, and there is no necessity on God’s part that He traverse the means that creatures must use so as to achieve the goal. Our knowledge of such an end state of perfection to the universe, philosophically speaking, seems dubious—could it be obtained from an ideal projection or idealized view of universal progress?—but at least the possibility that the universe be created in an end-goal state is logically possible if a mobile being need only be apt so as to move towards its goal and achieve it. Furthermore, there is a kind of motion which is imperfection and the motion of the perfect, which is activity and a sort of rest. The universe’s end lies in the latter, and so nothing prevents it from being created in such a state.

However, this also requires that we answer the quodlibetal question in the negative, simply speaking. A universe which must undergo motion to achieve its end cannot be free of natural evils, insofar as these are bound up in the notion of nature. This is a universe which must move in the sense that motion is an imperfection. Under the qualification that the universe is created in its state of achieved perfection, then there would come into effect a different physical order, and concomitant laws of physics that are different, that maintains this perfection in a state of active rest.

Yet, in the ordered power of God, that is, by His wisdom, it is still better that the universe must undergo motion to achieve perfection: “For we know that every creature groaneth and travaileth in pain, even till now.” (Romans 8:22)

As confirmation of this view, we can look at what St. Thomas claims concerning the end of the physical world (see also Q. Disp. de Potentia, q. 5, aa. 7–10). This is taken from the bodies of his replies to the eighth and ninth articles. We will let the Angelic Doctor have the last word, but notice how his arguments support the thesis just elaborated. It is especially pertinent to note how St. Thomas goes about eliminating various “effective physical laws” from the material bodies insofar as they were explained by the science of his day. What remains are physical bodies operating by natural laws in a state of elevated perfection, adapted to the mode of existence of active-rest or operation that characterizes the beatitude of the saints and angels.

It must be observed however that a body has a twofold action: one according to a property of a body, inasmuch as it acts by movement (for it is proper to a body that it be moved so as to move and act), the other by attaining to the order of separate substances and receiving a share in their mode of operation: thus lower natures are wont to share in a property of a higher nature, for instance certain animals share in a certain likeness to prudence which is proper to man. This latter action of a body does not aim at the transformation of matter, but at communicating a certain likeness to its form to the ‘medium,’ which may be compared to the spiritual ‘intention’ which things impress on the senses or intelligence: thus the air receives the light of the sun, and the ‘medium’ receives a reflection of coloured images. Now both these actions are caused here below by the heavenly bodies. Thus fire by its heat transforms matter by virtue of a heavenly body; and visible bodies reflect their images in the medium by the power of light, the source whereof is in a heavenly body. Hence if both these actions on the part of a heavenly body were to cease, no action would remain in this lower world. But if the heavens were to cease to be in motion, the first action would cease, but not the second: and consequently when the heavenly movement ceases, in this lower world the action whereby the ‘medium’ is illumined and affected by sensible things will continue, but not the action whereby matter is transformed and which results in generation and corruption. (St. Thomas, Q. Disp. de Potentia, q. 5, a. 8, c.)

I answer that in that renewal of the world no mixed body will remain except the human body. In support of this view we shall proceed in the order prescribed by the Philosopher (Physics II) namely by considering first the final cause, then the material and formal principles and lastly the moving causes.

The end of minerals, plants and animals is twofold. One is the completion of the universe, to which end all the parts of the universe are ordained: yet the aforesaid things are not ordained to this end as though by their very nature and essentially they were required for the universe’s perfection, since they contain nothing that is not to be found in the principal parts of the world (namely the heavenly bodies and the elements) as their active and material principles. Consequently the things in question are particular effects of those universal causes which are essential parts of the universe, so that they belong to the perfection of the universe only in the point of their production by their causes, and this is by movement. Hence they belong to the perfection of the universe not absolutely speaking but only as long as the latter is in motion. Wherefore as soon as movement in the universe ceases these things must cease to exist.—The other end is man, because as the Philosopher says (Politics I, 5) things that are imperfect in nature are ordained to those that are perfect, as their end, with the result that as he says (ibid.) since an animal’s life is imperfect as compared with a man’s which is perfect simply, and a plant’s life as compared with an animal’s, it follows that plants are for animals being prepared by nature to be the latter’s food; and animals are for man, to whom they are necessary as food and for other purposes. Now this necessity lasts as long as man’s animal life endures. But this life will cease in that final renewal of the universe, because the body will rise not natural but spiritual (1 Cor. 15:44): hence animals and plants will also cease to exist then.

Again this is consistent with the matter and form of these things: for since they are composed of contrary elements, they contain within themselves an active principle of corruption. Wherefore if they were prevented from corrupting by an external, principle only, this would be in a manner violent and inconsistent with perpetuity, since that which is violent cannot last for ever according to the Philosopher (De Caelo I). Nor have they an internal principle to preserve them from corruption, because their forms are in themselves corruptible through not being self-subsistent but depending on matter for their being. Consequently they cannot remain for ever identically the same; nor specifically the same when generation and corruption cease.

The same conclusion follows from the consideration of the moving cause. In plants and animals to be is to live, and in corporeal things this cannot be without movement. Hence animals die when the heart ceases to beat, and plants when they lack nourishment. Now these things have no moving principle that is not dependent on the first mobile body, since the very souls of animals and plants are wholly subject to the influence of the heavenly bodies. Therefore when the heavenly movement ceases it will be impossible for them to retain movement or life. It is evident then that at the renewal of the world the aforesaid things will be unable to remain. (St. Thomas, Q. Disp. de Potentia, q. 5, a. 9, c.)

 


St. Thomas Aquinas, In I Sent., d. 44, q. 1, a. 2

Whether God could have made a better universe


Obj. 1: It seems that God could not have made the universe better. Because, according to St. Augustine, the singular things which God established are good; however, all things together are very good. But what is superlatively good cannot be better. Therefore the universe cannot be better.

Obj. 2: The universe includes every good. But nothing can be better than every good. Therefore, God could not have made the universe better.

Obj. 3: According to Dionysius, the good and the better are found in things insofar as certain things participate more in the divine goodness than other things. For instance, living things are given preference in this regard compared to things that merely exist, and so forth. But all the divine perfections communicable to creatures have been communicated to certain creatures. Therefore, it seems that the universe could not have been better.

Obj. 4: Insofar as something is more ordered, it is better. Hence, evil is defined by St. Augustine through the privation of order. But in the universe, nothing is disordered, since even evil itself is ordained by God, as was said above (d. 36, q. 1, a. 2). Therefore, it seems that the universe could not have been better.

On the contrary: According to the Philosopher, what is whiter is intermingled with what is black. Thus, what is better is also intermingled with evil. Yet God could have made a universe in which no evil existed. Thus, since many things are evil in this universe, it seems that God could have made the universe better.

Furthermore: If something equal is added to something greater, the whole will become greater. Likewise, if something better is added to something better, the whole will become better. Thus, two angels are better than an angel and a stone. So, if some single part of the universe were to be an angel, the universe would be much better. However, God could do this. Therefore, etc.

I answer that: According to the Philosopher in Book [12]⁠1 of the Metaphysics, the good of the universe consists in a twofold order, namely (1) in the order of the parts of the universe mutually towards each other, and (2) in the order of the whole universe to the end, which is God Himself—just as in an army there is an order of the parts of the army mutually towards each other, according to their various duties, and there is an order to the good of the general, which is victory. And this second order is the more important, for the sake of which the first order exists.

(1) Thus, taking the good of order which exists in the parts of the universe mutually towards each other, it can be considered either (a) as to the ordered parts themselves, or (b) as to the order of the parts.

(a) If it is considered as to the parts themselves, then it is intelligible that the universe could be better: (i) either through the addition of more parts, namely, were many other species created and the many degrees of goodness were filled which can be filled, since even between the highest creature and God there is an infinite distance. Thus, God could have made and can make the universe better. But that universe would be related to this one as a whole to a part, and thus they would neither be wholly the same nor wholly different, and this additional goodness would be by the mode of discrete quantity.

(ii) Or this could be understood as to the parts becoming better intensively, as it were, by the change of all its parts for the better, because if some parts were bettered and other not, then there would not be a good of order among them, as is clear in the harp. If all of its strings were improved, there would be a better harmony; but is only some were improved, then there would be dissonance. This betterment of all the parts, however, [i] can either be taken according to accidental goodness,  and thus it would be possible that this improvement by God take place with the same parts remaining in the same universe; [ii] or it can be taken according to essential goodness, and even this is possible for God, who is able to create an infinity of other species. (But in this case, they would not be the same parts, and consequently not the same universe, as is clear from the aforementioned.)

(b) If, however, it is taken according to the very order of the parts, (i) this cannot become better by the mode of discrete quantity, unless some addition be made to the parts of the universe, because nothing in the universe is disordered. (ii) But intensively there could be something better, while the same parts remain, according to the order that follows upon what is accidentally good, for something redounds to a greater good to the degree that the order is better. (iii) But the order which follows upon what is essentially good cannot be better, unless other parts of the universe and another universe come to be.

(2) Likewise, the order which is for the sake of the end can be considered (a) either on the part of the end itself, and thus it cannot be better, such that the universe be ordered to a better end, since nothing can be better than God. (b) Or as to the order itself, and thus insofar as the good of the parts of the universe and their mutual order towards each other increases, a better order to the end could exist, because the closer to the end are the parts, the greater similitude to the divine goodness, which is the end of all things, accrues to them.

Reply to Obj. 1: St. Augustine speaks of the order of the universe on the supposition of the same nature of such parts, because thus a better order could not exist, as was said above.

Reply to Obj. 2: We are not speaking of the universe as to the very name, but as to the very thing, which is called a universe in a way—in which even though everything which is good in actuality is contained, nonetheless it does not contain every good which God could make.

Reply to Obj. 3: There are many modes of partaking in the same divine perfection, just as divine wisdom is participated by the intellectual substances in one way, and by rational beings, namely human beings, in another, and it even extends to the brute animals which have sensate cognition. Therefore, even though all perfections communicable to creatures have perhaps been communicated to them, nonetheless they have not been according to all the modes in which it is possible for creatures to participate.

Reply to Obj. 4: Even though the order of the universe could not have been better as to the order of the parts of the universe themselves, nonetheless it could have been better if it were ordered to a better good as a proximate end. This would have occurred if better parts of the universe had existed, as was said.

Reply to On the Contrary 1: A universe in which there was no evil would not be as good as this universe, because there would not be as many natural goods in such a universe as in this one, in which there are certain natural goods which are not attached to evil and certain ones which are. It is better that both kinds exist than only one of them.

Reply to On the Contrary 2: Even though an angel is, absolutely speaking, better than a stone, nonetheless both natures are better than one alone, and therefore that universe is better where there are angels and other things than a universe where only angels exist, because the perfection of the universe follows essentially upon the diversity of natures which fill the diverse degrees of goodness, and not the multiplication of individuals in one nature.


1 The text reads Book 11, but the citation is to Book 12 (see Metaphysics, Book 12, ch. 10). Prior to 1271, William of Moerbeke had not translated Books 11, 13, and 14. Thus, St. Thomas’s references to Book 12 prior to this date always number it the eleventh book of Aristotle’s Metaphysics.