The following is my presentation at the recent meeting of the American Catholic Philosophical Association. It is a slightly modified version of a previous Spanish presentation in Santiago, Chile.
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The Relevance of Neo-Aristotelian Formal Causality
to the Meta-Law Dilemma in Cosmology
This paper is a part of a larger project that aims to turn philosophical preconceptions from the notion that the cosmos is intelligible only through physical-scientific laws and towards the idea that the scientific intelligibility of the universe’s laws are such as they emerge from formal causality. The immediate aim in this paper is to dialectically engage a facet of this larger goal. This involves considering part of the philosophy of nature proposed by Roberto Mangabeira Unger and Lee Smolin in their two-part book, The Singular Universe and the Reality of Time: A Proposal in Natural Philosophy.1 They attempt to reshape the future of scientific cosmology by defending temporal naturalism, an ontology distantly inspired by Heraclitus. Among the many challenges faced by this project is the “meta-law dilemma.” I will sketch the nature of the meta-law problem, review the solution given by Unger and Smolin, and then propose why and to what extent an Aristotelian understanding of formal causality is the more promising answer. The general strategy here is to find in our contemporaries a familiar dialectical topos, namely one that engages Heraclitean difficulties as Aristotle does when discussing fundamental principles of nature, and thus draw out a perennially available, dialectical conclusion in the context of contemporary science.
§1. The meta-law problem
The “meta-law problem” is not original to Unger and Smolin. John Archibald Wheeler once encapsulated it thus: “There is no law except the law that there is no law.”2 Barrow and Tipler recount the development of ideas about lawless physics as follows, after noting that more and more fundamental constants and laws were shown to be mutable:
The natural conclusion of this trend from more laws of Nature to less is to ask the overwhelming question: ‘Are there laws of Nature at all?’ Perhaps complete microscopic anarchy is the only law of Nature? If this were even partially true, it would provide an interesting twist to the traditional Anthropic arguments which appeal to the fortuitous coincidence of life-supporting laws of Nature and numerical values of the dimensionless constants of physics.3
Barrow and Tipler go on to claim that, given this inductive trend, it may be possible that the rules governing matter and energy arise at random in the universe and that the stable features of atoms and the apples made out of them are only a “selection effect,” i.e., we unsurprisingly find them in our universe now, at low energies and ‘human-scale’ densities, because our own existence is predicated upon their being thus and so.4 On this view there is no intrinsic logic in the cosmos or teleological necessity for our own existence.
The essential background for understanding the meta-law problem in Unger’s and Smolin’s work is their idea of temporal naturalism. This notion allows them to, in Barrow and Tipler’s words, “generate the ensemble of possibilities within a single universe.”5 Temporal naturalism means that everything that exists does so by being contained within and subject to time. They define “time” as the very change of change, or the priority of becoming over being, in a manner reminiscent of the Heraclitus the Obscure. If everything that exists is subject to change, this includes the very laws of nature themselves. They are subject to change within the history of our given, unique universe and possibly through successive “generations” of universes.6 Between such stages, the laws governing phenomena are subject to change.
How then does the meta-law problem arise? This is the dilemma’s first horn.7
Suppose that the change of laws of nature is itself governed by laws: higher-order laws or meta-laws. Then the problem of the historicity of nature and of its regularities will simply recur at that higher level. We will have gained little or nothing in our effort to recognize the inclusive reality of time as well as the occurrence of a causality that may be lawless. Either we concede that the regularities of nature are themselves open to change, or we claim them to be exempt from time and change. We have simply postponed the problem, or transferred it from one level of explanation to another.
The recursion problem seems clear. The reason that Unger and Smolin are motivated by this recursion problem in the first half of the dilemma is their commitment to the “inclusive reality” of time. However, it is further supported by what they call “the cosmological fallacy” that arises from the use of a mathematical paradigm when understanding nature. That is, they claim that a mathematical way of understanding nature is “selective” of what is real and cannot exhaustively explain nature. It is a fallacy, they say, to apply what they call a “Newtonian” model of doing science to the whole universe as such. A “system” in this Newtonian paradigm is always a partial study of a subsystem of the universe; it cannot be applied to the universe as a whole. Thus, on this line of thought, it would be an error to ask about the mathematical law governing the change of laws in universe as a whole.
I proceed to the other horn of the dilemma.
Suppose, on the other hand, that the change of the laws is not itself law-governed. Then it seems that it is uncaused, which is to say arbitrary or at least without explanation, whether deterministic or probabilistic. Then indeed the idea of a history of the universe would have driven us to explanatory nihilism. Those would have been right who feared that a full recognition of the reality of time would undermine the project of science.
That is, in the absence of using laws as our sources of explanation in science, the alternative in the meta-law dilemma seems to be complete irrationality. However, Unger wishes to maintain a distinction between causal explanation and law. That is, “causes” include more than “laws” when it comes to explaining nature. It is not necessary that the inability to appeal to laws means we are cut off from causes as explanations.
In our ordinary experience, we regularly make causal judgments that assume some measure of stability in the workings of nature but make no reference, however remote, to general connections like those that physics represents in mathematical language.
The appeals to “ordinary experience” as well as “some measure of stability in . . . nature” are noteworthy. Unger doubts the sufficiency of laws of nature as causal explanations because, somehow, our “ordinary experience” reveals another way.
§2. Unger and Smolin’s proposed solutions to the meta-law problem
While Unger and Smolin propose a broad network of suggestions to solve the meta-law problem, I focus on four of their ideas: possibility landscapes, the adjacent possible, cosmological natural selection, and causal continuity. Borrowing language from evolutionary biology, they propose that the laws between stages of the universe or between successive universes change according to a “possibility landscape” of various laws, just as species evolve by exploring (in random or stochastic leaps) the “adjacent possibilities” available to them. This “adjacent possible” is “what [a phenomenon] can become next, given what it is then.”8 Our own existence in a universe with initial conditions and laws that permit human life can therefore be explained via a process of “cosmological natural selection” that operates on this possibility landscape. They oppose this “cosmological natural selection” to using some variation of the anthropic principle to select out our existence from a vast array of multiple, unconnected universes. The singular universe, they maintain, could evolve in either a linear or a branching fashion. In either case (and whether the innovation of new laws of physics occurs within one cosmos or between successive cosmoses), there is a “causal continuity” which could preserve vestiges or markers of the prior stage in the posterior stage. This is necessary as a philosophical proposal, for it permits the empirical testability of their theory. That is, it might be possible to confirm that we live in a child universe by looking for trace elements of a parent universe.
Causal continuity they describe as follows:
Causation always involves the force of sequence: the shaping of a before on an after. It need not always require that this shaping by sequence assume regular and recurrent form.9
Thus, this sequence has a “form,” just not one that is necessarily law-like, i.e., “regular and recurrent.” This regularity would make nature mathematically amenable. Thus, this causal continuity is of such a character that it is broader than what is mathematizable without giving way to the feared “explanatory nihilism.” Causal continuity is also described as follows:
[Why causality in the early universe] need not imply the break-up of causal connections is that in nature, as we observe it, what comes before always shapes what comes later, even if the mechanism of influence may change. … Nature can work only with the materials at hand, all of them products of transformation, including the transformation of transformation, which is the character of time.10
Laws that are assumed to change include the most fundamental, “principle” laws such as the principle of least action, the conservation of energy and momentum, the degradation of energy (entropy), and the principle of relativity: “[The principle laws] form part of time-drenched and changing nature, although they represent the part that changes least or less often. The fire must be yet greater for them to burn. Nevertheless, they too can change.”11 Here, Unger practically paraphrases Heraclitus: “This ordered [cosmos], which is the same for all, was not created by any one of the gods or of mankind, but it was ever and is and shall be ever-living Fire, kindled in measure and quenched in measure.”12
We should note four features about this proposal. I label them as follows: (1) stochastic causal connections, (2) anti-Platonism, (3) anti-nominalism, (4) real temporal influence. First, in order to avoid the first horn of the meta-law dilemma, the causal continuity or adjacent possible cannot itself be law-governed, but the stages must be realized at random. That is, “shaping by sequence” need not be “regular and recurrent.” Utterly unique changes from one regime of physical laws to the next are allowed.
Second, there is no higher-order mathematical law governing the landscape of possibilities because Unger and Smolin deny the reality of a Platonic realm of mathematical objects that causally influence the universe. Mathematics (on their view) is only “selectively real” and not “hyper-real” in a Platonic sense. This fits with our first observation and demands that Unger and Smolin envision that something exists which is a type of condition or cause that is itself not of a mathematical character, although it is susceptible to mathematization.
Third, because of their focus on empirical investigation, and to avoid the second horn of the dilemma, the changes in the laws of nature and the accompanying concepts of “the adjacent possible” and “causal continuity” cannot imply nominalism. That is, our concepts describe real, stable, and repeatable features of the universe, even if they are changing features. As Unger states: “The relative stability of the laws of nature is a feature of the established [i.e., cooled down, present-day] universe. Their relative mutability is a characteristic of the universe in formation or, more generally, in its extreme moments.”13
Fourth, Unger maintains that causal influence persists or lasts, in some way, through time, even in extreme states of energy and density; these stages are such that while “the range of the adjacent possible may be large, the before may nevertheless continue to influence the after in time. Causality survives laws.”14 In other words, the causal capacity of the universe is one of its unchanging features.
§3. The resolution of the meta-law dilemma through an appeal to form
Let us draw out three consequences of these four features. (A) The first consequence uses (2) and (3), anti-Platonism and anti-nominalism. In discussions of causal continuity and the adjacent possible, it is hard for Unger to stay away from verbs such as “shape” and “influence,” as well as qualifiers such as “finite conditions” and “traces” or “vestiges” of prior stages in the current stage of laws governing phenomena. On the one hand, the shape, finitude, and trace elements that characterize the changes of laws are not considered in light of a Platonic “possible space of laws.” On the other hand, however, Unger and Smolin are not nominalists: our descriptions reach real features of things. Let us call the shape, finitude, or trace elements that characterize the quasi-stable existence of laws and stand like inflection points between possible transition between sets of law a “causal form.”
Is this causal form merely a name that we ascribe to the universe? If so, then what makes our statements about these laws true at any point in time? Our authors cannot appeal to the substantial existence of mathematical entities, for Unger and Smolin maintain that mathematics is only selectively real. Furthermore, as Plato famously has Socrates point out in the Cratylus, if all “causal forms” are changing, then even the truth of a single sentence cannot be guaranteed, for the subject may have altered by the time the predicate is uttered.15 If propostions about nature can be true, some “causal form” exists and is stable enough to provide a ground for the truth of that proposition. If one is neither a Platonist nor a nominalist nor an idealist, then that causal form must be somehow found in existing things.
Now, it does appear from some texts that Unger and Smolin are nominalists. For instance, Smolin claims “As each event and each causal link is unique in the history of the universe, they make up a vast set, when fully described.”16 In the absence of common natures, is not pure history the only alternative? If so, this “causal form” appears to be a very weak claim. Let us proceed to the second consequence; perhaps a reply to the doubt will appear.
(B) The second consequence draws upon the real temporal influence exerted between “stages” where different laws are operative. If these distinct stages exhibit causal continuity, then this requires that features of the prior stage affect the features that will arise in the posterior stage. Indeed, it is crucial to Unger and Smolin’s account of nature that energies, densities, and generally the features of matter be finite; thus, causal continuity and “the adjacent possible” must be marked by a “causal form” that provides finitude and limitation to the various stages of physical laws. That is, not only does this causal form fulfill a truth-making function, it also does so by providing finite (even if wildly varying) contours to the phenomena and their laws.17
This idea is very reminiscent of Heraclitus’s “logos” of his ever-changing cosmos. However, as mentioned above, there is a self-referential problem with the only stable feature of the universe being its constant change. Speakers and thinkers exist and their activity as thinkers requires more stability than that. Furthermore, the amenability of this causal continuity in the universe to mathematical models betrays a tension in Unger and Smolin’s thinking. They claim that mathematics makes true statements about the world, albeit while abstracting away from the mutability and particularity of things. It is difficult to see how mathematical statements about shape, structure, and number can be true about the world, non-conventional, yet also nominalist.
(C) The third consequence draws upon the stochastic nature of causal continuity described by Unger. This is the idea that, even if the laws were to change drastically, “the before may nevertheless continue to influence the after in time,” or in other words, “Causality survives laws.”18 This is the case even if the change from stage to stage happens at random, without a governing law in the mathematical sense. An Aristotelian way of stating this is that causality is ontologically prior to law and serves as the ground of possibility for law. Now, for the Aristotelian, stochastic behavior arises within nature due to a principle of indetermination. Classically, this source of indetermination was named “matter” or “potency”. Hence, if the contintuity between stages is of a finite order, and (please recall) we are avoiding a Platonic space of possibilities or a “multiverse” scenario, then we must maintain that the “adjacent possible” is somehow contained within in the existence of the prior stage. However, to be a pre-contained, not fully existent feature in a prior stage is a hallmark of that Aristotelian “potency” which is limited by form. This is the strongest strike against Unger and Smolin being consistent nominalists: the causality they claim to exist in the universe conditions a real possibility for change. Since the condition for the change is not itself the process of change, it is distinct from the particularity and mutation that constitutes the process.
Why is this result something that deserves to be characterized as “Aristotelian form”? First, the “causal form” required by Unger and Smolin’s account is a ground of intelligibility in things and not in an abstract space or merely in the mind. Second, this “causal form” provides contours of the actuality of conditions and laws in the universe and its stages. Finally, this “causal form” cooperates with a type of potency in things by which successive stages of laws of physics come into being. However, an innate cause of the intelligibility, determinate actuality, and the limiting principle to potentiality in nature has typically been called the formal cause by Aristotelians. That is, form is the principle of finite, kind-granting actuality that also makes a natural object knowable and true statements about it possible.
§4. Various unsatisfactory points about this solution
Before concluding, I wish to offer three points that highlight the ways in which this alternative is incomplete. First, on the Aristotelian view, causal form must exist as a part of objects, and the singular universe is in some sense a set of these objects or substances. How, then, does this Aristotelian account for the apparently universe-wide or global character of physical laws? That is, physical laws apply in the same way to objects that have putatively widely different Aristotelian natures: if there is a cat-form and a dog-form, it is still the case that dogs and cats fall under the law of conservation of momentum. Thus, the account I have offered must be completed by explaining its commitments to essentialism, on the one hand, and its commitments to the priority of causal dispositions or powers of substances and how these dispositions give rise to global, law-like behaviors, on the other hand.
The idea of dispositions or powers are real parts of things, as opposed to a Humean view of mere regularity among natural phenomena, is making a comeback in analytic philosophy. Indeed, many analytic philosophers or “neo-Aristotelian” philosophers now defend a type of essentialism about powers as underlying the explanatory work of scientific laws. In the old neo-scholastic manuals on cosmology, one frequently finds discussions of what scientific laws are in terms of analogous naming, beginning with, for instance, the human or natural law. Apart from the plausibility of the name, these discussions usually invoke the axiom that as a thing is, so it operates. It seems very plausible that if (a) the activity of individuals follows upon their being and (b) the being of things requires a formal cause with various ‘parts’ (as it were, partes formae), then it is logically possible for scientific laws to emerge globally from a selective consideration of those parts of form held in common by essentially different kinds of substances. That is, laws that apply globally across essentially different kinds are selectively true because they are reducible to parts of form. Yet more than a general “likely story” is necessary.
Second, this account of form would have to come to grips with the possibility of the evolution or stage-like emergence and innovation of formal causes through the history of the universe. (I say “possibility” because, as far as I can tell, the possibility of evolution is philosophically indemonstrable; rather, it seems easier to show that you can’t show anything about it, philosophically speaking.) As far as the presence of Aristotelian form in modern biology is concerned, its logical necessity has been convincingly argued for by Christopher Austin, among others. What these sorts of biological accounts as well as cosmological accounts have in common, as far as I can tell, is that amid all claims of stage-like, successive change in the universe, there is always an operative element of repeatable stability. If the laws of physics are emergent from the natural form of substances, then perhaps the violent transitions which Unger and Smolin require in their cosmology can be explained in a similar way. Again, details about how this occurs would have to be worked out.
Finally, this basic account of causal form would still have to answer questions regarding “why these forms” in this universe and give some account for why physical laws differ from initial conditions. In part, I think this can be solved by appealing to a distinction between essence and matter as a principle of individuation, but there is surely more than that. If natural forms terminate our inquiry because, as natures, they are the causes of the effects that we observe, then necessarily why these forms exist as opposed to others requires a resolution to ultimate causality and the Wisdom behind creation.
1 See Roberto Mangabeira Unger and Lee Smolin, The Singular Universe and the Reality of Time: A Proposal in Natural Philosophy (Cambridge University Press, 2014).
2 Quoted in John D. Barrow and Frank J. Tipler, The Anthropic Cosmological Principle (New York: Oxford University Press, 1988) 255.
3 Ibid., 256.
5 Ibid., 255.
6 The multiverse in the sense of causally unrelated universes, a “pluriverse” is rejected by our authors, as the title of their book makes clear; they maintain that the universe is unique.
7 The following three quotations are from Unger, The Singular Universe, 275–76.
8 Unger, ibid., 27. See also these descriptors, on 245: “[W]hat theres we can reach from here,” and 301, n.: “The idea of the adjacent possible differs from the notion of degrees of freedom by accommodating novel emergent properties. Thus, Stuart Kauffman used the idea of adjacent possible to describe the set of new species that may arise by speciation from the present set. On this view, the number of degrees of freedom possessed by the underlying atoms from which the organisms of each species are built remains the same.”
9 Ibid., 293–94.
10 Ibid., 279.
12 Heraclitus, DK B30.
13 Unger, The Singular Universe, 272.
14 Ibid., 287.
15 See Plato, Cratylus, 439c–440e; 439d: “But if [the beautiful itself] is always passing away, can we correctly say of it first that it is this , and then that it is such and such ? Or, at the very instant we are speaking, isn’t it inevitably and immediately becoming a different thing and altering and no longer being as it was?”
16 Smolin, The Singular Universe, 383.
17 This would be true even in the situations where Unger and Smolin propose that laws and phenomena are “coeval” or “coemergent”. That is, the contour-providing power of “causal form” provides for the shape of each stage and the features which link the two stages.
18 Unger, The Singular Universe, 287.
This presentation was produced as part of my postdoctoral research project.
FONDECYT – POSTDOCTORADO, Proj. No. 3170446.