FoS COMMISSION: JOHN TAYLOR 2

In the previous essay, I commenced an investigation into the relationship between irreducible wholeness (IW), vertical causation (VC), and horizontal causation (HC). This investigation led to the principal conclusion that IW, VC, and HC are far more intertwined than Wolfgang Smith had previously imagined. More specifically, I argued that IW gives rise to VC and that VC manifests in two distinct forms. Firstly, as the conventional instantaneous form, that is so often mentioned by Smith, and secondly as a non-standard temporal variant that I latterly introduced myself. Meanwhile, I concluded that, HC operates as a quantitative shadow of VC while also participating in VC’s transcendent light.

Building on these solid foundations, I will now continue my investigation into irreducible wholeness but this time addressing four further questions concerning the interplay of IW, VC, and HC. In doing so, I will also reflect on a matter of particular significance that Professor Smith shared with me shortly before his passing: the Entanglement Theorem. Prior to his departure from this world, Smith was adamant that this speculative theorem holds the key to advancing what he called a “Platonist ontology of physics” or “Platonist physics” for short. 

Resultingly, the next stage of our inquiry will be guided by four very crucial questions: 1. How does IW give rise to the concepts and categories of Thomistic ontology? 2. What implications does IW bear for the ontic status of physical entities? 3. In what precise sense is HC a shadow of VC? 4. How should Smith’s final reflections on his so-calledEntanglement Theorem be understood?

With these questions set out before us we may now consider each of them in turn.

1. How does IW give rise to the concepts and categories of Thomistic ontology? 

As stated in my first essay Professor Smith concluded that irreducible wholeness is the wellspring of all being in the cosmos. However, what remains unsettled, here, is the question of how the concepts and categories of Thomistic philosophy arise from IW (if they even do at all)? 

Consider substantial form. On Smith’s account, the transcorporeal realm exists as a mode of potentiality; likewise, a corporeal object’s SX constitutes a form of potentiality. These potentialities are said to be actualized through the imposition of substantial form by way of vertical causation—that atemporal mode of causality Smith proposes operates beyond the purview of space and time.[1] 

However, for all its apparent coherence, this explanation does not address how the Thomistic categories such as substantial form come to exist in the first place? This same difficulty also applies to other key Thomistic principles, including material, formal, final, and efficient causation. Each of which seems to require an independent account of its ontological origin. For those unfamiliar: material causation refers to causality grounded in an object’s matter; formal causation concerns the defining structure or essence of a thing; final causation denotes the end or telos toward which a thing is directed; and efficient causation identifies the designing agent that brings that thing into being.[2]

Having previously established, that IW is the proximate source of all cosmic being one might, initially, be tempted to explain these categories using just IW.

However, the central difficulty, with this explanation, is that these categories cannot just pop out of IW. For, by its very nature, IW is an ethereal transcendence of summation, a universal, held in place by God, rather than a structured source of determinate metaphysical principles. Consequently, Prof Smith’s framework appears to require an additional explanatory input to bridge that gap between IW and the plurality of Thomistic categories in the cosmos. What could possibly supply such a monumental input? Well, in short, that input can only be supplied by God, the creator and sustainer of the universe. Therefore, it is at this intersection between IW and the Thomistic categories where, I propose, divine intervention becomes not just plausible but mandated to complete Smith’s cosmology. For, it is here, where the underlying principles of design appear unmistakably in the structured logic of Thomistic metaphysics as the true scaffolding underpinning the Smithian universe.

In Smith’s ontology we may think of IW, therefore, as providing the cement of the universe, and in that sense as being one cosmic principle of actualization. However, IW should not be confused with the Mold that choreographs this cement into its shape. Instead, that role is provided by the additional Thomistic metaphysical principles of teleology, material causation, substantial form, and of course by God who actively implements those principles in the first place.

A second, perhaps more illuminating analogy, clarifies the postulated relationship between IW and God even further. We might conceive of IW as a tributary feeding into a great river, while thinking of God as the river’s source and the river itself representing the continuous flow of vertical causation. Under this analogy IW plays two key roles in the implementation of Thomistic metaphysics. First, IW is a universal—a generalizable property capable of instantiation in multiple particulars. Second, IW functions as an “efficient-actualizer” participating in the being of God. That is, IW is not merely a universal property but the instrumental key through which God enacts design through vertical causation.

Like all things created, irreducible wholeness participates in the being of God. However, its participation is also singular and without parallel. For, it stands at the final threshold of created reality before the divine source itself: the last pit stop in the vertical ascent of being towards God.

As such, irreducible wholeness functions as the indispensable medium through which God’s efficient causality, expressed as intelligible design, flows outward along the ordered hierarchy of existence. From this emanation arise the Thomistic principles that confer form, coherence, and structure upon the cosmos.

2. What implications does IW bear for the ontic status of physical entities?

The question of what IW implies for the ontic status of “physical entities” is, at its core, a question of what IW entails regarding the nature of the entities described by physics.

In the preceding essay, we reached the striking conclusion that the underlying reality of a corporeal object X is an SX. An SX is, in the most general terms, a quantitative potentiality that participates derivatively in the irreducible wholeness of X, and in this way, it qualifies as an irreducible wholeness itself. The derivative character of an SX’s irreducible wholeness is conferred by the substantial form of X through vertical causation. In short, the core question that remains is how quantitative objects like SX exist. Put differently, do they exist merely as conceptual fictions, or do they possess literal, objective reality?

Funnily enough, this question is a major problematic in the philosophy of science, colloquially known as the “realism vs anti-realism debate”.[3] Within this field some scholars, such as Bas Van Frassen, have even speculated that physics does not necessarily prove the existence of physical entities SX.[4]Electrons, for example, do not need to be regarded as real; since they may instead be understood as useful fictions that allow for accurate quantitative predictions. 

In short, the force of the anti-realist position stems from the “principle of underdetermination of theory by evidence”.[5]According to this principle, distinct and even radically incompatible theories can account for the same observable phenomena while positing diametrically different underlying entities.[6] A classic example of this underdetermination is the historical explanation of heat. To this end, the original caloric theory, of Lavoiser, conceived of heat as basically being a weightless fluid, called “caloric”, that flowed from hotter to colder bodies. Remarkably, the Caloric theory generated predictive patterns totally indistinguishable from those of the later molecular theory of heat, despite the two frameworks positing diametrically opposite ontologies.[7]

In Professor Smith’s ontology, scientific data manifest in one of two forms: a “presentation” or a “display.” This distinction is articulated clearly in The Quantum Enigma. A presentation can be understood as the visual appearance of a corporeal object that reflects an underlying physical phenomenon. For example, the green colour of a leaf corresponds to a particular frequency of light, while blue litmus paper turning red indicates the presence of an acidic substance. A display, by contrast, is the output of a physical instrument that registers a material phenomenon. Examples include the clicking of a Geiger counter in response to a beta particle, or the tracks of an electron in a cloud chamber. This raises a fundamental question: within a Smithian ontology, are these entities, presentations and displays, considered real qua entities?

In my view, the most elegant solution to this quandary comes from Smith’s notion of irreducible wholeness, as it provides a framework in which seemingly conflicting realist and anti-realist dogmas about physical entities can be both true at once.

To elaborate, at the subcorporeal level, physical entities can be regarded as real, but only in an “embryonic form”. That is, as the irreducible substrata that underlies the corporeal objects to which they belong. What is not real, in the Smithian sense, is the mathematical formalism that can be associated with such an entity (SX). This mathematical structure arises not from the IW itself but from our imposition of a quantitative description “from on high.” As Arthur Eddington famously wrote, “the mathematics is not present until we put it there.”[8]

However, what is genuinely present is a receptacle in the form of a quantitative irreducible wholeness. This wholeness is quantitative in so far as it admits mechanistic interpretation, yet irreducible in that it cannot be fully captured by any single quantitative description.

One further, more analogous, way of thinking about this is that an SX is the reservoir from which the quantitative predictions about an X bubble up. These predictions manifest in the form of results observed at the corporeal level.[9]Whether those results be observed in what Smith calls a “presentation” i.e. phenomenal appearance (e.g. the colour of litmus paper) or in what Smith calls a “display” i.e. the physical manifestation of a measuring instrument (e.g. the ticking of a Geiger counter or the positioning of a pointer reader).

3. In what precise sense is Horizontal Causation a shadow of VC?

In the previous essay, I arrived at the consequential conclusion that Horizontal Causation is a shadow of vertical causation. In particular, a shadow of the second temporal mode of VC that I introduced myself, and, to a lesser extent, of the first mode originally proposed by Wolfgang Smith. But what exactly does this claim amount to? In what exact sense can Horizontal Causation reasonably be characterized as a shadow of Vertical Causation? 

To answer, Horizontal Causation can be understood as being a shadow in the following sense. The second temporal mode of Vertical Causation, which I introduced, is irreducible, i.e. it operates in time, but in a manner that cannot be decomposed using quantitative analysis. By quantitative analysis, I mean the methods characteristic of physics and, more broadly, of the hard sciences such as chemistry and biology. For our present purposes, it is helpful to think of this second mode of Vertical Causation as analogous to what Henri Bergson termed la durée, that is an irreducible modality of time that allows for genuine succession and becoming, while resisting the mathematical formalism characteristic of physical theories.[10] 

In a sense, the second (temporal) mode of Vertical Causation (VC) corresponds to irreducible teleological sequences initiated by substantial form. This mode represents a kind of irreducible causality that carries one moment into the next, directed toward a specific end—whether a local, personal goal or a higher spiritual or sacramental reality. Fundamentally, the second mode of VC is goal-oriented, with its sequence resistant to further reduction. Consequently, it can be understood as a limiting case of the first mode of VC, which is genuinely instantaneous and supratemporal. The second mode is “limited” in that it is constrained by the temporal relations of before and after. These temporal bounds, however, may themselves be further restricted by the theoretical frameworks employed in physics.

It is precisely at this boundary, where the second mode of VC reaches the limits of explanation within a physical description, that Horizontal Causation emerges. Horizontal causation “begins” when the physicist imposes an analytic framework from above, typically in the form of mathematized quantization. Importantly, such quantization is not uniquely determined; it can vary drastically depending on the chosen analytical perspective.

As any physicist will acknowledge, there exists a plurality of physical theories through which nature may be described, ranging from Newtonian mechanics, to Lagrangian mechanics, and extending to quantum theory. Regardless of the model employed, the essential point is that the physicist exercises a choice in how to represent reality—a choice that is, to some degree, subjective. In this sense, Horizontal Causation may be understood as a “shadow”: it is the outcome of a deliberate decision by the physicist to describe the second mode of Vertical Causation in particular quantitative terms. Put differently, the physicist casts an illuminating light in the form of mathematical formalism; when this light falls upon a quantitative IW, unfolding in time, what emerges is a rigorous, mathematically sober account of reality—a quantitative shadow of what ultimately lies beyond.

4. How should Smith’s final reflection on his so-called Entanglement Theorem be understood?

In an unpublished and incomplete manuscript, which Smith entrusted to me, shortly before his death, he writes:

“What defines the Platonist Weltanschauung is the notion that being is not a sum of parts. This finds its expression in a basic theorem:

Entanglement Theorem: Entanglement is the effect of IW. Here, then, we have the ontological key to the Platonist physics. One might perhaps say that quantum phenomena arise from IW, of which they are a direct effect. It may perhaps be said that QM is inherently a Platonist effect—which is why it generally strikes us as incomprehensible. What generally renders it such is that we tend to think in atomistic terms: for us, as a rule, separation precedes unity. And yet, on a deeper level, the matter stands just the other way round. Take the origin of a higher organism: it originates in a single cell. The organism arises, thus, through a process of multiple division”.[11] 

From these unpublished writings, together with my recollection of our personal conversations, it is clear to me that the development of a genuinely “Platonist ontology of science” greatly occupied Smith’s thoughts throughout the final period of his life.

In my judgment, Smith’s Entanglement Theorem, encapsulated in the claim that “entanglement is the effect of Irreducible Wholeness”, connects directly with the argument I advanced in my previous article. There I maintained that IW constitutes proper being, corresponding to what the classical tradition calls substantial form, whereas the mode of being possessed by aggregates or sums of parts is derivative and secondary—flowing from proper being. Put differently, a sum of parts cannot stand on its own. Since, it is always ontologically dependent upon some prior instantiation of irreducible wholeness. Such aggregates flow, as it were, centrifugally from an originating act of IW.

In his final book, Physics: A Science in Quest of an Ontology, Smith arrives at the startling conclusion that quantum mechanics itself results from irreducible wholeness having been “injected into the transcorporeal domain.”[12] By the transcorporeal realm Smith means that “being-less” domain, separate from an SX, into which IW may be introduced, thereby giving rise to a new physics which is no longer governed by classical reasoning.

Reflecting on Smith’s ontology of science I believe we can extrapolate two important conclusions from his so-called “Entanglement Theorem”. However, before expositing these conclusions it is necessary to outline two foundational points from which these conclusions follow.

First, quantum entanglement is widely regarded as the uniquely distinctive feature of quantum theory. Indeed, it was entanglement that Erwin Schrodinger identified “as the defining feature of quantum mechanics that distinguishes it from classical reasoning”.[13] Second, entanglement constitutes the sole element within conventional quantum theory wherein the whole is manifestly more than the sum of its parts. In quantum mechanics, when two wave functions X and Y are combined, they become entangled. The resulting wave function Z now possesses a time evolution that is in no way reducible to the time evolutions of X and Y. In effect, Z is now a new object that is irreducible to its antecedent components.[14]

With these two pre-requisite points stated let us now turn to the two conclusions that follow from Smith’s entanglement theorem.

The first conclusion is that quantum entanglement constitutes the mathematical expression of Proper Being as it enters the transcorporeal domain. It serves, that is, as the formal sign of IW crossing into transcorporeality and, in so doing, gives rise to what we call quantum theory. In this sense, it is no accident that Schrödinger identified entanglement as the distinctive feature of quantum mechanics and characterized it as an irreducible wholeness. Given what has already been established, it could not be any other way. 

The reducible, sum-of-parts ontology encountered in standard quantum theory must itself grow from a prior, irreducible wholeness. Since, the reducible nature that defines distinct quantum entities, other than entangled ones, presupposes a more fundamental unity from which such distinctions receive their clarity. Consequently, quantum entanglement represents precisely this irreducible wholeness or the underlying unity out of which the derivative, reductive being of singular quantum objects arise and thus represents the unique and defining feature of the theory itself.

The second conclusion, which can be drawn from Smith’s entanglement theorem, takes the form of a conjecture. This conjecture proposes that while IW provides the foundational principles for a science, its presence becomes evident only at the “higher levels” of that science. To put things more clearly: irreducible wholeness is what brings a science into existence—for example, quantum theory. However, at the theory’s most elementary levels, such as the fundamental particles of quantum mechanics, IW is less obvious. It shows itself instead at higher, composite levels, as seen in entangled systems. Hence, what Smith’s entanglement theorem perhaps teaches us is that there is a kind of “grounding-to-emergence” relationship between IW and the structure of scientific theories. Undoubtedly, this relationship requires further exploration not only in physics but across many other sciences, as well, particularly in chemistry and biology, as I will argue in a later essay. 

With that in mind, one possible reason why irreducible wholeness appears “more hidden” at the lower levels of a science is that, as we descend the great chain of participation, we move progressively farther from being itself. Since irreducible wholeness serves as the custodian of cosmic being, it is hardly surprising that its presence becomes increasingly more subtle and less detectable in the deeper strata of reality.

Where do we go from here?

Having uncovered and examined Smith’s entanglement theorem it is now time to fully develop Smith’s  Platonist ontology of physics. This ontology of physics, I propose, is based partially on the principle that Irreducible Wholeness is the key element of any science that allows it to hang together and to stay in-tact. I will commence outlining the nature and principles of a Platonist ontology of physics in the next essay. From this I will attempt to show how the principles of a Platonist ontology of physics extend organically to the other hard and even soft sciences.

Bibliography:

Smith, Wolfgang (2005). The Quantum Enigma: Finding the Hidden Key (TQE). Edition 3 Hillsdale, N.Y.: Sophia Perennis.

Smith, Wolfgang (2023), Physics: A Science in Quest of An Ontology (PSQ). Edition 2. Philos-Sophia Initiative Foundation.

IEP, Aquinas: Metaphysics: https://iep.utm.edu/thomas-aquinas-metaphysics/ 

Okasha, S. (2015). Philosophy of Science: a very short introduction (2nd edition). Oxford University Press.

Eddington, A.S. (1939) The Philosophy of Physical Science. Macmillan, New York.

Schrödinger E. Discussion of Probability Relations between Separated Systems. Mathematical Proceedings of the Cambridge Philosophical Society. 1935;31(4):555-563. doi:10.1017/S0305004100013554

[1] TQE, P.109

[2] IEP, Aquinas: Metaphysics

[3] Okasha, P.58-60

[4] Okasha, P.58-60

[5] Okasha, P.58-60

[6] Okasha, P.71-76

[7] Okasha, P.71-76

[8] Eddington, The Philosophy of Physical Science, P.137

[9] TQE, P.35

[10] Bergson, Time and Free Will

[11] Unpublished Smith manuscript entitled: The Platonist View of Physics

[12] PSQ, P.31

[13] Schrodinger (1935), P.55

[14] Schrodinger (1935), P.55