FoS COMMISSION: JOHN TAYLOR

This essay explores Wolfgang Smith’s notion of irreducible wholeness. 

Firstly, by outlining/defining IW and the role that it plays within the three metaphysical domains of Smith’s cosmology: the corporeal, the physical and the transcorporeal. It is stated that IW sits at the centre of the cosmic icon as the “proximate source of all cosmic being”. 

From this, it addresses three questions which I take to be central to furthering Smith’s research program:

1) How can IW stand alone? 

2) If IW is the source of all cosmic being how then can sums of parts have any being? 3) What is the relationship between vertical causation, horizontal causation and irreducible wholeness?

Supporting audio version may be found here: https://drive.google.com/file/d/1KLpSansUrxTxAR8o0wWn9BN96vFGoJi2/view?usp=sharing

WRITTEN BY JOHN TAYLOR

In his final book, Physics: A Science in Quest of an Ontology (PSQ) Wolfgang Smith introduces a concept largely truant from modern ontology called Irreducible Wholeness (IW). 

In contrast to what might be called “ordinary wholeness”, Smith defines IW as a kind of wholeness that is greater than a sum of parts.  Although, IW is undoubtedly a universal, that is a generalized property[1], like all universals IW comes equipped with exemplars in the corporeal (perceivable) world. Included among the most compelling of these exemplars are colours and sounds—which owing to their continuous nature and lack of self-contained parts must be IWs.

At first inspection, Smith’s definition of IW appears to fully capture the concept: IW is simply that which is more than a sum of parts. But is this really all there is to IW? Is IW just an abstracted super-wholeness, or is there more to IW than being “more than a sum of parts”?  After all, if IW is the proximate source of all cosmic being, as Smith maintains, then it must possess a greater depth than the generic transcendence of summation. 

Motivated by these quandaries, in this essay, I will probe more deeply into Smith’s notion of irreducible wholeness. To this end, I will present my thoughts in two parts followed by a conclusion. In part 1, I will summarise the nature of and role that IW plays in Smith’s ontology. Following suit, in part 2, I will address several questions concerning the ontological role and metaphysical depth of irreducible wholeness. Questions which I believe must be answered to begin furthering Smith’s research programme.

Part I: IW in Smith’s Ontology

To understand the role that IW plays in Smith’s ontology of science you have to firstly understand a few background concepts, which I will now introduce.

The first of these concepts is that, according to Wolfgang Smith, the cosmos we inhabit can be split into two core domains: the corporeal and the physical. 

What Smith calls the corporeal domain is basically the world of sensory qualities—similar to what Husserl calls the “phenomenal world”. That is the world of colours, sounds, tastes, textures and smells as we perceive them. Departing from conventional wisdom, Smith holds that sensory qualities carry a genuine mind-independence.[2]Meaning that they are not mental paint being brushed onto a blank canvas of quantity, as Descartes or Locke might assert. But are instead external properties of objects possessing substantial being.[3] 

By contrast what Smith calls the “physical domain” is the domain of quantities—particularly those quantities deployed by the physicist in his physical theories. Thus, for any corporeal object X, there is a corresponding subcorporeal object SX: X as conceived by the physicist.[4] Importantly, the specific theoretical framework which the physicist uses to describe SX is largely a matter of his choice. For instance, if he were a Newtonian, he might choose to conceive of our red apple as a Galilean point-mass following f=ma and a quantum theorist as a collection of wave functions. While the physicist’s theory does shape how SX is described this fact does not mean that SX is literally subjective. On the contrary, SX is a quantitative potentiality ordered towards prediction-making (isomorphic to all physical theories).[5] However, what is “subjective” or supplied by the physicist, is the mathematical formalism attached to an SX. As Arthur Eddington once said, “the mathematics is not present until we put it there”.[6] With Wolfgang Smith’s ontology, in hand, Eddington’s statement thus becomes more transparent than ever before.

In addition, to harbouring the subcorporeal world, the physical domain also encompasses the transcorporeal realm: a domain of quantity not directly tied to an SX. In his final book Smith identifies the physics of the transcorporeal with that of quantum theory.[7]Nevertheless, despite its transcorporeal origins, quantum theory can still be applied to an SX. However, the precise mechanism behind this applicational process is so complex and, in many respects, under-interpreted—that it arguably requires an entire essay of its own to be explained![8] 

At this juncture, one might be forgiven for thinking that the only factor distinguishing the corporeal from the physical is the presence of qualities. However, crucially, this is not exactly the case. In fact, what really allows for the demarcation of the corporeal from the physical is the ontology of St Thomas Aquinas, aptly called Thomism.[9]While a full exposition of Thomistic metaphysics vastly exceeds the scope of this essay, I can and will now explain the basic distinctions of Aquinas’ ontology and how it applies to Prof Smith’s thought. 

To this end, the first fundamental distinction in Thomistic ontology is that between essence and existence. Put simply, existence refers to that a thing is, whereas essence refers to what a thing is.[10] For example, an apple’s essence is its being an apple, while its existence is its being instantiated in reality—present in a way that allows it to be encountered and interacted with. According to Aquinas, in God there is no distinction between essence and existence. God’s essence is identical to His existence. By contrast, in all beings other than God, essence and existence are totally distinct. Furthermore, self-standing beings that possess this distinction and can also instantiate properties called accidents are what Aquinas calls “substances”.[11] For example, a dog can be said to exist independently (excluding its participation in God) and can instantiate sets of properties—such as being black or white—without inducing any change to its essence (i.e. accidents).

Moving on, the second major distinction in Thomistic ontology is that between potency and act. In this regard, the term potency (potentiae) refers to the potential for something to acquire a possible future state (usually a new property). Whereas the term act refers to the actualization of said possibility.[12] For example, an oak tree seed has the potency to grow, and this potency can hopefully be actualized, with enough water and sunlight, into a fully-fledged oak. 

Furthermore, the angelic doctor’s distinction between actuality and potentiality is further illuminated by his closely related concepts of matter and substantial form. In Thomistic terms, matter does not represent “physical stuff” but potentiality awaiting actualization.[13] This actualization is brought about by substantial form: a metaphysical principle that actualizes matter into one specific natural kind rather than another.[14] For instance, a dog possesses a unique substantial form that arranges its matter into the distinct characteristics of a dog, as opposed to those of a cat.

In embracing a branch of Thomism, rooted in Neo-Platonism, Wolfgang Smith’s ontology thus distinguishes the physical from the corporeal through the presence of substantial form. It is by possessing substantial forms proper to objects perceivable that the corporeal world can be truly demarcated from the physical.[15] Better still we might say that the subcorporeal is an essential part of the corporeal participating as “quantitative potency” in the substantial forms of corporeal objects. By way of example, a tree is different from its subcorporeal object SX by virtue of possessing a substantial form corresponding to that of a tree. The SX of a tree participates, that is serves as an active part of, the tree which reduces it quantitatively and undergirds any quantitative predictions to be made about that tree.

Having distinguished the corporeal from the physical, by aid of Thomistic-Platonist philosophy, Smith also makes explicit a distinction only implicit in the thought of Aquinas: that between Horizontal and Vertical Causation.[16] Intriguingly, this distinction has even begun to influence the cultural zeitgeist, having been referenced by the atheist Alex O’Connor in a recent interview![17] As defined in Smith’s book The Quantum Enigma (TQE) Horizontal Causation is a causality that acts in time by way of a sequence of events.[18] Basically, horizontal causation is the causality revealed to us by the hard sciences—particularly by physics. In contrast, Vertical Causation (VC) is a causality operating outside of time and space that acts instantaneously. It is the causality proper to substantial form and allows for the resolution of the quantum measurement problem.[19]

As a result, Smith’s acknowledgement of vertical causation brings us to his concept of Irreducible Wholeness and its role within his ontology. As outlined in his final book Irreducible Wholeness acts as the proximate source of all Vertical Causation (and of being).[20] I say proximate because the ultimate agent responsible for initiating VC is of course God, owing to His supreme nature as ipsum esse subsistens. However, at the relative or proximate level, the dispensation of Vertical Causation is achieved by irreducible wholeness. One way of understanding this is that because irreducible wholeness is more than a sum of spatio-temporal parts and VC is a causality acting outside of space and time the two must, in some-way, be conceptually paired. It can be reasoned, therefore, that it takes an “IW to produce a VC and a VC to produce an IW”.[21] 

In terms of Smith’s over-arching ontology IW consequently takes on the monumental role of breathing life into the cosmos.[22] In fact, Smith explicitly states that IW sits at the centre of the “cosmic icon”, as a stand-alone entity, in a plane that he calls the Aeviternal realm[23].

For Aquinas, the Aeviternal realm refers to a modality of duration that is not strictly speaking temporal. Whereas, for Smith, the aeviternal realm is a plane of genuine unchangeability. In this sense, aeviternity might be understood as the eternal now “packaged just for us,” complete with its full range of ontological modalities.[24] Most notably, the aeviternal realm encompasses the modality of mathematical and geometric forms, as well as a further modality that Smith calls “celestial corporeality”.[25] 

However, beneath all these modalities of aeviternity lies irreducible wholeness: that which is more than a sum of parts. On my reading of Smith, it seems that, at a cosmic level, the existence of Thomistic substances, as well as the other aeviternal modalities, emanates, by way of vertical causation, from irreducible wholeness. Irreducible wholeness in other words provides the actualization necessary for all things in the cosmos to exist in the first place—emanating in an outward fashion from God to IW to the Aeviternal modalities to Substances to the quantities of physics etc. Resultingly, on this basis, we can declare that irreducible wholeness functions as the yardstick for what it is to be or to have being in the cosmos. In fact, Smith said as much to me in a phone call when he clarified that: “IW is the source of all cosmic being”.

Part II: Making Sense of IW

Having outlined Smith’s notion of IW and its role within his ontology let us now turn to several important questions regarding Smith’s understanding of irreducible wholeness and its implications.

To this end there are three core questions, which I suggest, must be answered regarding irreducible wholeness: 1) What does Smith mean when he asserts that IW stands alone? 2) If IW is the source of all being, how then can sums of parts possess any being? 3) What is the relationship between vertical causation, horizontal causation and irreducible wholeness?

Let us now consider these questions in turn, starting with the first:

How can IW stand alone?

The question of how Irreducible Wholeness can “stand alone” is crucial because wholeness is traditionally thought to not be a substance, but an essential or accidental property of a substance.

Conceptually speaking, properties are always understood as belonging to something else that’s more fundamental. Namely to an object or substance distinct from the property itself. For example, we never encounter the property of being six feet in isolation—as it always comes tethered with a particular substance. In consequence, this gives rise to a genuine conundrum: if wholeness is ordinarily a property, how then can Smith’s IW exist independently, without a corresponding substance instantiating it? In his final writings, Smith certainly speaks as if IW lacks any underlying substance—calling it the “pivot of the cosmic icon”.[26] (A “pivot” is certainly not a property but a stand-alone entity!)

Nevertheless, in my view, there is a pretty simple resolution to this conundrum. One which rests on the recognition that the substance-accident distinction is only an ontological approximation that collapses in light of Aquinas’ metaphysics of God.

In his letters to Fr Malachi Martin Professor Smith references Catherine Pickstock’s Esoteric Thomism. And concurs with her conclusion that the substance-accident dichotomy is “stretched to breaking point” by Aquinas’s metaphysics of transubstantiation.[27] (The ability of our Blessed Lord to become manifest under the appearances of bread and wine.) 

To break this down, a substance, as Aquinas and Aristotle understand them, are objects that stand on their own. However, as Aquinas holds, according to his emanationist cosmology, to “stand alone” is also relative.[28] In relation to their accidents substances such as trees, flowers, and rivers stand alone. However, in relation to God nothing truly stands alone. In fact, everything we encounter, including substances, receives its being by participating in the divine act.[29] Consequently, in an “esoteric” sense, the substances we encounter are not substances at all, and the traditional distinction between object and property collapses when viewed in relation to God.[30]

In turn, this basic recognition from what Pickstock calls “esoteric Thomism” hands us a “get out of jail free card” for our conundrum facing IW. Irreducible wholeness can legitimately stand alone as a property without a substance because it is upheld by the divine act alone. Not as a property of God, but as something independent which receives its being by participating in the Being of God. Just as our God upholds the accidents of bread and wine without their usual corresponding substance of bread, so too we might reasonably speculate that God upholds the property of irreducible wholeness as the first “cosmic principle” of actualization, in the Smithian cosmos.

If IW is the source of all cosmic being how then can sums of parts have any being?

Unlike the previous question this one is not concerned with IW’s intrinsic nature, but more so with its effects. As Smith states in PSQ irreducible wholeness is the source of all cosmic being. In fact, at times Smith seems to suggest that, to have cosmic being, something must ipso facto be an IW.[31] However, this leads to a problem with the existence of entities and properties which are just sums of parts. At face value we want to say, wholeheartedly, that quantities (i.e. sums) exist. For example, that a collection of tennis balls exists. The tension which arises, however, from making this commitment is that quantities, which are sums of parts, are canonically not IWs and so should not exist according to Smith’s metaphysical commitments. 

One possible resolution to this issue is to distinguish between the proper being defined by irreducible wholeness and the derivative existence of sums of parts. While IW might define what it means to have true, substantial being in the cosmos, this doesn’t preclude the existence of sums of parts in a secondary sense. In this view, sums of parts could be understood as accidents: contingent collections that emerge from irreducible wholeness, without undermining the primacy of IW in defining “proper being”.

It is important to note that when Smith refers to sums of parts, he is not merely talking about literal collections of parts. Rather, he refers to any configuration of parts, including those manipulated by mathematical functions. These functions could range from simple addition to more complex operations used in physics, such as momentum or acceleration. Within Smith’s framework, it is likely that mathematical functions are considered universals. That is generalized properties which exist in the aeviternal realm of forms. By their very nature, these forms are themselves IWs, which implies that every "sum of parts" is, in a sense, infused with a trace of irreducible wholeness that powers its very existence.

Thus, even sums of parts ultimately derive their existence from IW, which affirms Smith’s claim that IW and cosmic being are equivalent, even in the presence of summed entities.

What is the relationship between vertical causation, horizontal causation and irreducible wholeness?

At first glance, the relationship between these elements seems fairly straightforward: irreducible wholeness gives rise to vertical causation, while horizontal causation operates alone at the physical level. However, this initial clarity dissolves once we recognize that, within Smith’s ontology, all levels must mutually participate in one another.[32] Smith explicitly states that the cosmos, in its entirety, is an irreducible whole or as Thomas Taylor would say “a whole mundane animal”.[33] In short, this requirement suggests that irreducible wholeness, vertical causation, and horizontal causation are far more tightly interwoven than previously conjectured by Smith. Furthermore, this situation is made even more complicated by Smith’s account of time, which he characterizes as “irreducible” in two distinct ways: first, as a cosmic bound that orders events into before and afters; and second, as the indivisible phenomenal flow of time that carries us from one moment to the next.[34]

Arguably, the non-reducibility of time to some sort of sequential ticking implies a far more subtle relationship between the aforementioned concepts—one which I will now begin to elucidate.

As a necessary first point of analysis, I propose that Smith’s definition of vertical causation should be broadened to include modes of causality that are clearly irreducible but also temporal. For example, as corporeal objects, we, as human beings, evidently cause things to happen. And this causation, for the most part, happens temporally. Evidently, owing to our corporeal nature the causation that we enact cannot be boiled down to a measurable construction of time—since we act as irreducible wholes at the corporeal level. This implies that there must exist temporal modes of causality that resist reduction in any measurable sense.

In his seminal work The Quantum Enigma Smith defines vertical causation as an “instantaneous causality that operates without a direct sequence of events”.[35] However, given the existence of temporal causalities that are clearly irreducible it seems that Smith’s initial definition of VC should be expanded to account for these irreducible temporal causalities. To this end, while one may posit a primary mode of vertical causation that operates entirely outside of time, and without sequential mediation, it is also possible to propose a second modality of vertical causation that is temporal yet nonetheless irreducible. This second mode of VC, I conject, cannot be broken down into any measurable sequence of events but is, nonetheless, temporal in so far as it consists of before and afters that cannot be analysed further.

To give a suitable analogy a wave is prima facie irreducible because it is a continuous set of peaks and troughs. However, those peaks and troughs can also be conceptually understood as a collection of particles travelling up and down. Similarly, our conjectured second mode of VC can be understood as irreducible, and temporal, but also as something that can be analysed using measurement. 

In turn this brings us to horizontal causation, which I suggest should not be understood as something wholly distinct from vertical causation. Indeed, horizontal causation is no more separate from vertical causation than a shadow is separate from the object to which it is tethered. Just as a shadow is an “object” in name only, so too is horizontal causation a “causality” in name only. Meaning, that the quantitative “causality” attached to horizontal causation is effectively inert and not responsible for the temporal outcomes that we encounter in the corporeal realm. To illustrate, when we walk down the street, the causality driving our movement is not simply the result of particles or any reductive entity obeying pre-existing physical laws. Rather, it emerges from that second mode of vertical causation, which is both temporal and irreducible. We walk as an irreducible whole, and in doing so, we exist within a modality of time that resists reduction to mere measurement. The causal explanations we rely on through physics are, therefore, semi-real fictions, bound to a corporeal IW; much like how a shadow is bound to us as we walk down a sunlit path.

Given all of this, the relationship between IW VC and HC can be summed up as follows: IW is what conditions VC which comes in two forms. The first is the standard form of VC, described by Smith, which is instantaneous and totally non-temporal. The second is the temporal kind, mentioned before, which is totally irreducible in nature and also in its effects. In turn VC, especially the second kind, casts a shadow in the form of horizontal causation. This shadow is what the physicist observes and tracks using his quantitative methods.

Some Closing Thoughts:

In this essay, I have sought to address several key questions surrounding Smith's concept of irreducible wholeness. While the responses provided here are brief, I hope they offer valuable insight into these critical issues. However, it is worth noting that there remain many further questions to explore, particularly regarding the relationship between IW and Thomistic ideas like substantial form. I will delve deeper into these questions in the next article.

Bibliography:

Smith, Wolfgang (2016), In Quest of Catholicity, Edition 1, Angelico Press

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

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

Smith, Wolfgang (2013), Ancient Wisdom and Modern Misconceptions: A Critique of Contemporary Scientism. Edition 3. Angelico Press.

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

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

Alex O’Connor Interview: https://www.youtube.com/watch?v=aqWTlUOhowk(timestamp, 6.44) 

Smith, Cosmic versus Measurable Time, PSIF, 2021, https://philos-sophia.org/cosmic-measurable-time/?srsltid=AfmBOorYvBBiIYfBVKbbbwNV_Cl7135PmymcKhY48F2UDVFWPDUVWFgH 

Smith, From Schrodinger’s Cat to Thomistic Ontology, PSIF, 2018 https://philos-sophia.org/schrodingers-cat-thomistic-ontology/?srsltid=AfmBOooI30rahk2EFKKcLOEZjY71rO54oPqto95zKizh2Y4nIdto0hBH 

The Works of Plato, 1804, Vol II, Thomas Taylor, London, R. WILKS, CHANCERY-LANE

[1] PSQ, P.45

[2] TQE, P.26

[3] TQE, P.26

[4] TQE, P.34

[5] TQE, P.34

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

[7] PSQ, P.30-31

[8] PSQ, P.30-31

[9] PSQ, P.26

[10] See, IEP, Aquinas: Metaphysics

[11] See, IEP, Aquinas: Metaphysics

[12] See, IEP, Aquinas: Metaphysics

[13] See, IEP, Aquinas: Metaphysics

[14] See, IEP, Aquinas: Metaphysics

[15] See, Smith, From Schrodinger’s Cat to Thomistic Ontology

[16] PSQ, P.15

[17] https://www.youtube.com/watch?v=aqWTlUOhowk (timestamp, 6.44)

[18] TQE, P.116

[19] TQE, P.118

[20] PSQ, P.25

[21] PSQ, P.25

[22] PSQ, P.25

[23] PSQ, P.21

[24] PSQ, P.21

[25] See, Smith, Ancient Wisdoms and Modern Misconceptions Chapter 4

[26] PSQ, P.21

[27] Smith, In Quest of Catholicity, P.127

[28] See, IEP, Aquinas: Metaphysics

[29] Smith, In Quest of Catholicity, P.127-128

[30] Smith, In Quest of Catholicity, P.127-128

[31] PSQ, P.28

[32] PSQ, P.99

[33] Taylor, P.415

[34] See, Smith, Cosmic vs Measurable Time

[35]Smith, The Quantum Enigma, P.110