The Logical Problem of the Trinity: A New Solution

Abstract

This article aims to introduce a new solution to the Logical Problem of the Trinity. This solution is provided by utilising a number of theses within the field of contemporary metaphysics in order to establish a conceptual basis for a novel account and model of the doctrine of the Trinity termed Monarchical Aspectivalism, which will provide the means for proposing an alternative reading of the Athanasian Creed that is free from any consistency problems.

1. Introduction

According to the doctrine of the Trinity, there exists one ‘God’ (θεός) and three distinct ‘hypostases’ (ὑπόστασις): the Father, the Son and the Spirit, each of whom is of one ‘ousia’ (οὐσία). These hypostases are identified as ‘persons’ that are ‘relationally’ distinct—in the sense that they are solely individuated by their relations to one another: the Father is individuated by being ‘unbegotten’ (i.e., being uncaused), the Son is individuated by being ‘begotten’ by the Father (i.e., being ‘caused’ to exist by the Father) and the Spirit is individuated by being ‘spirated’ by the Father and/through the Son (i.e., being ‘caused’ to exist by the Father and/through the Son).1 Moreover, each of the persons of the Trinity is ‘God’ by being (in some manner) related to the one divine ousia (i.e., one divine nature). Yet, despite each of the persons being ‘God’, there is solely one ‘God’ within the Trinitarian life. In contemporary analytic and historical theology, certain ‘models’ of the doctrine of the Trinity have been proposed to further clarify the nature of the central tenets of this teaching.2 One model is that of Monarchical Trinitarianism, which centres on two tenets:

(1) (Monarchical Trinitarianism)

(a) There are three relationally distinct persons within the Trinity: the Father, the Son and the Spirit, each of whom shares one divine nature, and thus are each equally termed ‘God’ (in the predicative sense). (b) The one ‘God’ (in the nominal sense) is numerically identical to one of the entities: the Father, who is the sole ultimate source of the Son and the Spirit.

The Trinitarian model of Monarchical Trinitarianism—centred on the doctrine of the ‘monarchy of the Father’—has been most recently defended by John Behr (2004, 2018), in the historical theological literature, as well as by Beau Branson (2022) and Joshua Sijuwade (2021, 2022), in the analytic theological literature, and is primarily grounded upon the idea that the Father is the sole ultimate (unsourced) source of everything else and thus possesses a specific priority within the Trinity (and reality as a whole). This specific priority grounds the fact of the Father being designated as ‘God’ in the primary (i.e., nominal) sense of the word. That is, the Father is numerically identical to the one ‘God’. Whilst the Son and the Spirit are each, with the Father, ‘God’ in a secondary (i.e., predicative) sense of the word (by each of them sharing in the one divine nature). Therefore, this specific view of the Trinity posits the existence of three entities: the Father, the Son and the Spirit, who are each ‘God’ in the secondary (predicative) sense. Yet, there is only one ‘God’ within the Trinity, as only one of those entities: the Father, is ‘God’ in the primary (nominal) sense of the word.

The authoritative sources for Monarchical Trinitarianism are the creedal declarations made at the Council of Nicaea (325 CE) —termed the ‘Nicene Creed’—and the Council of Constantinople (381 CE)—termed the ‘Niceno-Constantinopolitan Creed’. These specific creedal declarations provide the standard for Trinitarian ‘orthodoxy’, which is evidenced by their wide spread acceptance amongst distinct ecclesial communities within Christianity. Now, for the ‘Greek-speaking’ Trinitarian trajectory (hereafter, Greek Trajectory)—influenced historically by that of the work of the Cappadocian Fathers (i.e., St. Basil of Caesarea, St. Gregory of Nyssa and St. Gregory Nazianzus), and found, in a contemporary ecclesial context, in Eastern Orthodoxy—Monarchical Trinitarianism is the teaching of these creedal declarations and expresses the ‘orthodox’ or ‘pro-Nicene’ conception of Trinitarianism. Yet, this conception or model of the Trinity has not gained much traction in the ‘Latin speaking’ Trinitarian trajectory (hereafter, Latin Trajectory)—that has been influenced historically by that of the work of the St. Augustine and St. Thomas Aquinas, and is found, in a contemporary ecclesial context, in Roman Catholicism. However, what will now be our central focus is to show how Monarchical Trinitarianism can indeed be of great benefit in providing grounds for dealing with an important problem that plagues the conception of the Trinity found within the Latin Trajectory, which we can begin to see as follows: in addition to the Niceno-Constantinopolitan Creed (and Nicene Creed), the ‘Athanasian Creed’ (hereafter, AC) has played an important role in forming the conceptual framework for the doctrine of the Trinity within the Latin Trajectory—with this specific creed helping to shed light on issues such as the relation between the persons of the Trinity and ‘God’, the manner in which these persons are distinct from one another, and the monotheistic foundation of the Trinity as a whole.3 Moreover, within the field of analytic theology—which has been developed within an Anglo-American context that has ‘conceptual roots’ within the Latin Trajectory—this specific creedal declaration has often been taken as a starting point for analysing the coherence and cogency of the central elements of the doctrine of the Trinity—with the progenitors to this form of analysis within the field of analytic theology being that of Richard Cartwright (1987)—with his identification of the ‘Logical Problem of the Trinity’,4 Richard Swinburne (1994)—with his ‘Social Trinitarianism’ account,5 Brian Leftow (2004)—with his ‘Latin Trinitarianism’ account,6 and Peter van Inwagen (1995)—with his ‘Relative Identity Trinitarianism’ account.7 Hence, in proceeding down the same path as these individuals, and thus assuming this creedal declaration as our conceptual starting point, it is quite clear that (AC) uses specific terms that have a certain level of ambiguity and thus are open to different forms of interpretation. Nonetheless, the standard interpretation of (AC) is that of an ‘identity reading’ (IR), which we can state succinctly alongside a summary statement of (AC) as follows:8

Athanasian Creed (AC)	Identity Reading (IR)9
1. The Father is God. 2. The Son is God. 3. The Spirit is God. 4. The Father is not the Son. 5. The Father is not the Spirit. 6. The Spirit is not the Son. 7. There is exactly one God.	1*. The Father = God. 2*. The Son = God. 3.* The Spirit = God. 4*. The Father ≠ the Son. 5*. The Father ≠ the Spirit. 6*. The Spirit ≠ the Son. 7*. There is exactly one God.

The standard interpretation of (AC) provided by (IR) takes there to be, first, solely one ‘God’ within the Trinitarian life, and, second, the copula ‘is’ featured in (AC) is taken to be that of a numerical identity relation (=), which results in each of the three hypostases: the Father, the Son and the Spirit, being numerically identical to the one ‘God’. Given this specific reading of (AC), it is quite clear that a proponent of this reading would face a logical incoherence challenge, which has been termed the ‘Logical Problem of the Trinity’ (LPT). Specifically, the (LPT) can be raised against the consistency of elements (1*)–(7*) of (IR) on two fronts: first, by the ‘is’ featured in (1*)–(3*) being that of a numerical identity relation, then, by the transitivity of identity (i.e., if x = y and y = z, then x = z), the Father would be identical to the Son (and the Father and the Son would also be identical to the Spirit), which would thus render (4*), (5*) and (6*) as inconsistent—let us call this issue the distinction issue. Second, as (1*)–(6*) takes each of the members of the Trinity to be numerically distinct entities that are each God and as (7*) takes there to be only one ‘God’, there seems to be an inconsistent affirmation of there being exactly one ‘God’ and also more than one ‘God’ within the Trinitarian life—let us call this issue the oneness issue. So, taking these two issues together, it seems as if (1*)–(7*) are inconsistent statements and thus one (or more) of these statements must go. However, as each of these statements, or ‘elements’, is required to be held by a proponent of the doctrine of the Trinity, one cannot simply jettison any of these statements. Rather, the task for one who holds to this specific reading of (AC) is either for them to defend (IR)—by showing the distinction and oneness issues to not really be problematic—or, for them to provide an alternative reading of (AC)—in a way that wards off the distinction and oneness issues—without, however, transgressing the boundaries set by (AC).

In taking the second option on the table, one can adopt the alternative reading of (AC) that can be provided by Monarchical Trinitarianism, which will allow one to clearly deal with the oneness issue. How this specific issue is dealt with within a Monarchical Trinitarian context is simply through equivocating on the usage of the word ‘God’. As, on the one hand, in (1)–(3) of (AC), it is used as a predicate in reference to each of the entities who possess the one divine nature—each of the persons is ‘God’ (in the predicative sense). Yet, on the other hand, in (7), it is also used as a name that solely designates the Father, who is thus taken to be numerically identical to the one ‘God’ (in the nominal sense). Moreover, this also provides a means for one to deal with the distinction issue as each of the Trinitarian persons is taken to ‘possess’ the divine nature (hereafter, Divinity), rather than being identical to it—as each is predicated the term ‘God’ by possessing Divinity. Hence, there is no transitivity in play that requires one to identify each of the persons with one another. We can thus state this Monarchical Trinitarian interpretation of (AC)—termed the Monarchical Reading (MR), as follows (where ‘ins’ stands for ‘instantiates’):

Athanasian Creed (AC)	Monarchical Reading1 (MR1)
1. The Father is God. 2. The Son is God. 3. The Spirit is God. 4. The Father is not the Son. 5. The Father is not the Spirit. 6. The Spirit is not the Son. 7. There is exactly one God.	1*. The Father ins Divinity (Universal). 2*. The Son ins Divinity (Universal). 3*. The Spirit ins Divinity (Universal). 4*. The Father ≠ the Son. 5*. The Father ≠ the Spirit. 6*. The Spirit ≠ the Son. 7*. There is exactly one God, the Father.

At the heart of the equivocation strategy that is offered by (MR₁) is the conception of Divinity as a universal that is instantiated by each of the members of the Trinity.10 More specifically, Divinity is a numerically singular universal that renders the persons as homoousios (i.e., them ‘possessing’ or ‘being of’ one nature) due to each of them individually instantiating this universal. Hence, by adopting this specific conception of the Trinity, one is thus presented with a consistent reading of (AC). However, one is not entirely out of the woods yet, as, by one adopting this reading, they are presented with another important issue. More specifically, the ‘instantiation-based’ position that grounds the solution provided by (MR) faces a problem,11 termed the ‘multiple-natures problem’—namely, it enables a proliferation of particular divine natures within the Trinitarian life. That is, as Timothy Pawl (2020) has highlighted,12 an instantiation relation seems not to ‘fit the bill’ for the task of tying the persons of the Trinity to the divine nature, due to the fact that it will need to preserve the ontological unity on which the doctrine of the Trinity is built upon—namely, the persons being homoousios.13 However, as the objection goes, the relation of instantiation, unfortunately, allows a form of ontological disunity to creep into the depths of the foundation of the Trinity, which an adherent of this doctrine would clearly find problematic. However, an adherent of Monarchical Trinitarianism can themselves now ask the question of why does a construal of the model as an instantiation-based position results in there being a multiplicity of instances of the divine nature within the Trinity? In answering this type of question, Pawl (2020, p. 12) has given an interesting parity example, which he states as follows:

When my daughters, Mary, Beatrice, Edith, and Agnes, each instantiate the universal, Humanity, and each has proper characteristics such that we don’t confuse them, what we have here are four humans, not a single human.

In other words, when we count human people, we count by individual instances of humanity. Thus, if there are a multiplicity of instances of humanity, then there are multiple humanity universals (i.e., humanity natures). The Trinitarian persons, in a similar manner, can be taken as individual instances of a specific universal (i.e., Divinity). However, understood in this way, it does not seem as if there is only one Divinity universal (i.e., one nature) within the Trinity, which is surely problematic. More specifically, if we posit the existence of an instantiation relation between the Trinitarian persons and the divine nature, then it seems that when we are counting the number of natures within the Trinity, we are also to count by individual instances of that specific universal. Since there are three instances of this Divinity universal, each of the Father, the Son and the Spirit, we can take there to be three particular natures (i.e., attributes) within the Trinity. Therefore, taking this issue into account, instead of Monarchical Trinitarianism solely positing one nature—it appears to allow a proliferation of particular natures that correspond to the number of instances within the Trinitarian life.14 One would thus not want to adopt the conception of the relation of possession that is posited by (MR). Given this, one can thus see that Monarchical Trinitarianism can provide a way out of the oneness issue—namely, by identifying the one God as the Father alone—yet, as it stands, it does seem to provide any progress in dealing with the important distinction issue—which will be indeed problematic for a proponent of a Latin Trinitarian conception of the Trinity, given an additional doctrine that has played a formative role in this specific trajectory—namely, that of the doctrine of the Divine Simplicity (hereafter, the DDS). From a historical standpoint, this specific doctrine was a central component of the Latin Trajectory that provided the motivation for one to adopt (IR), as Lewis Ayres (2004, p. 281) writes:

God is non-composite: God has no parts, is incapable of division, and is not composed of a number of elements. In other words, God is simple… Thus, in pro-Nicene texts, the primary function of discussing God’s simplicity is to set the conditions for all talk of God as Trinity and of the relations between the divine ‘persons’.

Within the Latin Trajectory, the DDS was not a doctrine that was accidentally linked to the Trinity; rather, these two doctrines were ‘two sides of the same coin’. The DDS was viewed as being a foundational teaching concerning the Christian doctrine of God, as it was the means by which Trinitarianism could be spoken of as monotheistic—in a similar manner to how the monarchy of the Father was for the Greek Trajectory. That is, alongside the one God being identified as the Father—which was emphasised more prominently within the Greek Trajectory—the DDS provided the Latin Trinitarian theologians with the resources to securely ground the Trinity within a monotheistic framework—as the nature shared by each of the members of the Trinity was taken to be one because it is simple and thus numerically identical to each of the members. More specifically, the classical conception of the DDS, in its most basic sense, posits the fact of Divinity not being composed of ‘parts’. At a general level, a part is a portion of any given entity, and if a portion of a given entity is less than the whole entity itself, then it is a ‘proper’ part, whereas if a portion of a given entity is not less than the whole itself, then it is an ‘improper part’. The DDS negates the compositional nature of Divinity in a proper sense, which allows one to understand that Divinity is a metaphysically simple entity by it lacking any type of proper part (i.e., proper spatial, temporal or metaphysical parts). More precisely, according to the DDS, no portion of Divinity is numerically distinct from it. Hence, Divinity is a being that is intrinsically within itself and does not have any division or ontological composition. That is, Divinity must be such that it does not have any sort of complexity involving composition. Rather, any intrinsic property attributable to Divinity must be numerically identical to it. For example, if goodness is attributed to Divinity, then one is not properly attributing to it an ontologically distinct property that it has. Moreover, given that Divinity is identical to each of the entities that are predicated of it, one must also infer—given the transitivity of identity—that these entities are identical to each other. Thus, in short, according to the DDS, there is no numerical distinction between Divinity and anything that is related to it—as this would render it as metaphysically complex. So, this is the position; however, one can indeed see that the assumption of this specific doctrine within the Latin Trajectory provides a further deepening of the problem that is provided by the distinction issue, as how can there indeed be three (relationally) distinct entities within the Trinity—as is required by (MR)—and yet there only be one, metaphysically simple nature within the Trinity: Divinity, that is also numerically identical to each of these distinct entities? It seems, at least at a prima facie level, that if we want to affirm (MR)—then one cannot do this within Latin Trajectory, given the working of the DDS that requires one to identify each of the members of the Trinity with Divinity itself. Hence, it seems to be the case, as was stated succinctly and sharply by Christopher Hughes (1989, p. 240), that ‘the full-strength account of divine simplicity…describes a God who could not possibly be triune’. Therefore, in taking this all into account, one can see how Monarchical Trinitarianism provides grounds for dealing with an important problem that plagues the Latin Trajectory: the (LPT); however, as it stands, it can only serve the role of being a partial solution as it itself is plagued by some problems that cause it to lack correspondence with some important elements of the Latin Trajectory. The central question that is now presented to us is: how are we to proceed forward? How, within the framework of the Latin Trajectory, is one to maintain the gains provided by (MR), yet without one having to either adopt an instantiation-based position—and thus face the multiple-natures problem—or face the problem raised by its assumption of an identity-based position and the DDS? I believe that the best way forward is for one to indeed not abandon an ‘identification approach’,15 but simply re-configure it so as to ward off the remaining issue presented by the (LPT) (i.e., the distinction issue).16 This re-configuration will be made possible by utilising certain important theses that have been proposed within the field of contemporary metaphysics. Specifically, this article will focus on utilising a ‘heavy duty’ metaphysic that includes various concepts such as: powerful tropes, multiple location, aspects, first-person perspectives, onto-thematic roles and fundamentality/grounding in order to introduce a new Monarchical account of the doctrine of the Trinity—termed ‘Monarchical Aspectival Trinitarianism’—Monarchical Aspectivalism for short, which will provide us with an alternative reading of (AC) that is not plagued by the issues raised by the (LPT). As introduced previously in our exposition of Monarchical Trinitarianism, at the heart of the solution offered in this article to the (LPT) is an equivocation move. Specifically, through the use of the metaphysical concepts that will be employed in this article, one can ward off any form of the (LPT) and the issues raised by it by ‘biting the bullet’ and taking each of the members of the Trinity to be numerically identical—which will allow one to re-construe (4*)–(5*) in such a manner in Monarchical Aspectivalism so as to ward off any charge of inconsistency, given that the members of the Trinity are not numerically distinct, but only qualitatively distinct. That is, more fully, one can indeed affirm the numerical identity of each of the members of the Trinity with Divinity and one another, whilst being able to also maintain their distinctiveness—which is that of their qualitative distinctiveness. Hence, according to the proposed account, one is able to affirm the fact that each of the members of the Trinity is numerically identical to Divinity—the copula ‘is’ is one of numerical identity (i.e., the Father is (numerically identical) to Divinity, the Son is (numerically identical) to Divinity, and the Spirit is (numerically identical) to Divinity), and one can also affirm that the members of the Trinity are distinct from one another. However, there is then an equivocation on the copula ‘is’ with it now being one of qualitative distinctiveness (i.e., the Father is not (qualitatively identical to) the Son, the Father is not (qualitatively identical to) the Spirit and the Spirit is not (qualitatively identical to) the Son. Given that there is solely a qualitative distinction between the members of the Trinity, and not that of a numerical distinction, there thus can indeed be solely one Divinity that each of them is numerically identical to. That is, one will also have a conception of the Trinity that allows one to unproblematically affirm the existence of solely one, metaphysically simple particular object within the Trinity: Divinity, yet there also being three (relationally) distinct entities that are numerically identical to this object—and each other. Thus, this equivocation move—which is underwritten by the metaphysical concepts that will be further unpacked in this article—allows one to ward off the distinction issue—as the members of the Trinity are distinct from one another—and the oneness issue—as, in addition to the monarchy of the Father, there is only one (metaphysically simple) nature (i.e., Divinity) within the Trinitarian life. Monarchical Aspectivalism provides a reading of (AC) that is not plagued by the issues raised by the (LPT) and thus should be favoured over other accounts. To achieve this goal, we will proceed in a step-wise manner over four stages that focus on philosophically elucidating and re-construing each of the elements of (MR₁)—with elements (1*)–(3*) being under focus in stage one and two, elements (4*)–(6*) being under focus in stage three and element (7*) being under focus in stage four.

It will be important to further flesh out the proposal that has been briefly introduced here; however, prior to doing this, it will be helpful to highlight two things: first, it is important to highlight the fact that there is a linguistic assumption that will be made throughout—namely, the term ‘God’ that is featured in (AC) will now be substituted for the term ‘Divinity’, which will enable the present account to fit within the present Monarchical context that holds to the term ‘God’ (in the nominal sense) being solely applicable to one person within the Trinity: the Father. Thus, the dilemma to be faced is trying to show how the members of the Trinity are numerically identical to Divinity (i.e., the one divine nature), whilst retaining the simplicity and oneness of Divinity, the distinction of the members, and the monarchy of the Father. Second, it will also be important to highlight the similarity, or more specifically, the dissimilarity between that of Monarchical Aspectivalism and other available models in the field of analytic theology. That is, Monarchical Aspectivalism—which seeks to utilise a number of important concepts in contemporary metaphysics—might seem to some to either be a version of J.P. Moreland and William Lane Craig’s (Moreland and Craig 2003) ‘Trinity Monotheism’ or Peter van Inwagen’s (1995, 2003) ‘Relative Identity Trinitarianism’. However, first, for the former model, Monarchical Aspectivalism is clearly to be distinguished from Craig and Moreland’s Trinity Monotheism by the mere fact that this model does not conceive of the persons of the Trinity to be ‘parts’ of Divinity, and neither does it take the persons to lack divinity as the Trinity Monotheism account does. In short, Monarchical Aspectivalism does not assume a compositional view of the Trinity and affirms the divinity of each of the persons. Second, for the latter model, there are two important distinctions between the proposed account and van Inwagen’s: first, the metaphysical concepts utilised to formulate this Trinitarian account (such as location, tropes, aspects, relations, etc.)—unlike van Inwagen’s account—are found within the broader field of philosophy and thus, the charge of ad hocness (which is regularly raised against van Inwagen’s account) cannot be raised against this account. Second, and most importantly, the identity in play within the proposed account—unlike van Inwagen’s relative identity—is not an ‘esoteric’ notion of identity, but the ordinary notion of identity that is taken to conform to a ‘restricted’ form of Leibniz’s Law—which is not to be had by van Inwagen’s account through it denying the absoluteness of identity and Leibniz’s Law in a restricted or unrestricted sense. With that said, the proposed account might indeed be some type of ‘relative identity’ account—in that there is a distinction affirmed between numerical-identity and qualitative-identity. Nonetheless, as it stands, it is clearly not one that is to be located within the van Inwagian tradition, and thus does not face the objections raised against that type of model.

So, in taking all of these things into account, the plan of action is as follows: in section two (‘Constructing Monarchical Aspectivalism: Stage One’), I detail the first set of metaphysical concepts—tropes and powerful qualities—and apply it to the task at hand, which will provide the first part of our re-construal of elements (1*)–(3*) of (MR₁). Subsequent to this, in section three (‘Constructing Monarchical Aspectivalism: Stage Two’), I detail the second set of metaphysical concepts—multiple location and aspects—and apply it to the task at hand, which will provide the second part of our re-construal of elements (1*)– 3*) of (MR₁). Then, in section four (‘Constructing Monarchical Aspectivalism: Stage Three’), I detail the third set of metaphysical concepts—first-person perspectives and onto-thematic roles—and apply it to the task at hand, which will provide a re-construal of elements (4*)–(6*) of (MR₁). After this, in section five (‘Constructing Monarchical Aspectivalism: Stage four’), I detail the fourth set of metaphysical concepts—fundamentality and grounding—and, again, apply it to the task at hand, which will provide a re-construal of element (7*) of (MR₁). This will complete the construction of Monarchical Aspectivalism and provide an alternative reading of (AC)—termed (MR₂)—which is not subject to any of the issues raised by the (LPT) (i.e., the oneness issue and the distinction issue). In section six, there will be a concluding section (‘Conclusion’) which will summarise the above results and conclude the article.

2. Constructing Monarchical Aspectivalism: Stage One

The first stage of our constructive tasks focuses on providing a philosophical elucidation and re-construal of elements (1*)–(3*) of (MR₁). This element, in its standard reading, posits the fact of the Father, the Son and the Spirit instantiating the divine nature (i.e., Divinity) that is conceived of as a universal. The standard and alternative readings of this element are stated as follows:

Monarchical Reading1 (MR1)	Monarchical Reading2 (MR2)
1*–3*. Divinity = Universal	1’–3’. Divinity = Powerful Trope

In this re-construal of the nature of Divinity in (1*)–(3*) of (MR₁), there is a utilisation of the metaphysical notion of a ‘powerful trope’—which allows one to identify the Divinity as a powerful trope—rather than as a universal (that is to be instantiated). It will be important to now further unpack the nature of a powerful trope, and then apply it to the task at hand, which will provide a further clarification of this specific element of (AC) and complete the first stage of our constructive task.

2.1. The Nature of a Powerful Trope

In stage one of our constructive task, we introduce the notion of a powerful trope, the nature of which is stated as follows:

(2)	(Powerful Trope): An abstract particular nature of a modifier or modular kind that can be considered as a disposition or as a quality.

This concept of a powerful trope can be further divided into two sub-concepts: as a module or modifier trope and as a powerful quality. These two sub-concepts will now be unpacked in further detail.

Modifier and Module Tropes. A trope is an abstract particular nature of a modifier or modular kind. Abstractness is a word, as A.R.J Fisher (2020, p. 44) notes, that ‘is vague, imprecise, and ambiguous, like many other words in our philosophical theories and ordinary language’. That is, there is not a single conception of the term ‘abstract’. However, trope-theorists, in disambiguating this term, focus on the original and broadest sense of the word, as D.C. Williams (1953, p. 186) writes: ‘At its broadest the ‘true’ meaning of ‘abstract’ is partial, incomplete, or fragmentary, the trait of what is less than it’s including whole’. Thus, a trope is abstract in the sense that it does not exhaust its content or is, in some sense, less than its content. This is in contrast, firstly, to the meaning of the word ‘concrete’, which, according to Williams (1986, p. 3), is ‘if not the main thing which this means is that, however discontinuous the placetime, or ‘plime’, which just contains such an object, the object exhausts or is the whole content of it’. Thus, as Williams (1986, p. 3) further adds, ‘abstract entities differ from concreta in that many of them can and do occupy the same plime’. Thus, for example, a shape-trope that a table possesses is abstract because it does not exhaust its content, as other tropes, such as a colour-trope and a mass-trope, are also collocated with the shape-trope by occupying the same content. However, in contrast, the table would be concrete by itself exhausting its content and thus not allowing another table (or object) to also occupy this content—hence, this example also reveals that a trope needs to be in some way predicable of the whole. The table would be a concrete entity, whilst the shape of the table would be an abstract entity. Thus, in further emphasising this distinction, Keith Campbell (1990, pp. 2–3) helpfully writes:

Abstract here contrasts with concrete: a concrete entity is the totality of the being to be found where our colours, or temperatures or solidities are. The pea is concrete; it monopolises its location. All the qualities to be found where the pea is are qualities of that pea. But the pea’s quality instances are not themselves so exclusive. Each of them shares its place with many others.17

This conception of ‘abstractness’ shows us that an entity is abstract, not because of its relation (or lack thereof) to spatiotemporal reality—as is often held in areas of contemporary metaphysics—but simply because it fails to exhaust the content of the region that is located (or is a part of the content of that region).

In a similar vein to the abstractness of a trope, a trope’s particularity is defined in a specific way within a trope-theoretic framework. In a general setting, universals are regularly taken to be entities that can be wholly present in different locations simultaneously (Macbride 2004, pp. 181–94). In contrast, particulars are taken to not be able to be wholly present in different locations simultaneously. However, Williams and other trope-theorists have proposed an alternative means of distinguishing properties as universals from properties as particulars through Leibniz’s Law, which is taken here to be comprised of two principles: the Identity of Indiscernibles and the Indiscernibility of Identicals, can be formally defined as such:

(3) (Leibniz’s Law)

(a) Identity of Indiscernibles: ∀x∀y(x = y ↔ (φ(x) ↔ φ(y)). (b) Indiscernibility of Identicals: ∀φ(φ(x) ↔ φ(y) → x = y).

In further elucidating this view, Williams (1986, p. 8) writes that:

Entities determined and named in the first principle, by definition not subject to the identity of indiscernibles, are cases or particulars; entities determined in the second way, by definition subject to the identity of indiscernibles, are ‘general’ entities, that is, kinds or universals.

The central contention here is that of universals, but not particulars, conforming to Leibniz’s Law (Ehring 2011, pp. 32–25). Thus, by not conforming to Leibniz’s Law, particulars are entities, as Williams (1986, p. 3) further writes, which ‘may be exactly similar and yet not only distinct but discrete’. For example, according to this account, a shape-trope is particular because it is possible that there is a duplicate of this shape, that is, an entity that is exactly similar, but also distinct from this shape. If a property (or a given entity) obeys Leibniz’s Law, then it is universal. If it does not obey this principle, then it is particular. Thus, for properties as universals, the principle holds in that exactly similar entities (universals) are identical (i.e., if universal x and universal y are indiscernible, then x = y). Whereas for particulars (e.g., tropes), the principle does not hold, as exactly similar entities can be distinct (i.e., if trope x and trope y are indiscernible, then x ≠ y). Given this conception of particularity, a trope is thus particular if it can have a duplicate.

Closely related to the concepts of abstractness and particularity is the primitive nature of a trope. That is, the concept of a nature within this theoretical framework is taken to be an unanalysable notion (i.e., a primitive) that directly applies to a given trope (Fisher 2018, p. 154). A trope is thus a (qualitative) nature in that it does not have, or possess, a nature of its own; rather, the nature of a trope is intrinsic to it. A helpful way to construe intrinsicality, as noted by James Alvarado (2019), is through Rae Langton and David Lewis’ (1998, pp. 334–37) Independence Account of Intrinsicality—where a property P, according to Alvarado (2019, pp. 53–54)18, following Langton and Lewis (1998), is ‘combinatorially intrinsic if and only if the instantiation of P by an object x is indifferent to the fact that x is alone or accompanied in a possible world’. An object x is alone in a possible world w if and only if there is no other object besides x in w. An object that is not alone is accompanied. Thus, the nature of a trope is combinatorially intrinsic if and only if this nature of the trope is invariant under the scenarios in which the given trope is alone or accompanied (Alvarado 2019, p. 554). However, the modal invariance of a trope, unlike other entities, is not grounded upon the possession of an intrinsic nature, but that of it being its intrinsic nature. There is nothing more to a trope than its nature and thus, as noted by Anna-Sofia Maurin (2018, §2.2), tropes, at a general level, ‘have no constituents, in the sense that they are not ‘made up’ or ‘built’ from entities belonging to some other category’. Tropes are thus primitively qualitative and irreducible entities—they are, in a sense, metaphysically simple (i.e., they lack proper parts). However, a trope can be conceptualised in two ways: as a ‘trope’ or as a ‘troper’. Michael Loux (2015, p. 31) introduces this distinction as such:

Whereas tropes are particular properties—things like this redness, this triangularity, this pallor, tropers are thin individuals—things like this individual red thing, this individual triangular thing, and this individual pale thing. The claim would be that familiar objects are bundles of compresent tropers. So the view would again dispense with properties and insist that the ultimate constituents of familiar particulars are intrinsically characterised or natured, but would construe those constituents as particulars rather than universals. Such intrinsically characterised particulars would be the ultimate or underived sources of character: a familiar particular would be, say, pale because it has a pale troper as a constituent.

The central difference between a trope and troper is that of the former being a singly (or minimally) characterising property, whilst the latter is a singly (or minimally) charactered property in a ‘stretched’ (or analogical) sense—it is a ‘propertied thing or object’—where an object is a countable, property-bearing particular that has determinate existence and identity conditions and is not borne or possessed by anything else.19 Thus, there is an ontological difference between tropes that are ‘tropes’ and tropes that are ‘tropers’. However, off of this distinction, Robert K. Garcia (2015a, 2015b) notes that Loux’s division between a trope and a troper is not a novel suggestion, but is, in fact, the prevalent view of tropes found within the literature (Garcia 2015a). According to Garcia, Loux’s distinction between a ‘trope’ and a ‘troper’ is thus best described as a distinction between two different concepts of a trope. Hence, Garcia sees that the two terms ‘trope’ and ‘troper’ are potentially misleading, and thus he introduces the more helpful terms of a ‘modifier trope’ (for Loux’s ‘trope’) and a ‘module trope’ (for Loux’s ‘troper’). At a general level, modifier tropes and module tropes are both taken to be non-shareable, maximally thin (i.e., singly charactered) character-grounders (Garcia 2015b). The central difference between these two types of tropes is that of a modifier trope being a property that does not exemplify this character, but simply bestows it upon (i.e., ‘makes’) something else to be charactered in that specific way. Thus, for example, a particular object is spherical in virtue of its modifier trope, which ‘spherises’ that object by simply making it spherical, without it sharing in that character as well. The character grounding provided by a modifier trope is thus de novo (or sui generis) (Garcia 2015b), whilst a module trope is an object that exemplifies the character that it grounds (i.e., is self-exemplifying). Thus, for example, a particular (thickly charactered) object is spherical and red in virtue of its module tropes, which are themselves spherical and red (i.e., exemplify sphericity and redness), and together (compresently) are parts (or constituents) of that object. A module tropes’ character grounding, rather than being de novo, can thus be taken to be some type of parthood (or constitution) relation (Garcia 2015a). Furthermore, an additional distinction between modifier and module tropes is the role played by these types of tropes in causation. As Maurin (2018, §4.1, emphasis in text) writes,

According to a majority of the trope theorists, tropes have an important role to play in causation. It is, after all, not the whole stove that burns you, it is its temperature that does the damage. And it is not any temperature, nor temperature in general, which leaves a red mark. That mark is left by the particular temperature had by this particular stove now or, in other words, it is left by the stove’s temperature-trope.

At a more specific level, it is solely module tropes, rather than modifier tropes, that can play any direct role in causation. As in Maurin’s example, a modifier hotness trope cannot fulfil the role of being the direct cause of the burn mark, as it is not itself hot—something else must thus be the direct cause of the burn mark. Yet, this is not a unique problem for the modifier view, as Garcia notes, ‘mass tropes are not massive, charge tropes are not charged, and so on. Thus, unlike module tropes, modifier tropes seem ineligible to play a direct role in causation’ (Garcia 2015a, p. 643). Modifier tropes, in a similar manner to universals, are thus causally inert. However, the modular view does not have this issue, given that module tropes are self-exemplifying entities, resulting, in our example above, in a modular hotness trope being the direct cause of the burn mark. Thus, again, at a more specific level, it is module tropes, and not modifier tropes, that are uniquely suited to be the basic terms of causation (Garcia 2015a). Thus, a trope, identified as an abstract particular nature, can either be a modifier—and thus be a maximally thinly charactered property that is not self-exemplifying (i.e., does not exemplify the character that it bestows)—or, it can be modular, and thus be a maximally thinly charactered property* that is self-exemplifying (i.e., exemplifies the character that it bestows). We can now turn our attention onto the second sub-concept noted above: a powerful quality.

Powerful Qualities. As a modular or modifier trope, a trope is a powerful quality. More specifically, according to Charlie B. Martin (2008) and John Heil (2012),20 every trope possesses a dual-nature (or character),21 where, as Martin and Heil (1999, p. 45) note, it is in ‘in virtue of possessing a property [a trope], an object possesses both a particular dispositionality and a particular qualitative character’ (Martin and Heil 1999). The dispositionality of a trope conveys, upon the object that possesses it, specific powers to behave in certain ways, in certain circumstances. More fully, a trope’s dispositionality, following Molnar (2003), can be understood in at least five ways: it is, first, directed—in that a trope is directed towards some characteristic and distinctive manifestation.22 Second, it is independent—in that a trope is ontologically independent of its manifestations; that is, it can exist when it is not being manifested. Third, it is actual—in that a trope is an occurrent feature of the object that possesses it. Fourth, it is intrinsic—in that a trope is intrinsic to its bearer.23 Fifth, it is objective—in that the existence of a trope is not dependent on the existence of any conscious, observing minds. In addition to these five characteristics of the dispositionality, one can also conceive of a trope as ‘multi-track’—which is that of it being capable of bringing about distinct ‘manifestation types’ (i.e., different types of effects), and it often does this in conjunction with other powerful tropes. One way to understand the outworking of this is through the notion of a threshold that has been introduced by Stephen Mumford and Rani Lill Anjum (2010)—where a given effect occurs when certain powers have accumulated to reach the requisite threshold.24 This accumulation can then be plotted as vectors which, according to Mumford and Anjum (2010, p. 145), ‘is a useful way of modelling powers because, like powers, they have a direction—the possible manifestation the power is for—and they have a strength or intensity, indicated by the length of the vector’. This would thus be depicted on a one-dimensional quality space with F and G representing two possible manifestation types of some accumulated dispositions. For example, F could be the property of being cold, and G could be the property of being hot, as illustrated by Mumford and Anjum (2010, p. 146) in Figure 1. as follows (where ‘T’ is the threshold and ‘R’ is the resultant effect):

In this illustration, for one to calculate the final effect, one has to take into account the strength and direction of each individual vector with the resultant vector R, representing the fact that an effect is caused when the dispositions under question have accumulated to reach a certain point in which that effect is triggered (Mumford and Anjum 2010). Taking this all into account, a trope, of a modifier or modular kind, is thus dispositional in that it fulfils the roles of directedness, independence, actuality, intrinsicality and objectivity. Additionally, one can understand the effects of a multi-track powerful trope, in a ‘fine-grained’ manner, through the utilisation of the notion of a threshold and plotting vectors.

Now, the qualitativity of a trope—which is a less developed concept than the concept of dispositionality in the Powerful Qualities view—is that of the trope being a ‘real’ or ‘actual’ feature of the object that possesses it. That is, as Heil (2012, p. 59) writes, qualities are ‘here and now, actual, not merely potential, features of the objects which they are qualities’. Thus, the qualitativity of a trope essentially contributes to the overall makeup of its bearer—in the here and now (Taylor 2013).25 In other words, the trope provides a qualitative contribution to its bearer, where, as Joaquim Giannotti writes, ‘a bearer is in some way or other by virtue of having a property [a trope]’ (Giannotti 2019, p. 81, square parenthesis added). It is thus a matter of how the bearer is actually like by having that specific quality. Therefore, taking the dispositional trope of fragility as an example, one would rightly say that this trope is an actual or occurrent feature of the vase, in that it is really present within the vase in a ‘here and now’ fashion, and thus contributes to the way that it is, or the overall make up of it.26

Dispositionality and qualitativity, as Martin and Heil write, must thus be ‘thought of as unrealizable limits for different ways of being of that property [trope]’ (Martin and Heil 1999, pp. 46–47, square parenthesis added). Where the ways of being a trope can be conceived, as John Levinson (1978) has noted, as the ways that a trope is. More specifically, as Levinson (1978, p. 2) writes, they are ‘the varied fashions in which it goes about the complicated business of existing’. There is thus a correspondence between the dispositional and the qualitative in such a way that they are to be taken as inseparable and correlative ‘traits’ or ‘ways’ of any given trope.27 They are ‘built into a trope’ in such a manner, as Martin and Heil note, that they are that trope, and thus, because of this, a trope’s dispositionality or qualitativity ‘cannot be abstracted as entirely distinct or separable ingredients’ (Martin and Heil 1999, p. 46). There is thus no ‘real’ distinction between the dispositionality and qualitativity of a given trope.28 That is, within the Powerful Qualities view, there is, in fact, a ‘surprising identity’ between the dispositional and the qualitative (Martin and Heil 1999). A trope’s dispositionality is not grounded upon its qualitative nature and thus is, in some sense, separable from it. Instead, a trope’s dispositionality is its qualitativity and vice versa (see note 22). (Martin and Heil 1999).Thus, whilst it might seem that the terms ‘dispositionality’ and ‘qualitativity’ are referring to two distinct and separable types of tropes, it is, in fact, that the dispositional and qualitative are identical to each other, and that each is also identical to the single unitary trope itself (Taylor 2013).29 Importantly, however, there is no ontological priority between the dispositional and the qualitative; rather, they equi-fundamental. Moreover, there is, in fact, a deflation between the dispositional and qualitative, where the same trope can simply be regarded, or considered, as a disposition or a quality. Dispositionality and qualitativity are thus not parts or sides of a given trope, but the one trope itself, just differently considered. They are, as Martin and Heil write, ‘different ways of representing the self-same property [trope]’ (Martin and Heil 1999, p. 47, square parenthesis added). For example, in illustrating this, we can turn our attention to the case of a ball and an inclined slope in Figure 2. (with the black arrows representing the dispositionality of the ball and the circular object representing the geometrical shape had by the object):

In this specific example,30 if we consider a rubber ball that possesses a spherical-trope, this trope can be considered qualitatively when we regard it as the distinctive and actual geometrical shape that contributes to the overall makeup of the ball (i.e., it provides it with its shape). However, we can also consider the spherical-trope dispositionally when we regard it as the power that the ball has to roll in a certain way when placed in a certain circumstance (e.g., on an inclined slope) (Giannotti 2019). Thus, we can see here that there is no demarcation of a numerical distinction in reality between the dispositional and qualitative, but instead, the dispositionality that conveys upon a ball the certain powers that it has is indeed identical to the qualitativity that gives that ball a certain shape and both of these are identical with the single unitary spherical-trope itself that is possessed by the ball (Taylor 2013).31 Thus, at a more general level, when one considers a trope as qualitative or as dispositional, they are considering the whole trope—and not a part of it—in a certain way, at a given time. Thus, in other words, when we are dispositionally considering a trope at a given time, we consider that trope as bestowing upon its bearer certain dispositional powers. Additionally, when we are qualitatively considering the same trope at another given time, we are simply considering it as contributing to the overall ‘real’ or ‘actual’ make up of its bearer.

In summary: a trope is an abstract particular nature that either can be modular—a self-exemplifying, maximally thinly charactered property* (i.e., an object)—or, it can be a modifier—a non-self-exemplifying, maximally thinly characterising property—with a dual-character: a dispositionality and a qualitativity, that are identical to the trope itself. This is the philosophical framework within which we will be operating. However, one can raise an objection against the cogency of this powerful trope theoretic framework. Specifically, one can raise an issue against the dual-character that is identical to a given trope. As, given Leibniz’s Law, how could the dispositionality of a trope be identical to its qualitativity and the trope itself when each bears different qualities? That is, the dispositionality of a trope is its ability to empower its bearer to behave in a certain way, the qualitativity of a trope is what contributes to making the trope what it is, and a trope possesses this dispositionality and qualitativity, without, however, its dispositionality and qualitativity having this dual characteristic as well—dispositionality does not have a dispositional and a qualitative character; qualitativity does not have a qualitative and a dispositional character. Thus, what is true of the dispositionality of a trope is not also true of its qualitativity and of the trope itself (and vice versa). Hence, we have a transgression of Leibniz’s Law here, which indicates that the dispositional and the qualitative are not identical to each other, nor with the trope itself. Thus, an important question to be faced is: is there a way to re-construe the powerful nature of a trope in order not to transgress Leibniz’s Law? I believe that there is, once we have introduced the notion of an aspect.32 We will thus leave this question unanswered until the penultimate section and focus on applying the above set of concepts to the task at hand.

2.2. Divinity as a Powerful Trope

In this stage of our constructive task, we are utilising a powerful trope-theoretic framework, and thus we take Divinity to be a powerful module trope—an abstract particular nature of a modular kind that can be considered as a disposition or as a quality. More specifically, Divinity is, first, abstract because it has the trait of being ‘less than the including whole’—Divinity does not exhaust its ‘content’ or ‘plime’ (or is less than its ‘content’ or ‘plime’)—where, in assuming Christian theism, we take this content or plime to be the Trinity, which would include three ‘reiterations’ of Divinity (identified as the Father, the Son and the Spirit)—resulting in it not exhausting either of these things.33 Second, Divinity is particular by it failing to abide by Leibniz’s Law, and thus permitting the possibility of the existence of an entity (i.e., a duplicate) that is exactly similar in its intrinsic properties (i.e., its nature) to it—specifically, Divinity, as will be shown below, can have certain ‘region-specific’ reiterations of itself (i.e., Divinity reiterated as the Father, the Son and the Spirit). Third, Divinity is the specific character that it bestows, which is that of it being divine. In other words, Divinity’s nature is intrinsic to it—not in the sense of it possessing a further intrinsic ‘property’, but simply by that of it being numerically identical to this nature. Furthermore, it is plausible to take Divinity as a module trope, rather than as a modifier trope, in the sense of it being a maximally thinly charactered object—a property in an analogous sense (i.e., a property*)—that is self-exemplifying and serves the role of bestowing this characteristic upon another object: the Trinity, which it constitutes. Moreover, since Divinity is a trope of a modular kind, it plays a direct role in causation and is thus a basic term of a causal relation.34 Fourth, Divinity is a powerful quality in the sense of it being dual-charactered—it has a particular dispositional and qualitative character. The dispositionality of Divinity is the disposition for it to behave in a certain way (which empowers the Trinity to behave in a certain way). That is, as a module trope, Divinity is powerful in five ways: it is, firstly, directed—in that Divinity (or its action) is directed towards some characteristic and distinctive manifestations, such as that of creating or sustaining the universe. Secondly, it is independent—in that Divinity is ontologically independent of its manifestations; that is, it exists when its power is not manifested.35 Thirdly, it is actual—in that Divinity is an occurrent feature of the object that possesses it: the Trinity. Fourthly, it is intrinsic—Divinity is intrinsic to its bearer, which is, again, the Trinity.36 Fifthly, it is objective— in that the existence of Divinity is not dependent upon the existence of any conscious, observing minds. Divinity, as a module trope, is thus powerful in that it fulfils the roles of directedness, independence, actuality, intrinsicality and objectivity. However, it does this without any of the limitations that certain other powerful module tropes may have. In short, Divinity is a maximal power trope (i.e., an omnipotence-trope), in that it is multi-track—it is cable of producing distinct manifestation types—yet it can do this without any limitation except for logic—and thus is able to act in different scenarios without limitation (i.e., being maximally powerful/omnipotent) and being able to know all things without limitation (i.e., being maximally knowledgeable/omniscient), or being present at all points of space (i.e., being maximally present/omnipresent), etc. One way in which one can further understand the limitlessness of the dispositionality of Divinity is through the utilisation of the notion of a threshold and a vector depicted on a one-dimensional quality space with F and G representing two possible effects of Divinity. For example, F could be the property of resting on the ground, and G could be the property of being suspended in the air, which can be illustrated in Figure 3. as follows (where ‘T’ is the threshold and ‘R’ is the resultant effect):

In this illustration, for one to understand the effect brought about by Divinity—which, in this case, is to cause something to be suspended in the air—is not produced by an aggregation of operative dispositions that have reached a certain threshold for the effect. Rather, Divinity, in all cases when it exercises its power, is unopposed and does not require other dispositions to reach a threshold. In short, Divinity can bring about any effect—and thus reach the needed threshold for the occurrence of an effect—without limitations from anything—aside from logic. In all, limitless dispositionality (i.e., maximal power/omnipotence) is thus a ‘trait’ of Divinity—it is ‘built’ into it, whereas the qualitativity of Divinity is what makes it a ‘real’ or ‘actual’ entity. The qualitative character of Divinity thus essentially contributes to the overall makeup of Divinity, which is that of it having various theoretical roles that it fulfils and thus provides a qualitative contribution to Divinity, such that Divinity is what it is because of it. Qualitativity is thus another ‘trait’ of Divinity—it is also ‘built’ into it. Furthermore, there is a ‘surprising identity’ between this dispositionality, qualitativity, and Divinity itself—in that Divinity’s dispositionality is just its qualitativity, and these both are Divinity. In other words, the dispositional and qualitative characters of Divinity are numerically identical with one another and with Divinity itself. Thus, Divinity’s dispositionality—which disposes it to act in a certain way—is not really distinct from Divinity’s qualitativity—which bestows upon it the qualitative characteristic of being a certain way. This dispositionality and qualitativity are the single and unitary powerful trope itself, and the distinction between these ‘traits’ or ‘ways’ of Divinity, and Divinity itself, do not demarcate a distinction in reality—rather, they are one and the same thing—namely, the unitary, metaphysically simple Divinity itself. Thus, the dispositionality and qualitativity of Divinity are not to be taken as parts, sides or additional properties possessed by Divinity, but the one self-same trope, just differently considered. We can illustrate in Figure 4. this ‘surprising identity’ as such (with the double-headed arrows representing a numerical identity relation):

Thus, Divinity can be regarded, or considered, as a disposition or as a quality, which are simply equi-fundamental, identical ‘traits’ or ‘ways’ of Divinity. Thus, despite the dispositional and qualitative distinctions that can be made of it, there is only one trope: Divinity, which is not composed of any proper parts—given the fact that there is an identity between Divinity and its qualitativity and dispositionality.

In summary: Divinity is a powerful trope, that is, it is an abstract particular nature that is modular—it is a self-exemplifying, maximally thinly charactered property* (i.e., an object)—with a dual character: a dispositionality and a qualitativity, that are identical to the one, metaphysically simple Divinity itself. This is the conceptualisation of Divinity that we will be working with. However, as in the mundane case, more indeed is required to be said concerning how the dual character of Divinity can, on the one hand, be identical in the manner stated above, whilst, on the other hand, each ‘character’ being able to differ to a certain extent. This task will be taken up in the next section once the notion of an aspect is on the table. However, what we have established, within the Trinitarian framework in which we are operating within, is that there is exactly one particular object posited by this account, which has been identified as one powerful divinity trope: Divinity. This account thus does not posit, in line with certain other Trinitarian accounts (such as Richard Swinburne’s (1994) ‘Functional Monotheism’ account), the existence of multiple ‘tropes of divinity’ within the Trinitarian life—each of which is related (in some manner) to the members of the Trinity. Rather, as we will see below, there is solely one (powerful module) trope of divinity that grounds the oneness and distinction of the members of the Trinity. Thus, on the basis of this conceptualisation of the nature of Divinity, we can now proceed onto the second stage of our constructive task, which focuses on explicating and applying the metaphysical notions of multiple location and aspects to the task at hand.

3. Constructing Monarchical Aspectivalism: Stage Two

The second stage of our constructive task focuses on providing a philosophical elucidation and re-construal of elements (1*)–(3*) of (MR₁). This element, in its standard reading, posits the fact of the Father, the Son and the Spirit instantiating the one universal of ‘Divinity’. The standard and alternative readings of this element are stated as follows:

Monarchical Reading1 (MR1)	Monarchical Reading2 (MR2)
1*. The Father ins Divinity (Universal). 2*. The Son ins Divinity (Universal). 3*. The Spirit ins Divinity (Universal).	1’. Father-Aspect = Divinity (Trope). 2’. Son-Aspect = Divinity (Trope). 3’. Spirit-Aspect = Divinity (Trope).

In this re-construal of (1*)–(3*) of (MR₁), there is an assumption made concerning the cogency of the metaphysical notions of ‘multiple location’ and ‘aspects’, which allows one to, first, take Divinity to be a multiply located object and, second, to identify the Father, the Son and the Spirit as ‘aspects’ that are numerically identical to the one Divinity. It will be important to now further unpack the nature of multiple location and aspects, and then apply it to the task at hand, which will provide a further clarification of this specific element of (AC) and complete the second stage of our constructive task.

3.1. The Nature of Multiple Location and Aspects

In stage two of our constructive task, we introduce the notion of aspectival multiple location, the nature of which is stated as follows:

(4)	(Aspectival Multiple Location): A particular object having more than one (disjoint) exact location and bearing different aspects at those locations.

This notion of aspectival multiple location can also be further divided into two sub-concepts: multiple location and aspects. These two sub-concepts will now be unpacked in further detail.

Multiple Location. A ‘chorological system’ is a system concerning location. Following Cody Gilmore (2018, §2), we can utilise a specific chorological system that takes the relation of ‘exact location’ as basic and construes it as such:

(5)	(Exact Location): An entity x is exactly located at a region y if and only if x has (or has-at-y) exactly the same shape and size as y and stands (or stands-at-y) in all the same spatial or spatiotemporal relations to other entities as does y (see note 27).

At the heart of this conceptualisation of the chorological relation of exact location is the fact of objects inheriting the same properties and relations of the regions that they are exactly located at—for example, small spheres are exactly located at small spherical regions and share all of the spatial properties and relations of these regions; large cubes are exactly located at large cubical regions and share all of the spatial properties and relations of these regions, etc. (Gilmore 2018). More precisely, following Nikk Effingham (2015a, p. 846), we can, first, state the chorological relation of exact location as such: ‘__ is exactly located at spatial region __ (at time __)’,37 and, second, express the inner workings of this relation through the following paradigm examples:

(6)	The cube is exactly located at just one cube-shaped region.
(7)	The Kuiper Belt is exactly located at a scattered region composed of lots of disjoint asteroid shaped regions.
(8)	A sphere is exactly located at some region with a volume equal to 4π/3 multiplied by the radius (of the sphere) cubed.

On the basis of the conceptualisation of the relation of exact location that is expressed by these types of paradigm examples, we can now—again following Effingham (2015a, p. 848)—define the chorological term of multiple location as such:

(9)	(Multiple Location) An entity x is multi-located if there are two or more distinct regions that x is exactly located at.

According to this construal of the notion of multiple location, to say that a given object is multiply located is simply to say that it possesses more than one (disjoint) exact location—it has the exact same shape/size as, and stands in the same relations of, more than one (disjoint) spatial region. Following Gilmore (2018, §6), we can illustrate in Figure 5. the inner workings of this notion through the following paradigm example (with the left image representing a scattered, single-located object and the right image presenting a non-scattered, multiply located object):

In this paradigm example, object o₁ is a scattered entity due to its shape being that of the sum of the two disjoint circles (Gilmore 2018). This type of entity is thus not multiply located as it has one exact location: the scattered region r₃. However, object o₂ is, in fact, multiply located as it has (solely) two exact locations—it is exactly located at region r₃ and at the (disjoint) region r₄, and thus—in assuming the construal of exact location noted above—as o₂ is exactly located at r₃ and at r₄, which are both circular in shape, o₂ must also be circular (at least whilst it is exactly located at r₃ and r₄) (Gilmore 2018). Given all of this, exact location is thus not a one-one relation, but a many-one relation, where a single object can be (exactly) located in more than one (disjoint) region at the same time. On the basis of this clarification of the notion of multiple location, we can now turn our attention towards the second sub-concept: ‘aspects’, which was noted above.

Aspects. The concept of an ‘aspect’ provides a coherent conceptual foundation for the notion of qualitative self-differing (hereafter, self-differing). Self-differing, according to Donald Baxter (1999, 2016, 2018a, 2018b), is the qualitative differing of some entity in one way (or respect) from itself in another.38 Self-differing is thus the qualitative differing of numerically identical aspects possessed by an individual (Baxter 1999). That is, the same individual can possess qualitatively differing aspects that are nevertheless numerically identical with the individual, and thus, given the transitivity of identity, with each other.

To help motivate the existence of aspects within this context, we can consider two different cases in which an individual is torn about what to do (or how to feel) in a certain situation:

The Case of David

The Case of Jane

David is an ardent philosophy professor and is also a loving and faithful father of two children, Jacob and Melissa. Now suppose that, firstly, David has an upcoming philosophy conference in which he is the keynote speaker and, due to other work commitments, has not prepared his speech yet. Secondly, suppose that David had previously promised that he would reward his children with a camping trip this upcoming weekend if they achieved A* grades in their A-Level results. And, thirdly, suppose that Jacob and Mellissa have both, in fact, recently achieved A* grades in their A-Level results.

Jane is an ambitious lawyer and a (volunteer) senior staff member of Humanists UK. Now, suppose Jane is on her way to an important meeting at her law firm. However, when she is walking, she observes an assault taking place in an alley. An inner struggle now ensues between her conscience, to stop and call for help, and her career ambitions, which tell her she cannot miss this meeting.

In these two specific scenarios, David and Jane are in situations of self-differing as, first, in the Case of David, he knows that he has an important keynote speech that he needs to prepare—and being an ardent philosophy professor, he wants to fulfil this commitment and thus complete his speech. So, the following proposition would be true: David ‘does not want to take his children on a camping trip this upcoming weekend’. However, having promised his children that he would reward them for their academic achievement, and being a loving and faithful father, he wants to fulfil his promise to them. So, the following conflicting proposition would also be true: David ‘wants to take his children on a camping trip this weekend’. David is torn. He is in conflict with himself. He thus differs from himself. David’s struggle is between two aspects of him: David insofar as he is a philosopher versus David insofar as he is a father. Now, second, in the Case of Jane, she knows that she has an important meeting that will lead to her becoming partner at her law firm—and has career ambitions that result in her wanting to go to her meeting to secure the promotion. So, the following proposition would be true: Jane ‘does not want to stop and call for help for the stranger’. However, being an ethically minded humanist—who thus tries to live a life of empathy and compassion towards her fellow human beings—she wants to help the individual who has been attacked. So, the following conflicting proposition would also be true: Jane ‘wants to stop and call for help for the stranger’. Jane, like David, is torn. She is in conflict with herself. She thus differs from herself. Jane’s struggle is between two aspects of her: Jane insofar as she is a lawyer versus Jane insofar as she is a humanist. These cases, and other cases of internal conflict, are cases of self-differing, where the subjects of what differs are the aspects of the individual that self-differs. Thus, for the case to be one of differing, one aspect must possess a quality that another aspect lacks. Additionally, for it to be a case of self-differing, the aspects must be numerically identical to the individual that bears them (Baxter 2018a, p. 907). The notion of an aspect can be further elucidated at two levels: the semantic level and the ontological level.

At the semantic level, aspects are expressed through ‘nominal qualifiers’ such as ‘insofar as’ (or ‘in some respect’ and to a lesser extent ‘as’ and ‘qua’). Nominal qualifiers serve a special role of referring to aspects—they are specifically present within self-differing cases, where the same entity can be discernible from itself. Furthermore, following Jason Turner (2014, p. 227), the use of a nominal qualifier in these cases (and other cases like them) can be further precisified via formalisation—where one takes ‘α’ as a regular term and ‘φ(y)’ as any formula open in y, and thus we can introduce a term to refer to aspects, namely an aspect term, written as such: ‘α_y[φ(y)]’. From this semantic basis, and with the notion of an aspect term to hand, we can now progress onto the ontological level, which will allow us to further elucidate the nature of an aspect.

At the ontological level, according to Baxter, aspects are difficult to distinguish from other entities.39 However, we can begin to acquire an understanding of their nature by describing their functional role and the relationship to the individuals that bear them. Primarily, the aspects of an individual function as the particular ways of being of that individual. A way of being is a conceptually primitive notion that, as noted previously, can be glossed in part by taking it to be the way or manner in which an entity exists. Thus, aspects function as the particular ways in which individuals are. However, as ways of being of an individual, aspects are not qualities (or properties) as they can, themselves, possess qualities (or properties) due to their numerical identity to the individuals that bear them.40 Aspects, however, do not possess all of the qualities that the particular individuals that they are aspects of have. Moreover, in a similar manner to their bearers, they are particular entities, rather than universals, through Leibniz’s Law (in an unrestricted sense) failing to hold for them.41 Secondly, despite the numerical identity between individuals and their aspects, aspects are not ‘complete individuals’ due to the fact that complete individuals are entities that can exist independently. Instead, according to Baxter, aspects are ‘incomplete entities’ due to them ‘having fewer properties than it takes to exist on one’s own’ (Baxter 2018a, p. 916). Aspects are thus incomplete in the sense of them being dependent upon the complete individuals that they are numerically identical to.42 The nature of a complete individual determines the aspects that they have, in that they depend entirely upon how that individual entity is—once we have the individual, we also have its ways of being (Giannotti 2019).43 Thirdly, aspects are not mereological parts of the individuals that they are aspects of, as, again, they are numerically identical to, rather than a ‘part’ of, these individuals (Baxter 2018a). Lastly, aspects are not mental abstractions. That is, even though a complete individual’s aspects are abstract entities (through them failing to exhaust the content or plime that they are aspects of),44 that can be considered by means of abstraction (where one abstracts a way that an individual is), it is important to note, as Baxter writes, that the difference between a complete individual and their aspects is ‘a less-than-numerical distinction but more than a mere distinction of reason’ (Baxter 2016, p. 99). Baxter terms this distinction, an aspectival distinction, which results in the aspects of an individual only ever being two (or more) in a ‘loose’ sense—when they are counted based on qualitative distinction. However, in a ‘strict’ sense—when the aspects are counted based on a numerical distinction—they are only ever one. Thus, aspects, as Baxter notes, provide a ‘complexity to the simple, i.e., a qualitative complexity to the quantitatively simple’ (Baxter 2016, p. 178). Taking this explanation of the semantic and ontological features of aspects into account, for further clarity, we can construe the concept of an aspect as such:

(10) (Aspect)

(a) An aspect is a qualitatively differing, incomplete abstract particular entity that is numerically identical to the complete individual that bears it (and any other aspect possessed by that individual). (b) It functions as a particular way that a complete individual is and is determined by that individual’s nature. (c) It is expressed through a nominal qualifier such as ‘insofar as’, which, at a precise level, can be captured through the use of an aspect term (such as αy[φ(y)]). (d) It is distinguishable through an aspectival distinction, rather than a numerical or conceptual distinction.

On the basis of this basic construal of an aspect, we can now re-construe the notion of self-differing as that of the qualitative differing of numerically identical aspects possessed by an individual. Therefore, in having motivated and clarified the notion of an aspect and aspectival self-differing it will be helpful now to turn our attention away from psychological cases, and apply this notion to the case of a multi-located object, which will show how such an object can differ from itself (without entailing a contradiction). We can state this case succinctly as follows:

The Case of a Multilocated Object

There is a particular object that is located at two (disjoint) spatial regions. As an entity inherits the properties (‘qualities’) and relations of the specific region that it is exactly located at, this particular object bears different properties (‘qualities’) and relations at each of the specific spatial regions that it is exactly located at.

In unpacking this case and example further: let the spherical region r₁ and the cubical region r₂ be disjoint regions in space. Let there exist a multiply located object O that is exactly located at r₁ and r₂, and bears the properties of sphericity S and cubicity C at its respective regions. Additionally, let ‘@’ stand for the chorological relation ‘__ is exactly located at spatial region __ (at time __)’. Then, we take the following aspects to exist and bear differing properties:

(11)	Oy[y@r1] is S

and

(12)	Oy[y@r2] is C

‘O_y[y@r₁]’ (i.e., O insofar as it is exactly located at spatial region r₁) refers to one, numerically identical aspect of O, which bears the property of sphericity, and ‘O_y[y@r₂]’ (i.e., O insofar as it is exactly located at spatial region r₂) refers to another, numerically identical aspect of O, which bears the property of cubicity. These region-specific aspects thus differ in the properties that are possessed at the regions in which they are exactly located—which, for some, would be problematic as it seems to be the case that45:

(13)	Oy[y@r1] is S

and

(14)	Oy[y@r2] is S

is contradictory, as assuming that it is not possible for an object to be both spherical and cubical at the same time, then the fact that O_y[y@r₁] is spherical in r₁ implies that it is not shaped in any other way in any other region in space (including r₂). Additionally, due to Leibniz’s Law (i.e., the Indiscernibility of Identicals), which was previously defined above, it follows that:

(15)	(Oy[y@r1]) = (Oy[y@r2]) → ∀O [((Oy[y@r1]) is F) ↔ ((Oy[y@r2]) is F].

This results in O_y[y@r₁] possessing all of the properties that O_y[y@r₂] has. More specifically, as O_y[y@r₁] is spherical in r₁, then so must (O_y[y@r₂]) be spherical in r₂. However, according to (12) O_y[y@r₂] is not spherical in r₂ (through it being cubical in r₂). Hence, contradiction. However, a way for one to deal with this apparent contradiction is to posit the existence of aspects. As, by doing just this, we can see that it is the aspects possessed by the multiply located object at the different regions in which it is exactly located that possess these properties and not the object itself. Thus, there is no entailment of a contradiction here. That is, through the use of nominal qualifiers such as ‘insofar as’ (i.e., formally α_y[φ(y)]), it removes any explicit contradiction, as the above case does not say that O, unqualified, is and is not spherical shaped. Rather, it is simply O_y[y@r₁] (i.e., O insofar as it is located at a spherical region) that is spherical and O_y[y@r₂] (i.e., O insofar as it is located at a cubical region) that is not spherical. The negation, in these types of cases, as Baxter writes, ‘is internal, that is, has short-scope relative to the nominal qualifier and so there is no contradiction’ (Baxter 2018b, p. 104). Aspects of O have these qualities, but not O (unqualified). Yet, O_y[y@r₁] and O_y[y@r₂]—as aspects of O—are identical to it, which indicates, as Turner (2014, p. 239) notes, that the following principle holds:

(16)	(Aspect Identity) ∀x(∃z(z = xy[φ(y)]) → x = xy[φ(y)]). Informally: Every aspect is numerically identical with a complete individual x.

In reality, O is O_y[y@r₁], and O is O_y[y@r₂]—O insofar as it is in a particular region (i.e., at r₁ or at r₂) is still O. Additionally, taking into account the transitivity of identity, this would result in:

(17)	Oy[y@r1] = Oy[y@r2]

which is that of O’s qualitatively differing aspects each being numerically identical to one another, yet without the resultant differences between them indicating that these aspects, and the object that bears them, are numerically distinct entities. That is, one can block the secundum quid ad simpliciter inference, which, following Baxter (2018a, p. 913), can be written formally as such:

(18)	(Block) ∼(∀x)(F(xy[φ(y)]) → Fx). Informally: It does not follow from the fact that an aspect of a complete individual x is F that x is F.

Thus, in this context, the same thing can be abstractedly considered in two ways, and in this discernment, it can differ from itself, whilst still being that same thing. O is numerically identical to the two above aspects (and a near-infinite number of other aspects), and these aspects are all numerically identical to each other. The same individual can possess qualitatively differing aspects that are nevertheless numerically identical to the individual that bears them and also with each other. This all seems to be conceptually coherent. However, a pertinent issue appears to be in sight. That is, at a prima facie level, Leibniz’s Law seems to be transgressed within an aspectival framework, as the existence of aspects allows for there to be numerically identical entities that do not share the same qualities. Any violation of Leibniz’s Law will certainly be problematic for most individuals. However, once this issue is further investigated, we can, in fact, see that there is no violation of Leibniz’s Law within an aspectival framework—as, according to Baxter (2016, p. 172, emphasis added), aspects allow ‘contradictories to be predicated of the same thing in a way that Leibniz’s Law is silent about’. We can begin to notice this ‘silence’ by asking the question of why Leibniz’s Law should be taken to apply to all entities, without restriction? Baxter sees that the issue might revolve around the frequently raised worry that a relation that is not characterised by Leibniz’s Law is not identity.46 However, Baxter (2018a, p. 908) sees that the only reason for this attitude is that the principle seems to express the truth that no entity both possesses and lacks a property—that contradictions cannot exist in reality. Thus, as Baxter writes, ‘It may seem that the original Indiscernibility of Identicals [Leibniz’s Law] is just another way of saying that nothing both has and lacks a property, which is just another way of saying that no contradictions are true’ (Baxter 2018a, p. 907, square parenthesis added). It thus seems that individuals regularly accord Leibniz’s Law (the Indiscernibility of Identicals) the same unassailable status that is regularly given to the Principle of Non-Contradiction (Baxter 2018a, p. 908). However, following Aristotle, Baxter sees that what is central to the latter principle is solely that of nothing both possessing and lacking a property in the same respect at the same time. Thus, this formulation leaves room to maneuver as it opens up the possibility that, as Baxter writes, ‘something in one respect has a property that it in another respect lacks’ (Baxter 2018b, p. 105). However, that claim is not contradictory, as a contradictory claim here would be for one to say that some individual in one respect possesses a property that in no respect it possesses. Baxter’s non-contradictory claim is thus simply that something in one respect is numerically identical with itself in another respect.47 Thus, based on this claim, some numerically identical things can qualitatively differ without an entailment of a contradiction. Baxter thus believes that we lack any substantial reason to believe that Leibniz’s Law applies to every entity without question, and states that ‘Leibniz’s Law should not be thought of as applying absolutely generally to anything that can be talked about; the argument that it must apply so generally, fails’ (Baxter 2018a, p. 907). Rather it is important to consider the domain of quantification for Leibniz’s Law. That is, according to Baxter (2018a, pp. 907–8), Leibniz’s Law solely applies to individuals (i.e., complete/independent entities) and thus does not generalise over to aspects, (i.e., incomplete/dependent entities).

The non-applicability of Leibniz’s Law here leads Baxter (2018a, p. 911) to propose a further distinction within Leibniz’s Law between the Indiscernibility of Identical Individuals—which is an iteration of the original principle (i.e., the Indiscernibility of Identicals)—and the Indiscernibility of Identical Aspects—both of which we can construe formally as follows (where (II) stands for the Indiscernibility of Identical Individuals and (IA) stands for the Indiscernibility of Identical Aspects):

(19) (Indiscernibility)	(II):	∀x∀y(x = y→(F(x) ↔ F(y)). Informally: For any things x and y, if x is numerically identical with y, then for any quality F, F is had by x if and only if F is had by y
	(IA):	∀x∀y(x = y→(∀F)(F(zk[Xk])↔ F(wk[Yk]))) Informally: For any things x and y, if x is numerically identical with y, then, for any property, any aspect numerically identical with x has it if and only if any aspect numerically identical with y has.

With this distinction in place, Baxter believes that the notion of an aspect does not present a counterexample to the Indiscernibility of Identical Individuals—as this principle is taken to be silent on aspects.Instead, the issue that we have here is that of there being problems with the Indiscernibility of Identical Aspects—as an individual might be numerically identical with an aspect that differs from an aspect that another individual is numerically identical with, even in the situation in which the first and second individuals are identical (Baxter 2018a). That is, an individual can differ from itself by having aspects that differ, yet without this requiring that the individuals are numerically distinct. Identicals that are considered unqualifiedly are indiscernible. However, identicals that are considered qualifiedly may be discernible—that is, something may qualitatively differ from itself (Baxter 1999). The non-contradictory internal negation in specific self-differing claims, such as O’s above, seems to suggest that Leibniz’s Law, properly so-called, does not apply to aspects. Thus, there are certain cases in which identicals are discernible, yet do not falsify the principle, namely, when an individual possesses aspects that are numerically identical to it (and each other). The same thing cannot be true and false of the same individual, in the same respect, without entailing a contradiction. Yet, phrases such as ‘O insofar as it is located in a cubical shaped region’ refer to aspects, which are incomplete entities, and not the complete individual that the aspect is numerically identical with. Thus, as Baxter (2018a, p. 907) notes, it is vital that one is sensitive to ‘aspectival reference’, which refers to aspects and is distinguishable from singular reference, which refers to complete entities. Singular reference, according to Baxter, is not sensitive to the aspectival distinction, whilst the former is. Additionally, once we are sensitive to this distinction, we can realise that the domain of quantification for Leibniz’s Law, in its original sense, as Baxter writes, ‘includes all the complete entities, but does not include the incomplete entities numerically identical to some of them’ (Baxter 2018b, p. 104). Thus, it follows that Leibniz’s Law does not preclude the numerically identical aspects of an individual from being qualitatively different from each other and the individual themselves.48 Assuming the reality of aspects thus does not lead to a complete denial of Leibniz’s Law. Instead, there is only a denial of an unrestricted understanding of Leibniz’s Law that includes all complete and incomplete entities within its domain. That is, more precisely, there is only a denial of an unrestricted understanding of Leibniz’s Law—which includes the two principles of the Indiscernibility of Identical Aspects and the Indiscernibility of Identical Individuals.49 In other words, Baxter is not seeking to provide counterexamples to Leibniz’s Law, when it is simply understood as a principle concerning objects of singular reference (i.e., the Indiscernibility of Identical Individuals), instead he is proposing counterexamples solely to the principle that ranges over aspects (i.e., Indiscernibility of Identical Aspects), and so to the Indiscernibility of Identicals, when it is taken as the conjunction of the former and the Indiscernibility of Identical Individuals (i.e., unrestricted Leibniz’s Law). More can indeed be said here. However, for the task at hand, we can conclude that Leibniz’s Law does not apply to aspects, and thus it is coherent to posit the existence of qualitatively differing, yet numerically identical aspects.

In summary: an object (such as a module trope) can be multiply located in the sense of it being exactly located at more than one (disjoint) region—it has the exact same shape, size as, and stands in the same relations of, more than one (disjoint) spatial region. At each of these regions, a given object can bear (region-specific) aspects—qualitatively differing, yet numerically identical abstract particular entities that function as ways in which that object is—which enable it to bear a range of incompatible qualities, without an entailment of a contradiction. We can now focus on applying the above set of concepts to the task at hand.

3.2. Divinity as a Multiply Located Aspect Bearer

In this stage of our constructive task, we take Divinity to be a multiply located particular object that possesses aspects.50 Divinity is multiply located in the sense that it is exactly located at more than one disjoint region—it is exactly located at three (disjoint) spatial regions. More specifically, within the present chorological system, we take the chorological relation of exact location: ‘__ is exactly located at spatial region __ (at time __)’, as basic, and thus state the multiple (exact) locations of Divinity as such:

(20) (Divinity Multiple Location)

(a) Divinity is exactly located at spatial region r1. (b) Divinity is exactly located at spatial region r2. (c) Divinity is exactly located at spatial region r3.

Divinity has three exact locations, and it inherits the ‘qualities’ and ‘relations’ of each of the regions that it is exactly located at. For a visual heuristic, we can illustrate in Figure 6. this case of multiple location as such:

Divinity, which is exactly located at r₁, r₂ and r₃, is now taken to bear different characteristics at each of its different regions. One can ask, however, how could this be so, given that it is the same single object that is exactly located in three (disjoint) regions at the same time? Well, how this can indeed be so is by Divinity possessing (region-specific) aspects. More precisely, Divinity possesses three aspects—termed ‘Divinity-Aspects’—that correspond to its exact locations, which, utilising the notion of an aspect term, we can succinctly state as such:51

(21) (Divinity-Aspects)

(a) Divinityy[y@r1] (i.e., Divinity insofar as it is exactly located at r1). (b) Divinityy[y@r2] (i.e., Divinity insofar as it is exactly located at r2). (c) Divinityy[y@r3] (i.e., Divinity insofar as it is exactly located at r3).

The nature of these Divinity-Aspects can be further elucidated by focusing on their specific functional roles and the relationship that they have to Divinity, which allows us to say that these aspects are not properties, complete entities, or mereological parts. Rather, they are incomplete abstract particular entities that are numerically identical to a specific complete individual: Divinity, and function as its ways of being. More fully, each of the Divinity-Aspects is numerically identical to Divinity, yet they do not possess the same characteristics as it—they are not the characteristic of being divine. Lacking this characteristic, the Divinity-Aspects are thus incomplete entities, in that they are dependent on Divinity, which exists as a complete entity (i.e., an independently existing entity). These Divinity-Aspects do not exhaust the content or plime that they are aspects of (i.e., they each do not exhaust Divinity), and they each function as ways that Divinity exists—which we can consider through a process of abstraction.

At a more specific level, these Divinity-Aspects are focused on the different particular ways in which the Divinity is. That is, by this module trope having (or, more specifically, being) the singular-character of Divinity, it would exist in a particular manner and have certain limitless abilities that enable it to fulfil different roles. This functional role fulfilled by Divinity allows one to establish an aspectival distinction that takes these differing ways to be aspects of this specific trope. More precisely, the subjects of this differing would be the Divinity-Aspects, with each aspect possessing a quality that each of the other aspects lacks. For instance, focusing on the qualitative differing of Divinity_y[y@r₂] and Divinity_y[y@r₃] from Divinity_y[y@r₁], we have the following example:

(22)	Divinityy[y@r1] has the qualities and/or relations of r1.
(23)	~Divinityy[y@r2] has the qualities and/or relations of r1.
(24)	~Divinityy[y@r3] has the qualities and/or relations of r1.

In this particular case, we have a case of differing, as there is a qualitative difference between the aspects of the Divinity. Additionally, importantly, it is a case of self-differing, as the aspects are numerically identical to Divinity itself. In other words, Divinity insofar as it is located at a certain region (i.e., r₁, r₂ or r₃) is still Divinity:

(25)	Divinity = Divinityy[y@r1]; Divinityy[y@r2]; Divinityy[y@r3].

Additionally, due to the transitivity of identity, each of the Divinity-Aspects is also numerically identical to another:

(26)	Divinityy[y@r1] = Divinityy[y@r2],
(27)	Divinityy[y@r2] = Divinityy[y@r3],
(28)	Divinityy[y@r3] = Divinityy[y@r1].

So, in making an aspectival distinction here, in a ‘loose’ sense—focused on qualitative distinctiveness—we can indeed count a multiplicity of aspects that correspond to the different spatial regions that Divinity is exactly located at. Yet, in a ‘strict’ sense—focused on numerical distinctiveness—there is solely one self-same particular object (i.e., property*): Divinity, which is differently considered at each of those regions. Taking all of these things into account, we can now proceed to rename the Divinity-Aspects as such:

(29)	The Father = Father-Aspect (i.e., Divinityy[y@r1]).
(30)	The Son = Son-Aspect (i.e., Divinityy[y@r2]).
(31)	The Spirit = Spirit-Aspect (i.e., Divinityy[y@r3]).

Each of the members of the Trinity is thus to be identified as Divinity insofar as it is exactly located at a certain spatial region. The members of the Trinity are Divinity-Aspects and thus are numerically identical to Divinity and each other—without, however, this resulting in them having the same qualities as each other—which will keep any issue of ‘Patripassianism’ at bay.52 That is, the Father is a qualitatively differing aspect of Divinity, the Son is a qualitatively differing aspect of Divinity, and the Spirit is a qualitatively differing aspect of Divinity. Yet, at the bottom level, they are each simply Divinity, despite there being a qualitative distinction between them. So, again for heuristic purposes, we can illustrate in Figure 7. this aspectival distinction as such (with ‘D’ standing for ‘Divinity’, ‘r₁’, ‘r₂’ and ‘r₃’, standing for distinct spatial regions, ‘A’ standing for an ‘aspect’):

Notably, however, there is no Leibniz’s Law (i.e., the Indiscernibility of Identical Individuals) failure here as this law solely applies to complete individuals and thus does not generalise over to the Divinity-Aspects, which exist as incomplete/dependent entities. Thus, within an aspectival context, the same thing: Divinity, is discerned in different ways in each of the spatial regions that it is located at. Additionally, in this discernment, it differs from itself, whilst still being that same thing. That is, within this aspectival framework, there is one particular object (i.e., property*): Divinity, that is located at more than one exact location. Additionally, within each of those locations, Divinity has a corresponding (region-specific) aspect, which it is identical to—with each of these aspects being identical to each other. In short: Divinity is the qualitatively differing Divinity-Aspects, and the qualitatively differing Divinity-Aspects are one another. The Divinity-Aspects provide a certain ‘complexity to the simple’—a qualitative complexity to the quantitatively simple (powerful) trope of Divinity. Divinity is thus a multiply located particular object that possesses aspects at its multiple (disjoint) regions—it is exactly located at three (disjoint) spatial regions, and it bears qualitatively differing, yet numerically identical aspects at those regions. Counting ‘strictly’, there is only Divinity, but counting in a ‘loose’ manner—a manner that takes into account qualities—then there are indeed three qualitied entities present. The numerical identity of the members of the Trinity with Divinity is indeed secured here—and thus there being an affirmation of the metaphysical simplicity and ‘oneness’ of Divinity. However, given that members of the Trinity are to be construed not simply as aspects of Divinity, but also as relationally distinct persons, what is the nature of personhood and relationality that is now in play here that enables them to actually be qualitatively distinct (yet numerically identical) to Divinity and each other? To answer this question, we will now proceed to the penultimate stage of our constructive task.

4. Constructing Monarchical Aspectivalism: Stage Three

The third stage of our constructive task focuses on providing a philosophical elucidation and re-construal of element (4*)–(6*) of (MR₁). This element, in its standard reading, posits the fact of the Father, the Son and the Spirit being numerically distinct from one another. The standard and alternative readings of this element are stated as follows:

Monarchical Reading1 (MR1)	Monarchical Reading2 (MR2)
4*. The Father ≠ the Son. 5*. The Father ≠ the Spirit. 6*. The Spirit ≠ the Son.	4’. Father-Aspect ≠ Son-Aspect. 5’. Father-Aspect ≠ Spirit-Aspect. 6’. Spirit-Aspect ≠ Son-Aspect.

As was pre-empted at the end of the previous section, in this re-construal of (4*)–(6*) of (MR₁), there is an equivocation on the notion of identity that is denied of the members of the Trinity. Specifically, the ≠ symbol is not to be taken as the denial of a relation of numerical identity between the Divinity-Aspects (which could not be the case given the fact that the aspects of an individual are numerically identical to that individual and one another). Rather, it is the denial of a qualitative identity (i.e., sameness) between these aspects. In other words, the Divinity-Aspects are qualitatively differing, yet numerically identical aspects of Divinity—and so the present (identity) reading of (AC), unlike that of (IR), allows one to affirm the numerical identity of the Father, the Son and the Spirit. This does not, however, lead one to affirm a form of ‘Patripassianism’—the notion that the Father suffered and underwent the Son’s other human experiences (Kelly 1968, p. 120)—as each of the members of the Trinity, conceived of as Divinity-Aspects, do not share the same qualities, and thus, at a qualitative level, are indeed distinct entities—and so, despite their numerical identity, the qualities (derivable from the experiences) that the Father (i.e., Divinity_y[y@r₁]) has are not (necessarily) the qualities (derivable from the experiences) that the Son (i.e., Divinity_y[y@r₂]) and the Spirit (i.e., Divinity_y[y@r₃]) have. That is, in other words, on the basis of (18), one can block the secundum quid ad simpliciter inference within an aspectival framework by the qualities of a qualitatively distinct aspect not being required to be shared by its bearer or by the other aspects of the bearer as well—which would’ve potentially led to this issue arising. Moreover, neither does it require one to affirm a form of ‘modalistic Monarchianism’ (i.e., ‘modalism’)—the notion that the Son and the Spirit were not distinct ‘persons’ from the Father (Kelly 1968, p. 119)—as the qualitative distinction between the members of the Trinity is a real (i.e., mind-independent) and eternal distinction between them, such that each of the members of the Trinity is a person—through each meeting the necessary and sufficient conditions for being one—and are distinct from one another by a relational distinction. It will be important to now detail the nature of this qualitative distinction—focused on the metaphysical notions of ‘personhood’ and ‘relations’—that play a part in grounding the distinction of the members of the Trinity, and then apply it to the task at hand, which will provide a further clarification of this specific element of (AC) and complete the third, and penultimate, stage of our constructive task.

4.1. Personhood and Relations

In stage three of our constructive task, we introduce the notion of relational personhood, the nature of which is stated as follows:

(32)	(Relational Personhood): A multiply located particular object that has (region-specific) aspects, each of whom has a first-person perspective and stands in a non-symmetric relation that enables it to fulfil certain onto-thematic roles.

As in stages one and two, this concept of relational Personhood can be further divided into two sub-concepts: personhood and relationality. These two sub-concepts will now be unpacked in further detail.

Personhood. The term ‘person’ can plausibly be taken to designate a primary kind. A primary kind determines what an entity fundamentally is, and thus a given entity could not exist without being of its primary kind. Specifically, for Lynne Rudder Baker (2005, 2007, 2013), what makes an entity of the primary kind person is that they have a first-person perspective essentially. As Baker (2007, p. 335) writes, ‘to be a person—whether a divine person, an angel, a human person, or a Martian person—one must have a first-person perspective’. ‘Person’ is thus a fundamental kind of which there are many instances: human, divine, bionic and Martian, etc.; however, despite the numerous instances of this specific kind, there is a shared, fundamental trait between them: their first-person perspective—where it is in virtue of an entity having a first-person perspective that it is a person and falls within this fundamental kind. A first-person perspective is thus the specific essential property that makes a person fundamentally what they are—it serves as the defining characteristic of all persons. Hence, a first-person perspective is thus necessary and sufficient for being a person—it is fundamental in grounding the personhood of an entity—and it comes in two stages: a rudimentary stage and a robust stage, which corresponds to the distinction between consciousness and self-consciousness (Baker 2013, p. 62). Following Baker (2013, pp. 41–42), and focusing firstly on a rudimentary first-person perspective, we can understand that this type of first-person perspective is, first, a perspective—it is a disposition to perceive the world from a particular location. Second, it is personal—not in a manner that it refers to a subject—but one that simply provides the default location in which the conscious subject perceives the environment that she is interacting with. Third, it is independent of linguistic or conceptual abilities, which enables entities such as human infants or non-infants—each of whom lacks concepts—to be able to have this basic form of a first-person perspective. Turning now to a robust first-person perspective, this type of first-person perspective is one that has the former features; however, it also includes the ability for an entity to conceive of oneself as oneself, in the first-person (Baker 2013, p. 108). Additionally, the specific means by which one conceives of oneself as oneself from the first-person is through a ‘self-concept’—a concept of oneself from one’s own point of view. Thus, a self-concept, such as ‘I’m glad that I am a father’, manifests an individual’s robust first-person perspective—it attributes to oneself a first-person reference—where the second occurrence of ‘I’ in the above statement directs one’s attention to the person, without, as Baker writes, any ‘name, description, or other third-person referential device to identify who is being thought about’ (Baker 2007, p. 334). Thus, the possibility to conceive of as oneself in the first-person through the use of a self-concept is the primary dividing line between a rudimentary and a robust first-person perspective.

Nonetheless, in both cases, a first-person perspective is an exemplification of the dispositional property (‘quality’) first-person perspective, which, in the human case, is an essential property (‘quality’) of any human being. That is, an animal can only have a rudimentary first-person perspective that it possesses contingently, whereas a person comes into existence, according to Baker (2005), at the specific point in which a human organism develops to the point of supporting a rudimentary first-person perspective.53 Specifically, a human organism firstly acquires a rudimentary first-person perspective and then proceeds, if uninhibited, to acquire a robust first-person perspective when they learn enough of a natural language to be able to conceive of themselves as themselves in the first-person. Thus, a first-person perspective establishes a distinction between thinking of oneself in the first-person and thinking of oneself in the third person. Once someone, as Baker writes, can ‘make this distinction, she can think of herself as a subject in a world of things different from herself’ (Baker 2007, p. 334). Hence, when a person comes into existence, her first-person perspective determines her persistence conditions: she exists as long as her first-person perspective is exemplified (Baker 2005, p. 28). Additionally, what makes a person that specific person is the state of affairs of them exemplifying a first-person perspective. Therefore, since a person has a first-person perspective essentially, the state of affairs of them exemplifying a first-person perspective is the same state of affairs at all times of their existence—at any time t and in any possible world w, a person exists at t in w if and only if their first-person perspective is exemplified at t in w (Baker 2013, p. 150). Thus, given this role that a first-person perspective fulfils, it is a dispositional property (‘quality’) that cannot be shared. That is, as Baker notes, it is one whose ‘instances cannot be divided or duplicated. So, a molecule-for-molecule replica of our body would not have your first-person perspective’ (Baker 2013, p. 65). A first-person perspective is thus a dispositional property (‘quality’) that is uniquely had by its bearer, specifically because the particular ‘default’ location, in which the entity perceives the environment, is not shareable, and thus a duplicate of this entity would not have the same disposition expressed by the former entity’s first-person perspective, but would instead perceive the world through a different perspective within the particular default location in which it resides in.

Hence, what we have here is that of an entity being a person—that is, they fall into the primary kind Person—if, and when, they possess a unique (i.e., non-shareable or divided) first-person perspective (rudimentary or robust), which is an essential dispositional property (‘quality’) of the person. From this unpacking of the ‘dispositional’ notion of personhood, we can now turn our attention onto detailing the second notion noted above: onto-thematic roles.

Relational Onto-Thematic Roles. Relations are certain entities whose nature and ontological status have produced a proliferation of views from the medieval to the contemporary period. According to Heil (2009, 2012), a helpful taxonomy of views is as follows:

(33) (Relations)

(a) Hyper-Realism: Relations are ontologically fundamental; truthmakers for relational judgements are relations. (b) Projectivism: Relations are creatures of reason, mental comparisons. (c) Reductionism: Relations are ‘reducible to’ non-relational features of relata. (d) Moderate Realism: Truthmakers for relational judgements are non-relational features of the universe.

Focusing on (a): Hyper-Realism, which is the default position within contemporary metaphysics today,54 relations are real and serve as the ontological counterparts of the relational predicates that feature in statements such as the following:

(34)	Dante loves Beatrice.

At a more specific level, within the Hyper-Realist framework, the term ‘relation’, as David Armstrong (1997, p. 87) notes, covers all types of polyadic properties ‘dyadic, triadic…n-adic’. That is, relations can firstly be distinguished by their ‘adicity’: relations (unlike properties that are ‘monadic’ and thus exemplified by a particular entity alone) are ‘n-adic’ (i.e., n > 1) in that they can hold between a particular and other particulars. So, a ‘dyadic’ relation, such as that which features in (34), holds between one particular and exactly one other particular, whereas a ‘triadic’ relation is one that holds between one particular and exactly two other particulars (Macbride 2020, §1).

Secondly, relations can be distinguished by the manner in which they hold between their relata: as an internal relation or as an external relation. An internal relation is one in which the existence of the relata entails the existence of the relation. Thus, external relations are those relations that are not internal. So, focusing on the former type of relation, the truthmakers for internal relations are nothing more than the terms of the relation—the identity of a given internal relation is determined by the identity (or the difference) of their truthmakers. Thus, an internal relation supervenes on the existence of the terms—where an entity Q supervenes upon another entity P if, and only if, as Armstrong (1997, p. 12) writes, ‘it is impossible that P should exist and Q not exist, where P is possible’. In other words, as Armstrong further notes, supervenience ‘in my sense amounts to entity P entailing the existence of entity Q’ (Armstrong 1997, p. 12). Thus, given this conception of supervenience, whatever supervenes in this manner is not something ontologically additional to the subvenient—it is ‘no addition of being’ or an ‘ontological free lunch’. The supervenient is ontologically nothing more than its base, and thus, as Armstrong adds, ‘you get the supervenient for free, but you do not really get an extra entity’ (Armstrong 1997, p. 13). Internal relations—as entities that supervene upon their terms—are thus not things that are ontologically more than their subvenient terms—as simply given the existence of their terms, internal relations ‘are not an addition to the world’s furniture’ (Armstrong 1997, p. 87).

Thirdly, relations can also be distinguished by their direction: a symmetrical relation or a non-symmetrical relation. A relation is symmetrical if it is the case that whenever an entity Q stands in a relation R to another entity S, then S also stands in R to Q. Thus, in contrast to this, a relation is non-symmetrical if it fails to be symmetric in this sense—Q standing in R to S, does not imply that S also stands in R to Q. So, for example, the marriage relation, under normal circumstances, would be asymmetrical relation, as if Q stands in the marriage relation to S, then S also stands in that same relation to Q, whereas the love relation, which featured in (34), is a non-symmetric relation, as Dante standing in the loving relation with Beatrice does not imply that Beatrice also stands in this same relation with Dante—namely, that she loves him as well.

So, focusing now on non-symmetrical relations, Kit Fine (2000) has identified a specific problem plaguing non-symmetrical relations: the Problem of Relational Order. Specifically, taking (34) as an example, the issue is that of non-symmetrical relations having a certain order that stems from the first relatum in a relational fact—Dante—to the second relatum in that fact— Beatrice. However, there also seems to be different relational order that goes from the second relatum in that relational fact—Beatrice—to the first relatum in that fact—Dante. Yet, the question is, how can this be so? Given that within this relational fact, there are exactly the same relata: Dante and Beatrice, that are standing in the exact same relation: loving. In response to this issue, Francesco Orilia (2008, 2011, 2014), who argues from a positionalist framework55, has introduced the notion of ‘onto-thematic roles’ (O-Roles). O-Roles are introduced by Orilia (2014, p. 283) in order to deal with the Problem of Relational Order, and are best understood as ‘the ontological counterparts of thematic roles such as agent, patient, beneficiary, instrument and the like, introduced by linguists in their syntactic and semantic analyses of verbs and prepositions’. O-Roles such as *agent*, *patient* *instrument* and *beneficiary*, etc., according to Orilia (2014), are sui generis properties (‘qualities’) that function as specific roles that relata fulfil in a given relation, with a requirement within this theory that a relation must always occur with a certain O-Role attached to it. This notion of an O-Role ultimately provides a plausible solution to the Problem of Relational Order, due to the fact that within a given relation, the relata have different relational orders based upon the O-Roles that they fulfil. Order is thus, as Orilia (2008, p. 172) writes, ‘nothing but the occurrence in a fact of arguments with different o-roles’. For example, focusing on the relational fact of (31) again, if one assumes the existence of the O-Roles of *agent* and *patient*, we have the case of Dante fulfilling the O-Role *agent* in the statement Dante loves Beatrice, whilst we have Beatrice not fulfilling that specific O-Role—instead, she fulfils the O-Role *patient* in that exact same relation. This relational fact has a different relational order from Beatrice loving Dante, as in this fact, it is Beatrice that fulfils the O-Role *agent* and not Dante—where, instead, Dante fulfils the O-Role *patient* in this specific relation. So, even though there are exactly the same relata that stand in the exact same relation, there is a relational order within these facts due to the different O-Roles that are fulfilled by the relata—in other words, order is established in a relation by it always being accompanied by a specific O-Role that can be fulfilled by the distinct relata that stand in that particular relation.

In summary: a given object is classed as a person if it bears a first-person perspective, which is best conceived of as a dispositional property (‘quality’)—that is tied to the ‘region’ (or ‘location’) that the entity resides within. Furthermore, relations can be distinguished by their adicity, form and direction, with the latter requiring the existence of O-Roles—ontological counterparts of thematic roles that play a part in establishing order within a specific relation. We can now, again, focus on applying the above set of concepts to the task at hand.

4.2. Divinity as Onto-Thematic Persons

In this stage of our constructive task, we take Divinity to possess a robust first-person perspective and fulfil a certain O-Role in each of the spatial regions that it is exactly located at. As noted previously, Divinity is a multiply located particular object, in that it is exactly located at three (disjoint) regions of space. At each of these regions, Divinity has a robust first-person perspective essentially. That is, Divinity insofar as it is exactly located at a certain region—Divinity_y[y@r₁] (i.e., the Father), Divinity_y[y@r₂] (i.e., the Son) and Divinity_y[y@ r₃] (i.e., the Spirit)—has a personal perspective—a disposition to perceive and interact with the world and surrounding environment from a particular default spatial region. Secondly, this personal perspective is robust in the sense that Divinity has the ability to conceive of itself as itself, in the first-person, which is expressible through a ‘self-concept’—a concept of Divinity from its’ own point of view. Now, given that Divinity bears the dispositional quality of a robust first-person perspective, it falls into the primary kind Person and thus can be classed as a person. More specifically, as Divinity is a multiply located particular object, what we have here is that of Divinity insofar as it is exactly located at a specific spatial region bearing this particular dispositional quality and thus is a person. We can state this more precisely as such:

(35)	The Father (Divinityy[y@r1]) is a person (i.e., has a robust first-person perspective).
(36)	The Son (Divinityy[y@r2]) is a person (i.e., has a robust first-person perspective).
(37)	The Spirit (Divinityy[y@ r3]) is a person (i.e., has a robust first-person perspective).

The persons that are Divinity insofar as it is exactly located at r_1, r₂ and r₃ (i.e., the Father, the Son and the Spirit) are not the same persons, given the fact that, first, it is the qualitatively differing Divinity-Aspects that bear these ‘dispositional qualities’ and, second, as noted above, an instance of a first-person perspective cannot be duplicated nor divided in any sense. Thus, the Father, even though he is an aspect of Divinity—and thus is numerically identical to it—does not have the first-person perspective of the Son and the Spirit (and so on for the Son and the Spirit as well). This is specifically the case here due to the fact that the particular ‘default’ location, in which, for example, the Father (Divinity_y[y@r₁]) perceives his environment, will not be shareable—that is, r₁ is solely occupiable by the Father_, with r₂ being solely occupiable by the Son and r₃ solely occupiable by the Spirit—and thus the Son and the Spirit (who are simply Divinity insofar as it is located in other (disjoint) regions) would not have the same disposition expressed by the Father’s first-person perspective. Rather, given that Divinity is a multiply located object, it would instead perceive the world through different perspectives within the particular ‘default’ locations in which it resides in—namely, r₁, r₂ and r₃.56 Hence, each of the members of the Trinity has a different robust first-person perspective—they each bear a different ‘dispositional quality’—and thus are distinct persons—and are ‘eternally’ so, given the essential nature of a first-person perspective. That is, as a first-person perspective plays a key role in the persistence conditions of an entity, the members of the Trinity—each of whom are eternally existing entities—would thus bear their distinct and unique first-person perspective essentially for as long as they exist, which is thus eternally. In short, contra modalism, the members of the Trinity are essentially and eternally distinct persons.

On the basis of this, we can now further elucidate the relational distinction between the members of the Trinity within this framework by focusing on the particular relation in which they stand to one another. Specifically, we posit that there is an internal, non-symmetrical relation that serves as an ontological counterpart to the relational predicates of the following statements:

(38)	The Father generates the Son.
(39)	The Father generates the Spirit through the Son.

Within the framework in which we are operating within, we can take this generation relation, which is expressed by (38) and (39), to be best conceptualised as a relation of ‘grounding’ that holds between the Father, the Son and the Spirit, due to the Father (i.e., Divinity_y[y@r₁]) setting the ‘location relations’ in both cases—such that Divinity is then exactly located at two other (disjoint) spatial regions (i.e., r₂ and r₃₎ as well—which (non-temporally) results in the existence of the Son and the Spirit. The Son and the Spirit (i.e., Divinity_y[y@r₂] and Divinity_y[y@r₃])) exist in the specific regions that they do in virtue of the Father (i.e., Divinity_y[y@r₁]).57 In regard to the nature of these generation (i.e., grounding) relations, we can understand that, firstly, the generation relation that holds between the Father and the Son in (38) is a ‘dyadic’ relation, as it holds between two qualitatively distinct things: the Father and the Son. Whereas the relation of ‘generation’ that holds between the Father, the Son and the Spirit in (39) is a ‘triadic’ relation, as it holds between three qualitatively distinct things: the Father, the Son and the Spirit. Secondly, this relation of generation in both cases is an internal relation—the existence of the Father, the Son and the Spirit entails the existence of this relation—in short, they serve as its truthmakers. Additionally, thus, the generation relation is supervenient upon the existence of the Father, the Son and the Spirit (i.e., it’s supervenient upon the existence of the Divinity, which serves as its subvenient base)—in other words, the generation relation is not ontologically additional to them—it is ‘no addition of being’ and an ‘ontological free lunch’. Thirdly, this relation of generation is non-symmetrical in the sense that the Son and the Spirit standing in a generation relation with respect to the Father does not imply that the Father also stands in the same relation with the Son and the Spirit—the Father is not generated by the Son, nor by the Spirit. Additionally, thus, given the non-symmetrical nature of this relation, there is a relational order present within it that stems from the Father to the Son and the Spirit, which is grounded upon the O-Roles that the Father, the Son and the Spirit fulfil in this relation. Specifically, we have three O-Roles present in the relational facts of (35) and (36)—*agent*, *instrument* and *patient*—which we can distribute amongst the persons as follows: first, as the Father is the generator of the Son and the Spirit, he fulfils the O-Role *agent*. Second, as the Son is generated by the Father, and is the means by which the Spirit is generated, he fulfils the O-Roles *patient* and *instrument*. Additionally, third, as the Spirit is generated by the Father (through the Son), he solely fulfils the O-Role of *patient*. The relational order that is present in (38) and (39) is thus founded upon the different O-Roles that are fulfilled by the Father, the Son and the Spirit, which is simply that of Divinity insofar as it is exactly located at r₁, r₂ and r₃ fulling these specific roles. Taking this all into account, we can now re-state (35)–(37) as that of there being three relationally distinct persons, the nature of which is to be understood as such:

(40)	The Father (Divinityy[y@r1]) is a person (i.e., has a robust first-person perspective) and fulfils the O-Role of *agent*.
(41)	The Son (Divinityy[y@r2]) is a person (i.e., has a robust first-person perspective) and fulfils the O-Roles of *patient* and *instrument*.
(42)	The Spirit (Divinityy[y@ r3]) is a person (i.e., has a robust first-person perspective) and fulfils the O-Role of *patient*.

The Father, the Son and the Spirit are thus each Divinity insofar as it is exactly located at a particular region of space, with a robust first-person perspective and the fulfilment of a certain O-Role at that region. However, as noted previously, the Father, the Son and the Spirit are Divinity-Aspects and thus are each numerical identical to Divinity and one another, yet can (and do) qualitatively differ by their possession of distinct robust first-person perspectives and the fulfilment of distinct O-Roles. So, we can see here that there is a basis for the present account dealing with the distinction issue. However, before we further explain how this is to be done, it will be important to now answer the further question of: what is the ontological nature of the first-person perspective and O-Roles that are fulfilled by Divinity in its specific spatial regions? Unlike in the more mundane cases, a first-person perspective and O-Role cannot be a dispositional or sui generis property of Divinity, if it is to continue to be conceived of as a metaphysically simple trope—as any property borne by it would not be numerically identical to it—resulting in Divinity not being identical to its nature through its possession of dispositional and sui generis proper metaphysical parts. So, the Father, the Son and the Spirit’s robust first-person perspectives and O-Roles must be construed in a different way, which we can do by combining together two previously adduced concepts: powerful qualities and aspects, and introduce the notion of an aspectival powerful quality.

More specifically, we can answer this question by utilising a reformulation of the powerful qualities concept that was previously introduced. As noted above, Divinity is a dual-charactered property* that has a dispositional character—conveying upon it a power to act in a certain way—and a qualitative character—contributing to the overall makeup of it. The dispositional and qualitative character of Divinity, as in the more mundane cases, are identical to each other and Divinity itself. So, on the basis of this identity between them, and in answer to the question concerning the nature of them that was also previously raised, we can now take the dispositional and qualitative character of Divinity to be dispositional and qualitative aspects of it. Within this reformulated framework, we are thus to perform a conversion of the dispositional and onto-thematic properties into dispositional and qualitative (onto-thematic) aspects, which will also result in the instantiation relation in the former case being converted into a relation of numerical identity. We can illustrate in Figure 8. this conversion for heuristic purposes as such:

This conversion allows us to construe the first-person perspectives and O-Roles featured here in an aspectival manner. More precisely, the robust first-person perspective had, and the O-Roles fulfilled by, Divinity insofar as it is in a certain spatial region, are dispositional and qualitative sub-aspects of it—dispositional and qualitative aspects of aspects. Divinity insofar as it is exactly located in one spatial region has the dispositional and qualitative sub-aspects that Divinity insofar as it is exactly located in another spatial region lacks. The Divinity-Aspects differ in their sub-aspects. For each of the Divinity-Aspects, identified as the Father, the Son and the Spirit, they have a dispositional first-person perspective aspect and a qualitative O-Role aspect. We can state this succinctly as such:

(43) (Divinity-Aspects (ii))

(a) The Father (Divinityy[y@r1]) is: Dispositional Sub-Aspect: A Robust First-Person Perspective Qualitative Sub-Aspect: The O Role *agent*. (b) The Son (Divinityy[y@r2]) is: Dispositional Sub-Aspect: A Robust First-Person Perspective Qualitative Sub-Aspect: The O-Role *patient* and *instrument*. (c) The Spirit (Divinityy[y@r3]) is: Dispositional Sub-Aspect: A Robust First-Person Perspective Qualitative Sub-Aspect: The O Role *patient*.

Within an aspectival framework, a ‘sub-aspect’ is an aspect of an aspect. Hence, the dispositional first-person perspective sub-aspect (i.e., Divinity_y[y@r_n] insofar as they have a first-person perspective), which is had by Divinity in each of its (disjoint) spatial regions, endows the Father, the Son and the Spirit with the power to—amongst other things—think of themselves as themselves in their respective regions, whereas the qualitative O-Role sub-aspect, which is fulfilled by Divinity in each of its (disjoint) spatial regions, contributes to making each of the Divinity-Aspects what they are—for the Father, by him bearing the qualitative O-Role sub-aspect of *agent* (i.e., Divinity_y[y@r₁] insofar as it is the O-Role *agent*), he is the Father. For the Son, by him bearing the qualitative O-Role sub-aspect of *patient* and *instrument* (i.e., Divinity_y[y@r₂] insofar as it is the O-Role *patient* and *instrument*), he is the Son. Additionally, for the Spirit, by him bearing the qualitative O-Role sub-aspect of *patient* (i.e., Divinity_y[y@r₃] insofar as it is the O-Role *patient*), he is the Spirit. Yet, each of these dispositional and qualitative sub-aspects of the Divinity-Aspects is not a numerically distinct entity but, in fact, are one and the same thing—the Divinity-Aspects, which are themselves numerically identical to Divinity. For heuristic purposes, we can illustrate in Figure 9. this as such (with all of the letters remaining as before with the addition being that of ‘D’ in the smaller circle standing for ‘dispositional aspect’ (with ‘F’ standing for ‘first-person perspective’) and ‘Q’ in the smaller circle standing for ‘qualitative aspect’ (with ‘A’ standing for ‘agent’, ‘IP’ for ‘instrument and patient’ and ‘P’ for ‘patient’)):

So, as noted previously, there is no Leibniz’s Law failure, as was found within the original Powerful Qualities framework introduced above. Rather, we have a cogent proposal that enables one to establish the metaphysical simplicity and oneness of Divinity, whilst continuing to maintain the relational distinction of the persons. As for a given Divinity Aspect—let us take the Father as an example—one can make an aspectival distinction by dispositionally regarding, or considering it in one way, through its first-person perspective that renders it as a person (i.e., as the person of Father), or one can also make another aspectival distinction by qualitatively regarding, or considering it in another way—through the specific O-Role that it fulfils (i.e., as *agent*), which together allows one to distinguish the Father from the Son and the Spirit (and vice versa). Nonetheless, it is the self-same, simple, powerful trope: Divinity, which is located at multiple (disjoint) spatial regions —at r₁ and r₂ and r₃. Divinity, as a multiply located powerful module trope, is thus one metaphysically simple entity despite the relational and personhood distinctions that have been made, which allows there to only be one Divinity (i.e., divine nature) posited here.

5. Constructing Monarchical Aspectivalism: Stage Four

The fourth stage of our constructive task focuses on providing a philosophical elucidation and re-construal of element (7*) of (MR₁). This element, in its standard reading, posits the existence of one God in the Trinitarian life who is numerically identical to the Father. The standard and alternative readings of this element are stated as follows:

Monarchical Reading1 (MR1)	Monarchical Reading2 (MR2)
7*. There is exactly one God, the Father.	7’. There is exactly one fundamental Divinity-Aspect, the Father-Aspect.

In this re-construal of (7*) of (MR₁), there is a utilisation of the metaphysical notion of ‘fundamentality’—which allows one to further understand the notion of ‘God’ (in the nominal sense) as centring on the metaphysical concept of ‘fundamentality’, and thus one can identify the one ‘God’—taken as the Father—to be the fundamental Divinity-Aspect within the Trinity. It will be important to now further unpack the nature of fundamentality, and then apply it to the task at hand, which will provide a further clarification of this specific element of (AC) and complete the final stage of our constructive task.

5.1. The Nature of Fundamentality

In stage four of our constructive task, we introduce the notion of fundamentality, the nature of which is stated as follows:

(44)	(Fundamentality) An entity is fundamental if it is independent (i.e., unbuilt/ungrounded) and complete (i.e., the builder/ground of everything else).

This concept of fundamentality can be further divided into two sub-concepts: independence/completeness and grounding. These two sub-concepts will now be unpacked in further detail.

Independence and Completeness. In contemporary metaphysics, the notion of fundamentality is used in reference to an entity (or entities) that is (or are) basic, primitive or rock-bottom in the hierarchical structure of reality. Two central aspects of the notion of fundamentality, according to Karen Bennett (2017), are those of independence and completeness (with the former being more central to the notion than the latter).58 In Bennett’s thought, fundamentality, construed as independence and completeness, is intimately tied to the further notion of building. Building is a technical term that ties together the following type of relations: composition, constitution, set-formation, realisation, micro-based determination, grounding and causation. These various relations are not intended by Bennett to be exhaustive but are instead relatively central notions that intuitively fit the mold of being a building-relation. How these paradigm relations fit this building mold is through them fulfilling the three necessary and jointly sufficient conditions of directedness, necessitation and generation. Firstly, the condition of directedness takes a building-relation to be antisymmetric, irreflexive and thus asymmetric. Secondly, the condition of necessitation takes builders to necessitate, in some sense, what they build. Thirdly, the condition of generation takes the built entities to exist in virtue of their builders, and thus the latter back an explanation for the former existing as they do (Bennett 2017, p. 32). These necessary and sufficient conditions distinguish building-relations from other types of relations and provide a basis for the claim that building-relations form a unified family (i.e., a natural resemblance class) despite the differences amongst them (Bennett 2017, p. 20). Off the basis of this further explication of the notion of building, we can now construe the independence aspect of fundamentality as such:

(45)	(Independence) x is independent if nothing builds x (Bennett 2017).

Additionally, we can now also construe the completeness aspect of fundamentality as such:

(46)	(Completeness) The set of the xxs is (or the xxs plurally are, or a non-set-like x is) complete at a world w just in case its members build (…) everything else at w (Bennett 2017, p. 109).

According to (Independence), absolutely fundamental entities are independent in the sense that they are unbuilt and thus do not depend on anything else. Moreover, for (Completeness), a certain set of absolutely fundamental entities are complete at a specific world in the sense that they build everything else in that world. That is, they are the things that ultimately account for everything else that does exist in that specific world. Fundamentality, as expressed by (44) and further elucidated by (45) and (46), reflects, as Bennett (2017, p. 111) notes, two halves of the familiar phrase ‘unexplained explainers’, the ‘unexplained’ part reflecting independence which says that nothing ‘presses upwards’ on them and the ‘explainers’ part reflecting completeness which says that a certain set of entities ‘presses upwards’ on everything else in a specific world. Furthermore, and more importantly, these two aspects are reducible to and defined by the notion of building. That is, within the building-fundamentality framework, there is thus a deflationism (or reductionism) about fundamentality, where the fundamentality facts are simply the building facts (Bennett 2017). Therefore, as Bennett notes, for certain fundamentality relations to obtain is simply ‘for certain complex patterns of building to obtain’ (Bennett 2017, p. 139). In short, there is an identification of fundamentality with building. Thus, the state of affairs of an entity being absolutely fundamental is that of them being independent and complete, which is reducible to the entity being, on the one hand, unbuilt and, on the other hand, part of a set at a world whose members build everything else in that specific world. However, it is important to remember that there is not a single, general relation of building. Rather there are a different number of building-relations that form a unified family. Thus, when the term ‘building’ is used in a singular sense, it is simply a generalisation about a class of relations (Bennett 2017, p. 3). Therefore, fundamentality, construed as independence and completeness, is to be indexed to particular building-relations. Hence, in indexing fundamentality to particular building-relations, to be absolutely fundamental is to be independent and complete, which, for the former, is ultimately reducible to either not being composed, or constituted, or realised, or determined, or grounded, or caused, by anything else—an absolutely fundamental entity does not feature as an output of a particular building-relation (Bennett 2017, p. 112), whereas for the latter, it is ultimately reducible to being a member of a set of entities at a world whose members compose, or constitute, or realise, or determine, or ground, or cause everything else, in that specific world—the set of absolutely fundamental entities builds, in one of the above ways, everything else (Bennett 2017, p. 112). Thus, there are various real distinctions between the indexed versions of fundamentality. We can focus attention now on one particular building-relation: grounding.

Grounding. This notion is one that is regularly characterised as a primitive expression of dependence, determination or explanation. This expression has been championed by ‘grounders’ (i.e., grounding theorists) such as Kit Fine (2012), Jonathan Schaffer (2009, 2016) and Gideon Rosen (2010), amongst others.59 For some of these grounders, such as that of Schaffer, grounding is best construed as follows:

(47)	(Grounding) An asymmetric, necessitating dependence relation that links the more fundamental entities to the less fundamental entities, and is best conceptualised as a type of causation: metaphysical causation.

As an asymmetric, necessitating directed-dependence relation, grounding is associated with the notion of ontological priority—this directed-dependency relation takes in terms from any arbitrary ontological category and links a more fundamental input to a less fundamental output (Schaffer 2016).60 Thus, according to Schaffer (2009), there is an ontological ordering within reality, in that some entities are derivative of other, more fundamental entities. The fundamental entities of reality ontologically undergird the derivative entities, and grounding is the relation that connects the undergirding entity to entities that are at a higher level in the structure of reality. Thus, within this perspective, there is a hierarchical view of reality that is ordered by priority in nature. Once one distinguishes more from less fundamental entities, it is natural to posit a relation linking certain more fundamental entities to certain less fundamental entities which derive their existence from them (Schaffer 2016, p. 145). Grounding is thus the name of this direct ‘linkage’ which is governed by the above formal and modal principles, connects the more to the less fundamental entities and thereby imposes a hierarchical structure over what there is (Schaffer 2009).

Now, closely related to ground’s ability to structure reality are two further roles that it serves: its explanatory and generative roles. That is, firstly, explanation tracks grounding, and grounding, in some sense, backs explanation. Grounding entails the explicability of the grounded on the basis of its grounds and thus serves the role of providing a synchronic metaphysical explanation for the nature and/or existence of a less fundamental entity on the basis of the nature and/or existence of another, more fundamental entity (Schaffer 2016). Thus, for example, if one is seeking an explanation for the existence of Singleton-Socrates (i.e., the set with Socrates as its sole member), a synchronic metaphysical explanation for this particular case would simply cite the relevant metaphysical laws (i.e., the principles of grounding) and the fact that Socrates exists. More fully, in this example, Socrates grounds Singleton-Socrates and thus a synchronic metaphysical explanation for the existence of the less fundamental entity: Singleton-Socrates, would cite the more fundamental source(s) of that entity, which is that of Socrates, as mediated through the principles of grounding. Thus, in this case, and others like it, the grounds provide an explanation for the grounded—grounding is thus a relation that is intimately tied to explanation. Secondly, grounding is super-internal in the sense that the existence and intrinsic nature of one of the relatum ensure, firstly, that the grounding relation obtains and, secondly, that the other relatum (or relata) exists with the intrinsic nature that it has (Schaffer 2016).61 So, for example, it is Socrates, and the intrinsic nature that he possesses, which makes it the case that Singleton-Socrates exists and has the nature that it does (namely, being the singleton set that includes Socrates as a member). Thus, as there is a generation of the grounded from the grounds, once there is a fixing of the intrinsic nature of the grounds, there is also a fixing of the intrinsic nature of what is grounded. This emphasises the fact that the existence of the grounds is sufficient to account for the grounded—grounding is thus a relation that is generative by nature.

Consequently, given the fulfilment of these explanatory and generative roles, grounding thus provides the direction and linkage needed for metaphysical explanation and generation in a similar manner in which causation provides the direction and linkage needed for causal explanation and generation. This leads one to infer that the best explanation of this striking similarity is that of grounding being identical to metaphysical causation—which is to be held in distinction from nomological causation. Specifically, following Alastair Wilson (2018),62, we can take the grounding relation to be a special case of the causal relation where, as Wilson (2018, p. 724) notes, ‘whenever A grounds B, A is a (metaphysical) cause of B and B is a (metaphysical) effect of A’. Metaphysical causation and nomological causation, are thus different species of the same genus: causation, such that, for the former, once one distinguishes the more from the less fundamental, it is quite natural to posit an explanatorily-backing, generative relation of metaphysical causation. Thus, the similarity between grounding (i.e., metaphysical causation) and causation (i.e., nomological causation) centres on the manner in which the causal sufficiency relation is mediated within a causal and grounding context. More precisely, if laws of nature mediate a given instance of the causal sufficiency relation, then it is a case of nomological causation—for example, the throwing of a stone is a sufficient nomological cause of the breaking of a window, as this causal relation is mediated by laws of nature. Whereas if the (law-like) principles of grounding fulfil the role of mediating a given instance of the causal sufficiency relation, then it is a case of metaphysical causation—for example, the existence of Socrates is a sufficient metaphysical cause of the existence of Socrates’ singleton set, as this causal relation is mediated by the (law-like) principles of grounding.63 Grounding (i.e., metaphysical causation) and nomological causation are thus simply different ways for the causal relation to be mediated and thus obtain (Wilson 2018).64 With this notion of grounding to hand, we can now further elucidate the notion of fundamentality in light of grounding, and re-state (44) in its indexed format as such:

(48)	(FundamentalG): x is fundamental if x is independentG and completeG.

In unpacking this, we, firstly, can state the indexed version of (45) as such:

(49)	(IndependenceG): x is independent if nothing grounds x.

Additionally, secondly, we can state the indexed version of (46) also as such:

(50)	(CompletenessG): The set of the xxs is (or the xxs plurally are, or a non-set-like x is) complete at a world w just in case its members ground everything else at w.

According to (48), as further elucidated by (49) and (50), an entity is fundamental if it is ungrounded (i.e., not grounded by any other entity) and is a member of a set of entities at a world whose members ground everything else in that specific world. Whereas an entity is derivative, that is non-fundamental (i.e., dependent and non-complete), if something grounds it and/or it is not a member of a set of entities at a world whose members ground everything else in that specific world.65 In further precisifying this connection between fundamentality and grounding, we can apply the various grounding principles within this framework resulting in the nature of a fundamental entity being as expressed by

Table 1. Fundamentality Grounding Principles.

Grounding Principles	IndependentG (Ungrounded)	CompleteG (Ground)
Directed	This entity does not rank below any other entity in the hierarchical structure of reality.	This entity is part of a set that ranks higher than any other entity in the hierarchical structure of reality within the specific world in which this set exists.
Necessitating	The existence of another entity does not necessitate the existence of this entity.	This entity is part of a set that necessitates the existence of every other entity within the specific world in which this set exists.
Generative	This entity’s existence and intrinsic nature are not fixed by the existence and intrinsic nature of any other entity.	This entity is part of a set whose existence fixes the existence and intrinsic nature of every other entity within the specific world in which this set exists.
Explanatory	This entity’s existence, at a specific time, is not explained by the existence of any other entity.	This entity is part of a set that, at a specific time, explains the existence of all other entities within the specific world in which this set exists.
Causal	This entity is not a grounded effect of any other entity.	This entity is part of a set that is the metaphysical cause of other entities, which are grounded effects within the specific world in which this set exists.

:

A fundamental entity is thus one that is not an output of a grounding relation, rather, it ultimately serves as the ground of everything else. For a fundamental entity, nothing presses upwards on it, instead, it serves the role of pressing upwards on all other (non-fundamental) entities—it is a basic feature of the hierarchical structure of reality (Bennett 2017, p. 111). We thus have a clear, and indexed precisification of the notion of fundamentality with a clarification here of how the building-relation of grounding fits neatly into this picture. We can now utilise these notions and apply them to the task at hand.

5.2. ‘God’ as the Fundamental Aspect

In this stage of our constructive task, we take the Father (i.e., Divinity_y[y@r₁])—unlike the Son (i.e., Divinity_y[y@r₂]) and the Spirit (i.e., Divinity_y[y@r₃])—to exist of himself, be the ultimate source of everything and thus be the one true ‘God’.66 More specifically, the Father is the ‘unexplained explainer’, in that he is, on the one hand, independent, which is to say that he is unbuilt and, on the other hand, he is complete, which is to say that he is a member of a set of entities at a world whose members build everything else.67 However, as noted above, the notions of independence and completeness are ambiguous as they stand. In that, we must index each of the notions to particular building-relations. Thus, focusing on the specific building-relation of grounding, the Father being independent is reducible to him being ungrounded and him being complete is reducible to him being a member of a set of entities at a world whose members ground everything else. In short, the Father is the ungrounded ground of everything else. Hence, in the reading of (AC) provided by Monarchical Trinitarianism—where the one ‘God’ is numerically identical to the Father—is now to be understood as him—in Monarchical Aspectivalism—being ‘God’ in a ‘fundamentality-sense’. The Father, as the fundamental Divinity-Aspect—in that this specific aspect of Divinity (i.e., Divinity_y[y@r₁]) is ontologically prior to all other things in the hierarchical structure of reality. He is independent of all things and exists as the complete entity within this structure, due to him—in the region in which he is located within—being ungrounded (i.e., unbuilt) and fulfilling the role of grounding (i.e., building) the Son, the Spirit and all other features of reality—with the former being done by setting their specific ‘location relations’. The Father (i.e., Divinity_y[y@r₁]) is thus fundamental by not being the output of any grounding relation, in that nothing ‘presses upwards’ on him; rather, he presses upwards on all other (non-fundamental) entities.

We can thus further elucidate the nature of the Father’s role as the fundamental aspect of Divinity—that is, the fundamental Divinity-Aspect within the Trinity—by applying the grounding principles, expressed by

Table 2. Trinitarian Fundamentality Grounding Principles.

Grounding Principles	IndependentG (Ungrounded)	CompleteG (Ground)
Directed	The Father (Divinityy[y@r1]) does not rank below the Son (i.e., Divinityy[y@r2]) and the Spirit (i.e., Divinityy[y@r3]) or any other entity in the hierarchical structure of reality.	The Father (Divinityy[y@r1]) ranks higher than the Son (i.e., Divinityy[y@r2]) and the Spirit (i.e., Divinityy[y@r3]) and any other entity in the hierarchical structure of reality within the specific world in which he exists.
Necessitating	The existence of the Son (i.e., Divinityy[y@r2]) and the Spirit (i.e., Divinityy[y@r3]) or any other entity does not necessitate the existence of the Father.	The Father’s (Divinityy[y@r1]) existence necessitates the existence of the Son (i.e., Divinityy[y@r2]) and the Spirit (i.e., Divinityy[y@r3])and every other entity within the specific world in which he exists.
Generative	The Father’s (Divinityy[y@r1]) existence and intrinsic nature are not fixed by the existence and intrinsic nature of the Son (i.e., Divinityy[y@r2]) and the Spirit (i.e., Divinityy[y@r3]) or any other entity.	The Father’s (Divinityy[y@r1]) existence and intrinsic nature fix the existence and intrinsic nature of the Son (i.e., Divinityy[y@r2]) and the Spirit (i.e., Divinityy[y@r3]) and every other entity within the specific world in which he exists.
Explanatory	The Father’s (Divinityy[y@r1]) existence, at a specific time, is not explained by the existence of the Son (i.e., Divinityy[y@r2]) and the Spirit (i.e., Divinityy[y@r3]) or any other entity.	The Father’s (Divinityy[y@r1]) existence, at a specific time, explains the existence of the Son (i.e., Divinityy[y@r2]) and the Spirit (i.e., Divinityy[y@r3]) and all other entities within the specific world in which he exists.
Causal	The Father (Divinityy[y@r1]) is not a grounded effect of the Son (i.e., Divinityy[y@r2]) and the Spirit (i.e., Divinityy[y@r3]) or any other entity.	The Father (Divinityy[y@r1]) is the metaphysical cause of the Son (i.e., Divinityy[y@r2]) and the Spirit (i.e., Divinityy[y@r3]), and all other entities that are grounded effects within the specific world in which he exists.

., to this specific case as well:

Grounding, conceived as a relation of directed-dependence, plays the needed role of a necessary explanation-backing link that stems from the Father to Son and the Spirit, and is mediated by the principles of grounding. The Son and Spirit—as Divinity Aspects— are dependent for their existence as aspects of Divinity upon the (eternal and necessitating) action of Divinity insofar as it is located at a different location—namely, r₁—fulfilling a certain role—namely, the O-Role *agent*. Hence, the Son and the Spirit do not exist as independent aspects but are grounded (or built) aspects. Thus, as the Son and the Spirit are the less fundamental result within this grounding relationship, they are subordinate aspects of Divinity. Therefore, there is a distinct ordering and status distinction between the Divinity Aspects within the Trinitarian life, where the Father as the independent and complete aspect (i.e., the ungrounded ground of everything else), is fundamental, and the Son and the Spirit, who, as dependent and non-complete aspects (i.e., grounded entities that are not the ground of everything else), are thus derivative, non-fundamental aspects.

We can now illustrate in Figure 10. for heuristic purposes this status distinction through the following fundamentality (hierarchical) structure (with (‘Ground’ standing for a ‘relation of grounding’, ‘LS’ standing for ‘location setting action’ and ‘CLS’ standing for ‘cooperative location setting action’):

There is a hierarchical structure within the Trinity as we have the case here of there being one entity: Divinity, which insofar as it is located in one region (having a perspective and fulfilling a certain role) is fundamental and undergirds itself in insofar as it is located in two other regions (having two perspectives and fulfilling two other roles) with the grounding relation connecting the latter aspects to the former aspect that is at a higher level in the structure of reality. Thus, the Son and the Spirit (i.e., the undergirded aspects) are linked by the grounding relation as less fundamental output, to a more fundamental input (i.e., undergirding aspect), the Father.68 Within this hierarchical structure, as noted previously, the Father is thus the fundamental and most ‘basic’ aspect in all of reality who serves as the ultimate (synchronic metaphysical) explanation for the nature and/or existence of the Son and the Spirit (and all other reality). He (i.e., (Divinity_y[y@r₁])) is thus the one ‘God’ (i.e., the fundamental Divinity-Aspect). Yet, the Son and the Spirit, are not rightly called ‘God’ (in the nominal sense), through them being aspects of Divinity that lack this fundamentality.

Given all of this, we can now, first, re-construe conditions (a) and (b) of (Monarchical Trinitarianism) as follows:

(51) (Monarchical Aspectivalism)

(a) There are three relationally distinct persons (i.e., three bearers of a first-person perspective that fulfil an onto-thematic role at their respective spatial regions) within the Trinity: the Father, the Son and the Spirit, each of whom is a (region-specific) aspect that is numerically identical to the one, multiply located, powerful trope: Divinity. (b) The one ‘God’ (in the nominal sense), who is the fundamental (i.e., independent and complete) Divinity-Aspect, is identified as one of the aspects: the Father, who is the sole ground (i.e., builder) of the Son and the Spirit.

Second, within the framework established by this account, we thus have a basis for providing a re-interpretation of the Athanasian Creed (AC) through an alternative Monarchical reading (MR₂), which was previously constructed in a step-wise manner but now can be brought together as follows:69

Athanasian Creed (AC)	Monarchical Reading2 (MR2)
1. The Father is God 2. The Son is God 3. The Spirit is God 4. The Father is not the Son 5. The Father is not the Spirit 6. The Spirit is not the Son 7. There is exactly one God.	1’. Father-Aspect = Divinity (Trope). 2’. Son-Aspect = Divinity (Trope). 3’. Spirit-Aspect = Divinity (Trope). 4’. Father-Aspect ≠ Son-Aspect 5’. Father-Aspect ≠ Spirit-Aspect 6’. Spirit-Aspect ≠ Son-Aspect 7’. There is exactly one fundamental Divinity-Aspect, the Father-Aspect.

Thus, according to (MR₂), in line with element (7), there is one ‘God’—identified as the Father, who is the fundamental Divinity-Aspect. However, in line with elements (1)–(3), The Father, construed as an aspect—termed ‘Father-Aspect’—is numerically identical to Divinity (i.e., a powerful trope); the Son, construed as another aspect—termed ‘son-Aspect’—is numerically identical to Divinity (i.e., the same powerful trope as the former aspect); and the Spirit, construed as another aspect—termed Spirit-Aspect’—is numerically identical to Divinity (i.e., the same powerful trope as both former aspects). Yet, and most importantly, given their relational personhood (i.e., the distinct first-person perspectives and onto-thematic roles) had by each of the Divinity-Aspects, we (fortunately) in this account, do not face the distinction issue (i.e., (4), (5), (6) being transgressed), and neither—given the metaphysical and Monarchical element of this reading—do we face the oneness issue, (i.e., (7) being transgressed)—as, for the former issue, the Father (i.e., Father-Aspect), the Son (i.e., Son-Aspect) and the Spirit (i.e., Spirit-Aspect), are qualitatively distinct, yet numerically identical to one another (and Divinity), which thus grounds their distinction from one another. Additionally, for the latter issue, there is only one entity who is identified as the one God (in the nominal sense) and the sole fundamental Divinity-Aspect: the Father, which preserves the oneness of ‘God’ within the Trinitarian life. Monarchical Aspectivalism thus provides a means for one to affirm the doctrine of the Trinity whilst also upholding a numerical identity of the Father, the Son and the Spirit with Divinity, and thus maintaining the metaphysical simplicity of the Divinity by forgoing relational and personal properties, for ‘personal’, ‘relationally determined’ aspects. Additionally, given the metaphysical framework that has been developed here, one can uphold all of these things without, however, falling into absurdity. Thus, the (LPT) does not, in fact, plague the reading of the Athanasian Creed (i.e., (MR₂)) that is provided by this Trinitarian account. The doctrine of the Trinity, as construed in an Aspectival manner, does not face the Logical Problem of the Trinity, and thus one can indeed proceed to adopt a Monarchical Trinitarian position, even within the Latin Trajectory as well.

6. Conclusions

In conclusion, a solution has been provided to the Logical Problem of the Trinity by introducing a new account of the doctrine of the Trinity: Monarchical Aspectivalism, and an alternative reading of the Athanasian Creed: the Monarchical Reading, in light of certain central theses within the field of contemporary metaphysics. In utilising these theses, one is able, in a coherent manner, to affirm the existence of three relationally distinct persons within the Trinity, with the Father being the one ‘God’ and each of the persons being numerically identical to one, metaphysically simple divine nature—whilst still being distinct from one another (in the most important sense of the word). Monarchical Aspectivalism thus allows a certain reading of the Athanasian Creed to be a viable option for future Trinitarian theorising.70