The doctrine of the monarchy of the Father

According to the doctrine of the monarchy of the Father (hereafter, the monarchy), the one ‘God’ is numerically identical to the first person of the Trinity, the Father, in such a manner as to establish a ‘hierarchical’ structure within the Trinitarian life.Footnote ¹ This specific doctrine furthered the New Testament's language about the one ‘God’, as found in various scriptural passages:Footnote ²

1. (a) ‘And this is eternal life, that they know you, the only true God, and Jesus Christ whom you have sent’ (John 17:3).

2. (b) ‘I am ascending to my Father and your Father, to my God and your God’ (John 20:17).

3. (c) 'For us, there is one God, the Father … and one Lord Jesus Christ’ (1 Corinthians 8.6).

4. (d) ‘The God and Father of the Lord Jesus, he who is blessed forever’ (2 Corinthians 11:31).

These paradigm scriptural passages provided a basis for the development of the doctrine that the one ‘God’ was simply the Father, as Catherine LaCugna helpfully notes that the term

Thus, as LaCugna alluded to, on the basis of this scriptural witness, we see that the creedal declarations made at the councils of Nicaea (325 ce) and Constantinople (381 ce) unmistakably express this doctrine in providing the correct referring expressions for each of the members of the Trinity: ‘I believe in one God, the Father … and in one Lord, Jesus Christ, the (only begotten) Son of God … and in one Spirit’ (Tanner Reference Tanner1990, 5, emphasis added). In these authoritative declarations, the referring expression for the Father is ‘God’, while the Son and the Spirit, though ontologically equal to the Father, are designated with different expressions based on the fact that the one ‘God’ is not the nature (essence or substance) shared between them, but is identified as a person, the Father.Footnote ³ Given this, the central question facing the creedal formulators was whether the Son and the Spirit could be affirmed to be divine in the same way as the Father (who is ho theos), and so also be referred to as theos (Behr Reference Behr2018). The answer to this question was clearly in the affirmative,Footnote ⁴ as we see the Constantinopolitan Creed declaring that the Son (and the Spirit) are ‘of the essence of the Father’. Thus, for the pro-Nicenes, the homoousion (i.e. the ontological equality) of the persons did not transgress the boundary of the monarchy due to this equality finding its basis in the Father.Footnote ⁵

In turning to the Greek-speaking theologians of the pro-Nicene trajectory,Footnote ⁶ specifically the Cappadocian Fathers: Basil of Caesarea, Gregory of Nyssa and Gregory of Nazianzus, we find a further elucidation made to the monarchy. As we firstly see Basil writing that ‘There is one God and Father, one Only-Begotten Son, and one Spirit … We proclaim each of the hypostases singly … We have never to this present day heard of a second God’ (Basil, Spir., 18.44–45 (NPF² 8:28)).Footnote ⁷ Thus, Basil expresses the fact that the one ‘God’ is simply to be identified as the Father, and there is no second ‘God’ (be it the Son or the Spirit) that exists alongside him. Moreover, we then see Gregory of Nyssa standing clearly in line with the monarchical position of his brother Basil, where he writes that ‘the God overall alone has as a special property of his hypostasis that is the Father and subsists from no cause, and again by this sign, he is recognized particularly' (Gregory, Ep. 4).Footnote ⁸ Thus, for Gregory, in a similar vein to Basil, the ‘God overall’ is identified as the Father, or even more importantly, it is ‘God’ himself who is identified (and individuated) as the Father, with the characteristic marks of the Son and the Spirit relating directly to him (Branson, n.d., 12). Therefore, for Gregory and Basil, the identity of the one ‘God’ is tied intimately to no other entity than the Father. Likewise, in Gregory of Nazianzus,Footnote ⁹ we also find a further expression of the centrality of this doctrine for pro-Nicene Trinitarian theorizing, when he writes, in Oration 25.15, that within the Trinity there is:

Gregory, along with the other Cappadocian Fathers, thus takes the one ‘God’ simply to be numerically identical to the Father who is the sole principle (archē), cause (aitia), and source (pēgē) of the Son and the Spirit, and thus is rightly designated as ‘God’ in the primary sense of the word. This unique designation for the Father, however, does not negate the usage of the word ‘God’ in reference to the Son and the Spirit, as when they are ‘mentioned separately’ (i.e. in respect of creation) they are also ‘God’ in a secondary sense, due to each of them possessing the divine nature, which they receive in their entirety from the Father (Beeley Reference Beeley2008, 198). Nevertheless, when we speak of the three together, the one (and only named) ‘God’ is solely the un-originated source, from whom the other persons derive their being, the Father.

Thus, in summary, within the Trinitarian life, according to the Greek-speaking theologians (i.e. the Cappadocian Fathers), 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 sense of the word. The Father is thus numerically identical to the one ‘God’, while the Son and the Spirit are, with the Father, ‘God’ in a secondary sense of the word by each of them sharing in the one divine nature. Taking this all into account, we can state this position succinctly as such:

1. (1) (Monarchy):

   1. (i) There are three entities: the Father, the Son, and the Spirit, who share one divine nature and thus are each equally termed ‘God’ (in the secondary sense).

   2. (ii) The one ‘God’ (in the primary sense) is numerically identical to one of the entities: the Father, who is the sole ultimate source of the Son and the Spirit.

The monarchy, as expressed by (Monarchy₁), is thus at the foundation of pro-Nicene Trinitarianism. However, a further precisification of the doctrine will aid us in properly grasping the nature of the hierarchical structure within the Trinity that is established by it. More importantly, a further clarification and unpacking of the doctrine will aid us in warding off a specific objection which charges it with a promotion of a type of subordinationism which is not in line with the central tenet of pro-Nicene Trinitarianism: the ontological equality (i.e. homoousion) of the persons. The focus of our precisification will therefore be on furthering our understanding of the nature of the status distinction between the Father, the one ‘God’, and the Son and the Spirit who, as noted above, are each not ‘God’ (in the primary sense), but are equal to him in an ontological sense.Footnote ¹⁰

Now, for some initial steps in this precisification task, we can further clarify the primary and secondary senses of the term ‘God’ by assuming a specific linguistic distinction concerning it.Footnote ¹¹ That is, on the one hand, the term ‘God’ can be used in its primary sense as a referring expression (i.e. a proper name) for a particular ‘person’, the ultimate source of everything else,Footnote ¹² which we can now call its ‘nominal sense’. However, on the other hand, the term ‘God’ can also be used in a secondary sense as a predicate (i.e. a common name) for a certain kind of ‘person’, a divine ‘person’, which we can now term its ‘predicative sense’. Using this linguistic distinction, we can take the three entities within the Trinity to each be ‘persons’ and, for clarity's sake, we can retain the usage of the term ‘God’ solely in its nominal sense and substitute the term in its predicative sense for the adjective ‘divine’. Thus, with this identification, distinction, and substitution in place, we can now further construe (Monarchy₁) as such:

1. (2) (Monarchy₂):

   1. (i) There are three persons: the Father, the Son, and the Spirit, who share one divine nature and thus are each equally divine (i.e. ‘God’ in the predicative sense).

   2. (ii) The one ‘God’ (in the nominal sense) is numerically identical to one of the persons: the Father, who is the sole ultimate source of the Son and the Spirit.

This specific doctrine, construed in this particular way, thus posits the existence of three divine persons, the Father, the Son, and the Spirit. Yet, there is only one ‘God’ that is located within the Trinity, as only one of those ‘persons’, the Father, is ‘God’ in the nominal sense. However, the question that is now presented to us is why the Father, and him alone, is ‘God’ in that specific sense. Well, as noted previously, the term ‘God’ (in its nominal sense) is solely ascribable to an entity who is ultimate and the source of everything else that exists. The term ‘God’ in the nominal sense is thus taken to imply fundamentality. And as the Father is the sole divine person within the Trinity, who is the ultimate source of everything else, he uniquely has the right to bear the name ‘God’. Thus, at a more precise level, the Father being the one ‘God’ in a nominal sense is reducible to him being the one ‘God’ in a fundamentality-sense. However, despite the plausibility of the clarification made here, the question still stands of what it actually means for the Father to be ‘God’ in this specific sense. What are the requirements for an entity to be deemed fundamental? And does the subordination of the Son and the Spirit to the Father in this fundamentality-sense create an ontological distinction (or subordination) between them?

The rest of this article will focus on answering these questions by providing a further metaphysical elucidation of the monarchy, as expressed through (Monarchy₂), and a metaphysical reconstrual of the inherent subordinationism posited by it. Specifically, this article will utilize the notion of ‘building-fundamentality’ provided by Karen Bennett, to deepen the fundamentality interpretation of (Monarchy₂) that has already been provided. And, on this basis, a demonstration will be provided for why the subordination of the Son and the Spirit to the Father does not lead to a further affirmation of a problematic ontological distinction (or subordination) between them. The monarchy will thus be further clarified and shown to not be inconsistent with pro-Nicene Trinitarianism. Thus, the plan is as follows: in the next section (‘Building-fundamentality’) I explicate the notion of building-fundamentality provided by Karen Bennett, and provide a further elucidation of this notion within the metaphysical grounding framework proposed by Jonathan Schaffer. In the subsequent section (‘Building the fundamental monarchy’) I apply the notion explicated in the previous section to the doctrine which will provide a further precisification of it. In the following section (‘An ontological subordination problem’) I detail the various forms of subordinationism that have been helpfully highlighted by Mark Edwards and R. T. Mullins and show how the type of subordinationism posited by the doctrine does not lead to a further ontological distinction (or subordination) between the Trinitarian persons. Finally, after this section, there will be a concluding section (‘Conclusion’) which will summarize the above results and conclude the article.

Building-fundamentality

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 (Reference Bennett2017), are those of independence and completeness (with the former being more central to the notion than the latter).Footnote ¹³ Given these two aspects, a distinctive conceptualization of the notion of fundamentality can be stated as such:

1. (3) (Fundamental): x is fundamental if x is independent and complete.

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, realization, 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 mould of being a building-relation. How these paradigm relations fit this building mould is through them fulfilling the three necessary and jointly sufficient conditions of directedness, necessitation, and generation. First, the condition of directedness takes a building-relation to be antisymmetric, irreflexive, and thus asymmetric. Second, the condition of necessitation takes builders to necessitate, in some sense, what they build. Third, the condition of generation takes the built entities to exist in virtue of their builders, and thus the latter support an explanation for the former existing as they do (Bennett Reference Bennett2017, 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 among them (Bennett Reference Bennett2017, 20). On the basis of this further explication of the notion of building, we can now construe the independence aspect of fundamentality as such:

1. (4) (Independence): x is independent if nothing builds x (Bennett Reference Bennett2017).

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

1. (5) (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 Reference Bennett2017, 109).

According to (Independence), 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 fundamental entities is complete at a specific world in the sense that these entities 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 (Fundamental) and further elucidated by (Independence) and (Completeness), reflects, as Bennett (Reference Bennett2017, 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 Reference Bennett2017). Therefore, as Bennett notes, for certain fundamentality relations to obtain is simply ‘for certain complex patterns of building to obtain’ (Bennett Reference Bennett2017, 139). In short, there is an identification of fundamentality with building. Thus, the state of affairs of an entity being 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 is 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 generalization about a class of relations (Bennett Reference Bennett2017, 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 fundamental is to be independent and complete, which, for the former, is ultimately reducible to either not being composed, or constituted, or realized, or determined, or grounded, or caused, by anything else – a fundamental entity does not feature as an output of a particular building-relation (Bennett Reference Bennett2017, 112). However, 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 realize, or determine, or ground, or cause everything else, in that specific world – the set of fundamental entities builds, in one of the above ways, everything else (Bennett Reference Bennett2017, 112). Thus, there are various real distinctions between the indexed versions of fundamentality. However, for a more precise discussion, we can now focus our attention on one particular building-relation: grounding,Footnote ¹⁴ which has played a large role in contemporary metaphysics and can help us to further elucidate the nature of fundamentality.

Grounding (or ground) is regularly characterized as a primitive expression of dependence, determination, or explanation. This expression has been championed by ‘grounders’ (i.e. grounding theorists) such as Kit Fine (Reference Fine, Correia and Schnieder2012), Jonathan Schaffer (Reference Schaffer, Chalmers, Manley and Wasserman2009 and Reference Schaffer2016), and Gideon Rosen (Reference Rosen, Hale and Hoffmann2010), among others,Footnote ¹⁵ and is typically introduced by paradigm example(s) such as the following:

1. (6) (Paradigm): Singleton-Socrates exists in virtue of the existence of Socrates.

What is of concern in this example for grounders, is not so much the truth value of the claim, but rather the fact that the connecting ‘in virtue’ clause (and others like it) expresses some form of ontological priority that is related to ‘determination’, ‘dependence’, or ‘explanation’. However, in explicating the nature of this ontological priority and the character of this expression, grounders usually focus on detailing the specific formal principles, modal pattern, explanatory and generative roles, and the analogous relationship to other relations which grounding has, which all help to further demystify it.

So, in following this demystification procedure, we can see that the consensus for grounders is that grounding, in its standard ‘full’ variety:Footnote ¹⁶

1. (7) (Full): A given x is the ground of y if x on its own is sufficient to ground y

is, first, governed by the following three formal principles:Footnote ¹⁷

1. (8) (Irreflexivity): No x is grounded in itself.

2. (9) (Asymmetry): If x grounds y, then y does not ground x.

3. (10) (Transitivity): If x grounds y, and y grounds z, then x grounds z.

And, second, grounding is also generally taken to be governed by the following principles that express a modal pattern:Footnote ¹⁸

1. (11) (Non-monotonicity): If x grounds y, it does not follow that y is grounded by x and any other fact (or entity) r.

2. (12) (Hyperintensionality): If x grounds y, it does not follow that x grounds any fact (or entity) that is intensionally equivalent to y.

3. (13) (Necessitarianism): If x grounds y, then x necessitates y.

Thus, given the formal principles, grounding induces a strict partial order over the entities that are in its domain (Trogdon Reference Trogdon, Hoeltje, Schnieder and Steinberg2013).Footnote ¹⁹ That is, grounding gives rise to a hierarchy of grounds, in which the grounds of a fact (or entity), as Johannes Korbmacher notes, ‘rank “strictly below” the fact (or entity) itself’ (Korbmacher Reference Korbmacher2018, 161, parenthesis added). And, given the principles that express a modal pattern, grounding entails a necessary dependence of the grounded on the grounds, in that the existence of the latter entails the existence of the former. In short, grounders guarantee what they ground (Trogdon Reference Trogdon, Hoeltje, Schnieder and Steinberg2013). However, they perform this necessitating action in a ‘fine-grained’, rather than a ‘coarse-grained’ manner, in that they do not necessarily ground other superfluous entities as well. Thus, grounding, in its most basic construal, is an expression that conveys some form of directedness and necessitation.

However, to aid us in our precisification task, it will be helpful now to narrow our focus to unpacking a specific ground-theoretic framework that has played an influential role within the contemporary literature, that of Jonathan Schaffer's grounding theory. Within this theory proposed by Schaffer, grounding is best modelled as a primitive ‘directed-dependency’ relation, 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 Reference Schaffer2016).Footnote ²⁰ Thus, according to Schaffer (Reference Schaffer, Chalmers, Manley and Wasserman2009), 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 which 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 Reference Schaffer2016, 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 Reference Schaffer, Chalmers, Manley and Wasserman2009).

Now, closely related to ground's ability to structure reality are two further roles that it serves: its explanatory and generative roles, which are captured by the following principles:

1. (14) (Separatism): If x grounds y, x backs an explanation for y.

2. (15) (Super-Internality): If x grounds y, then y exists and has its intrinsic nature in virtue of x and Rxy obtains in virtue of x.

First, for the explanatory principle of ‘separatism’,Footnote ²¹ 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 Reference Schaffer2016). Thus, for example, focusing on (Paradigm), if one is seeking an explanation for the existence of Singleton-Socrates, 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. Second, for the generative principle of ‘super-internality’, grounding is super-internal in the sense that the existence and intrinsic nature of one of the relatum ensure, first, that the grounding relation obtains and, second, that the other relatum (or relata) exists with the intrinsic nature that it has (Schaffer Reference Schaffer2016).Footnote ²² So, taking (Paradigm) as an example again, 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 emphasizes the fact that the existence of the grounds is sufficient to account for the grounded – grounding is thus a relation which 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. More specifically, we can say that as the relation of causation links the world across time (i.e. causes are diachronically linked to their ‘generated’ effects), the relation of grounding links the world across levels (i.e. grounds are synchronically linked to the ‘generated’ (grounded) effects) (Schaffer Reference Schaffer2016). Thus, as a directed-dependency relation, grounding is analogous to causation in such a manner as to render the former as one that has a species-similarity to the latter.Footnote ²³ That is, once one (again) distinguishes the more from the less fundamental, it is quite natural to posit an explanatorily backed, generative relation that is analogous to causation, which leads to the following final principle:

1. (16) (Causal Analogy): If x grounds y, then y is a generated ‘effect’ of x, as mediated by principles of grounding and aptly modelled by Structural Equation Modelling.

The systematic analogy between grounding and causation centres on the manner in which a directed-dependency relation is mediated within a causal and grounding context. That is, if laws of nature mediate a given directed-dependency relation, then it is a case of causation. Whereas if the (law-like) principles of grounding (or grounding principles) fulfil the role of mediating a given directed-dependency relation, then it is a case of grounding.Footnote ²⁴ This analogical link between grounding and causation can be further elucidated through the use of the prominent formal framework of Structural Equation Models, which were developed within a causal context by individuals such as Judea Pearl (Reference Pearl2009) and James Woodward (Reference Woodward2003).Footnote ²⁵ The primary advantage of Structural Equation Models, according to Schaffer (Reference Schaffer2016, 60), is that of them providing the most precise method for detailing directed-dependency relationships between entities. Hence, in a directed-dependency relationship, we have the sources (i.e. causes, grounds) via a link (i.e. causal law, grounding principle) generating a result (i.e. effect, derivative) which can be aptly modelled by the input-function-output structure of Structural Equation Modelling (Schaffer, Reference Schaffer and Kriegeln.d., 4). Thus, taking (Paradigm) as a grounding test case, in the first stage, a Structural Equation Model starts with a representation of the system under study, which is then divided into sets of independent and dependent variables. The independent and dependent variables (in this case, Socrates and Singleton) are then mapped to a specific range of allotted values as such:

In the second stage, one then implements the functions given the ‘dynamics’ of the system, where, according to (Schaffer, Reference Schaffer and Kriegeln.d., 6), there is a linking of the dependent variables by the function that maps the values of the input variables to their output value (where ‘<=’ is to be read as ‘is the output of’ (i.e. ‘Singleton is the output of the set-formation function on Socrates’)):

Finally, in the last stage one just needs to evaluate the ‘fundamentality conditions’,Footnote ²⁶ by assigning values to the independent variables according to what actually happened in reality:

By {(Socrates) = 1} being the case in reality, one can derive the result of {(Singleton) = 1} for the respective model. Utilizing a Structural Equation Model in this way enables one to ascertain a viable synchronic metaphysical explanation for why Singleton-Socrates exists, from the existence of Socrates, via the dependence function that captures the grounding principles (or more specifically, the set-formation principle).Footnote ²⁷ That is, given that Socrates exists (Socrates = 1) and the principles of grounding (set-formation) are at work, it is no coincidence that the Singleton-Socrates exists as well (Singleton = 1). Singleton-Socrates is the output of this principle on the input of Singleton ((Singleton) <=set-formation(Socrates)), leading to an explanation for Singleton-Socrates’ existence (Schaffer, Reference Schaffer and Kriegeln.d.). Thus, a Structural Equation Model expresses how grounding, in an analogous manner to causation, provides the directed connection needed for explanation and induces a hierarchical structural relationship that stems from a more fundamental source (e.g. Socrates's existence) via a link (e.g. the set-formation principle) to a generated, less fundamental result (Singleton-Socrates’ existence). Therefore, in a grounding relationship, the more fundamental input generates and provides an explanation for the less fundamental output analogously to how a cause generates an effect and provides an explanation for its occurrence – grounding is thus a relation which is analogous to causation. Taking all of these things into account, we thus can conclude that grounding names a relation that has the following characteristics:

1. (17) (Grounding):

   1. (i) Directed and Necessitating: A primitive directed-dependency relation that necessarily links the more fundamental entities to the less fundamental entities.

   2. (ii) Explanatory and Generative: Ultimately backs synchronic metaphysical explanations for the nature and/or existence of the less fundamental entities with reference to the more fundamental entities that generate them.

   3. (iii) Causal: Analogous to causation in such a manner as to be mediated by (law-like) principles of grounding and aptly modelled by Structural Equation Models.

Given this construal of grounding, we can now further elucidate the notion of fundamentality in light of grounding, and re-state (Fundamentality) in its indexed format as such:

1. (18) (Fundamental_G): x is fundamental if x is independent_G and complete_G.

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

1. (19) (Independence_G): x is independent if nothing grounds x.

And, second, we can state the indexed version of (Completeness) also as such:

1. (20) (Completeness_G): 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 (Fundamentality_G), as further elucidated by (Independence_G) and (Completeness_G), 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.Footnote ²⁸ 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 shown in Table 1.

Table 1. Fundamentality grounding principles

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 Reference Bennett2017, 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 utilize these two notions to further clarify (Monarchy2).

Building the fundamental monarchy

The monarchy takes the term ‘God’ (in the primary sense) to solely designate the Father, who is the ultimate archē anarchos (i.e. the ultimate source without source). Within pro-Nicene Trinitarianism, the Father, unlike the Son and the Spirit, is taken to exist of himself, be the ultimate source of everything and thus be the one true ‘God’. With our initial precisification of this position, through (Monarchy₂), we reconstrued it in a nominal and fundamentality sense, and thus the one true ‘God’, identified as the Father, is the only named ‘God’ and the sole fundamental divine person. Expounding this now within the building-fundamentality framework at hand, 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.Footnote ²⁹ 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. Given this, and the linguistic distinction introduced above, we can now further precisify (Monarchy₂) by reconstruing it as such:

1. (21) (Monarchy₃):

   1. (i) There are three persons: the Father, the Son, and the Spirit, who share one divine nature and thus are each equally divine (i.e. ‘God’ in the predicative sense).

   2. (ii) The one ‘God’ (in the nominal sense), who is the fundamental (i.e. independent and complete) divine person, is numerically identical to one of the persons: the Father, who is the sole ground (i.e. builder) of the Son and the Spirit.

Thus (Monarchy₃), which asserts that the Father is ‘God’ in the ‘nominal’ sense, is to be construed, as noted previously, as him being ‘God’ in a ‘fundamentality sense’. The Father, as the fundamental divine person, 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 being ungrounded (i.e. unbuilt) and fulfilling the role of grounding (i.e. building) the Son, the Spirit, and all other features of reality. The Father 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 entity within the Trinity by applying the grounding principles to this specific case as well (see Table 2):

Table 2. Trinitarian fundamentality grounding principles

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. Moreover, the importance of this role that is fulfilled by grounding within this specific context can be further emphasized by focusing on a particular element of the systematic analogy between grounding and causation: the possibility for one to utilize Structural Equation Models to map grounding cases. By focusing on this specific element, one can thus formulate an apt Structural Equation Model for the Trinitarian case as such:

By {(Father = 1)} being the case in reality, one can derive the result of {(Son, Spirit = 1)} for this specific model. We thus have, as in the more mundane grounding example above, an explanation of a more fundamental source (the Father's existence) via a link (procession principle) generating a less fundamental result (the Son and the Spirit's existence) which has been aptly modelled by the input-function-output structure of a Structural Equation Model. There is a viable synchronic metaphysical explanation here for why the Son and the Spirit exist (Son, Spirit = 1), from the existence of the Father (Father = 1), via grounding, or more specifically, the procession principle (<=procession).Footnote ³⁰ That is, given that the Father exists and the principles of grounding (procession) are at work, it is no coincidence that the Son and the Spirit exist too. The Son and the Spirit are the output of this principle on the input of the Father and thus are the necessary grounded ‘effects’ of the Father in a manner analogous to causation. The holding of this relationship within the Trinitarian life reveals that the Son and the Spirit are not independent through them being grounded (i.e. built) entities. That is, by them having the Father as their source, they derive their existence from him in the sense that they exist (and are divine) because of the Father grounding (i.e. building) them. The Father thus acts as the fundamental source within the Trinity – his existence is sufficient for the existence of the Son and the Spirit at any given time, ultimately backing a synchronic metaphysical explanation for them existing as they do. Thus, fixing the existence and intrinsic nature of the Father ensures, first, that the grounding relation obtains within the Trinity and, second, that the Son and the Spirit exist with the intrinsic nature that they have. The Son and Spirit are thus dependent for their existence upon an external entity, rather than existing in and of themselves in an ungrounded state. Thus, as the Son and the Spirit are the less fundamental result within this grounding relationship, they are subordinate entities. However, the Son and the Spirit are not only rendered as subordinate through being dependent entities, but are also rendered as such due to them each being non-complete entities, in that they are each not a member of the set of entities at a world that grounds everything else. This is primarily due to them not grounding at least one entity in that world, the Father, who exists as an ungrounded entity. Therefore, there is an essential asymmetry, distinct ordering, and status distinction between the Father who, as the independent and complete entity (i.e. the ungrounded ground of everything else), is fundamental, and the Son and the Spirit, who, as dependent and non-complete entities (i.e. grounded entities that are not the ground of everything else), are thus derivative, non-fundamental entities.

We can now illustrate this status distinction through the following fundamentality (hierarchical) structure featured in Figure 1.

Figure 1. Trinitarian fundamentality structure

There is a hierarchical structure within the Trinity as we have the case here of a fundamental entity undergirding some derivative (subordinate) entities, with the grounding relation connecting the undergirding entity to these entities that are at a higher level in the structure of reality. Thus, the Son and the Spirit (i.e. the undergirded entities) are linked, by the grounding relation as less fundamental output, to a more fundamental input (i.e. undergirding entity), the Father.Footnote ³¹ Within this hierarchical structure, as noted previously, the Father is thus the fundamental and most ‘basic’ entity 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 is thus numerically identical to the one ‘God’ (i.e. the fundamental divine person). Yet, the Son and the Spirit, are not ‘God’ (in the nominal sense), through them lacking this fundamentality. However, the question that is now presented to us is whether this lack of fundamentality entails a problematic ontological distinction (or subordination) between them. As if the one ‘God’ is numerically identical to the Father and thus the Son and the Spirit are simply not ‘God’ in that specific sense of the word (i.e. in the nominal-sense), what grounds do we have for upholding an ontological equality (i.e. a homoousion) between the persons? In answering these questions, it will be helpful to focus on identifying the type of subordinationism that is affirmed by the doctrine. To this issue, we now turn.

An ontological subordination problem

At the most basic level (Monarchy₃) is committed to the following:

1. (22) (Subordination) The Son and Spirit are subordinate to the Father.

However, in further elucidating the nature of (Subordination), Mark Edwards (Reference Edwards2020) and R. T. Mullins (Reference Mullins2020) have helpfully identified some different types of subordinationism prevalent within Church history, with the three types that are most relevant for our case being:Footnote ³²

1. (a) (Ontological Subordinationism) The Son and the Spirit are subordinate to the Father in that the Son and the Spirit have an essence which is inferior to the Father's.

2. (b) (Aetiological Subordinationism) The Son and the Spirit are subordinate to the Father in that the Son and the Spirit are caused to exist by the Father.

3. (c) (Axiological Subordinationism) The Son and the Spirit are subordinate to the Father in that (a) the Son and the Spirit are equal to the Father in essence, but (b) are inferior in rank or status.

Taking into account the different kinds of subordination relations, the question that is presented to us is what kind of subordinationism does (Monarchy₃) commit one to? Clearly, the answer seems to be that of an axiological subordinationism, where the Son and the Spirit possess the same essence as the Father and thus are (what Mullins terms) ‘minimally’ homoousios with him in the sense that they possess the same essential great-making properties as the Father (i.e. they are ‘extensively’ equal to him), and have these properties to the same degree of intensity (i.e. they are ‘intensively’ equal to him) (Mullins Reference Mullins2020, 7)).Footnote ³³ However, there is a difference in rank (or status) between them due to the Father being the only entity in the Trinity who is a fundamental divine person. That is, as previously noted, (Monarchy₃) takes the Father to be ground of the Son and the Spirit and thus is superior in rank (or status) to each of them. However, this difference in rank (or status) seems to entail, as Mullins (Reference Mullins2020, 6–7) notes in a related context, an ontological distinction (or subordination) between the persons, due to there being an inferiority in essence between them. Yet, if this is so, then the inherent subordination of (Monarchy₃) is incompatible with the central tenet of pro-Nicene Trinitarianism: the ontological equality of the persons. Thus, (Monarchy₃) seems to entail not only an axiological subordination but also a problematic ontological subordination as well.Footnote ³⁴

More fully, this problem has been termed by Mullins (Reference Mullins2020, 11–12) the ‘Ontological Subordination Problem’, and has been shown by him to centre around the following property:

1. (23) (Aseity₁)=_df. not having a cause for one's existence.

This property, according to Mullins (Reference Mullins2020, 13), is plausibly assumed to be a great-making property due to the prevalence of this assumption in Christian theological writings. The Father as the fundamental divine person and ground within the Trinity possesses the property of aseity, and the Son and the Spirit, who are entities that are (analogously) ‘caused’ to exist (i.e. grounded) by the Father, do not possess it. However, if this is the case, then the Son and the Spirit lack an essential great-making property that the Father has and thus possess an extensively inferior essence to the Father, resulting in them not being minimally homoousios.

Interestingly, however, this issue does not, in fact, plague the present proposal due to the relativity of the notion of building. That is, according to (Monarchy₃), the Father exists as the fundamental (i.e. independent and complete) divine person and the Son and the Spirit exist as the derivative (i.e. dependent and non-complete) divine persons that are ‘built’ by him. Yet, this building of the latter by the former is solely relative to the building-relation of grounding. Thus, given that the Father builds the Son and the Spirit, it does not, in fact, entail that they also lack the property of aseity. As for this to be the case, the Son and the Spirit would need to literally (rather than analogously) be built and derivative with respect to the building-relation of causation, given that the definition of aseity above solely requires an entity to exist uncaused.Footnote ³⁵ Thus, the Son and the Spirit are indeed uncaused entities and exist a se along with the Father through them being unbuilt with respect to the building-relation of causation. However, there is still a status distinction between them and the Father, as they continue to exist as built and derivate entities with respect to the building-relation of grounding. The Son and the Spirit are grounded, but uncaused, and thus are axiologically subordinate to the Father, who is ungrounded and uncaused. Nevertheless, despite this status distinction, there is no ontological distinction (or subordination) between the persons who are each a se in line with Mullins's definition of the property.

However, one might class this response as a quick move that is dependent upon a faulty definition. As if we take a more generalized definition of aseity, such as that provided by Sarah Adams and Jon Robson (Reference Adams and Robson2020, 253):

1. (24) (Aseity₂)=_df. not depending upon another distinct entity for one's existence and/or nature

the previous response to the Ontological Subordination Problem would not be applicable here, given that an entity could only exist a se if they lack any dependence relation. The Son and the Spirit, even though they may be uncaused, are grounded entities, and thus are dependent for their existence and/or nature on the Father who serves as their ground, while the Father is a se through depending on no other distinct entity for his nature and/or existence. Plausibly then, there is indeed an ontological distinction (or subordination) between the persons through the Father possessing a property which the Son and the Spirit lack.

However, a potentially fruitful way for one to respond to this reformulation of the problem would be to switch focus from utilizing the notion of building, to that of understanding the type of property that aseity is.Footnote ³⁶ Specifically, this response focuses on demonstrating the fact that aseity is correctly understood to be an extrinsic property, rather than an intrinsic one. Thus, given Mullins’ notion of minimal homoousios (and the conceptualization of this within Church history detailed below), there is no need for this property to be possessed by the Son and the Spirit for them to be ontologically equal to the Father.

So, in understanding and unpacking this property distinction, we see that intuitively an intrinsic property (e.g. the mass of an object) is one that an object has solely in virtue of how it is, and an extrinsic property (e.g. the weight of an object) is simply one that is not intrinsic. In further elucidating the former type of property, Jaegwon Kim (Reference Kim1982) suggested that a property is intrinsic if it is unaccompanied (i.e. can be possessed by an object that is all alone). David Lewis (Reference Lewis1983), however, replied to this suggestion by Kim that the property of ’being alone’ is not itself intrinsic, even though it meets the specific requirement of being unaccompanied. Thus, Lewis and Rae Langton (1998), whose view is generally taken to be the locus classicus on the subject, instead saw that a better understanding of intrinsicality is that of it being a necessary condition for an intrinsic property that it is independent of accompaniment. A property is independent of accompaniment if it is independent either of loneliness (i.e. it can be had by an object that does not coexist with a contingent object wholly distinct from itself) or accompaniment (i.e. it can be had by an object that coexists with a contingent object wholly distinct from itself). More precisely, as noted by Langton and Lewis (Reference Langton and Lewis1998, 334), a property P is independent of accompaniment if and only if the following four conditions are met:Footnote ³⁷

1. (25) (Independence Criterion):

   1. (a) It is possible for a lonely object to possess P.

   2. (b) It is possible for a lonely object to lack P.

   3. (c) It is possible for an accompanied object to possess P.

   4. (d) It is possible for an accompanied object to lack P.

An intrinsic property is thus one that can be had by an object regardless of whether it is lonely or accompanied, which captures the intuitive idea that an intrinsic property is such that the possessing or lacking of it is independent of the existence or non-existence of any other entity. Thus, contra Kim, even though an intrinsic property is compatible with loneliness, an object being lonely is not what makes this object possess this type of property – lacking the property is also compatible with loneliness. Likewise, with accompaniment, if a property is intrinsic, then an object being accompanied is not what makes something have that property – lacking the property is also compatible with accompaniment. Intrinsic properties are thus left unchanged by an object being accompanied or being lonely. In short: having or lacking the property is independent of accompaniment or loneliness. It is compatible with either of these states, and it does not imply either of them as well (Langton and Lewis, Reference Langton and Lewis1998). Interestingly, however, although (Independence Criterion) captures a necessary condition for intrinsicality, it fails to provide a sufficient condition for it. This lack of sufficiency had been noted by Langton and Lewis (Reference Langton and Lewis1998, 335) themselves, because there are certain properties (such as the disjunctive property of being lonely and cubical or accompanied and non-cubical) which meet the condition (i.e. are independent of accompaniment) and yet are intuitively extrinsic properties. Nevertheless, given that (Independence Criterion) is indeed a necessary condition for a property being intrinsic, we need not focus on the additional means that Langton and Lewis (Reference Langton and Lewis1998) provide for establishing a sufficient definition of an intrinsic property.Footnote ³⁸ Rather, one only needs to appeal to the necessary condition on intrinsicality expressed by (Independence Criterion) and, specifically, the sub-condition (b) of the criterion stating that if a property P is intrinsic then, possibly, there exists a lonely object that lacks the property. In applying this to the issue at hand, we can see that the assumption of the intrinsicality of the property of aseity (i.e. the property of not depending on any other entity), given the specific sub-condition above, seems to be incorrect, because this property is not independent of accompaniment. For if this property were to be independent of accompaniment, then a lonely object must be able to lack this property as well, which is clearly not the case.

More fully, as noted above, if a property is to be independent of accompaniment, then the fact that an object possesses or lacks this property does not rely on the existence or non-existence of any other, wholly distinct entity. However, it does clearly seem to be the case that for an object to lack the property of aseity (as defined by (Aseity₂)) it must rely on the existence of another, wholly distinct entity for it to do so. For it is indeed not possible that a given object could, in fact, be lonely (and thus exist unaccompanied) and be a dependent entity, which is to say that it lacks the property of aseity (i.e. it is not a se according to (Aseity₂)). As for an object to lack possession of the property of aseity it would indeed require that the object under question be accompanied. Thus, because of this, the property of aseity is not independent of accompaniment, which is enough to disqualify this property from being intrinsic, given the necessity of (Independence Criterion) for intrinsicality.Footnote ³⁹ The property of aseity must thus be extrinsic, and as an extrinsic property, its possession by the Father, and its lack of possession by the Son and the Spirit, does not result in there being any ontological subordination within the Trinity. Since, as noted previously, the minimal homoousion of the persons requires that they possess the same great-making properties. However, as Mullins (Reference Mullins2020, 3, emphasis added) himself notes, a ‘great-making property is an intrinsic property that would improve the greatness of any being that has it’. Thus, the great-making properties that make up the essence of the Trinitarian persons, and thus renders them as minimally homoousios, are solely to be taken as intrinsic properties of them. Thus, these great-making properties are possessed independently of accompaniment and are the sole type of properties that could not differ among the persons, as Richard Swinburne (Reference Swinburne2018, 422, 424, emphasis added) helpfully notes in support of the latter statement: ‘it was agreed that each of the persons has the same essential intrinsic properties which alone make them divine … what none of the Fathers would advocate is that the Son and Spirit differ from each other in virtue of any intrinsic properties … for in that case they would not have a common ούσία’. Therefore, despite the Father's possession of the property of aseity and the fundamentality distinction/axiological subordination of the Son and the Spirit to him, the essence of the Son and the Spirit is not inferior to that of the Father. There is indeed a possession of the same intrinsic essence between the Trinitarian persons, with the Father, as the fundamental entity within the Trinity, having the intrinsic divine essence and existing in a fundamental way. Yet, the Son and the Spirit, despite their axiological subordination to the Father, still possess the same intrinsic divine essence as him, with each of them only existing in a derivative way. We thus still have the same intrinsic essence being shared between the persons regardless of the status distinction between them and the Father's possession of the extrinsic property of aseity. All of this enables the Trinitarian persons to be extensively (and intensively) equal to each other and thus the ontological equality between them within the hierarchical structure of the Trinitarian life can be preserved, rather than negated, by the monarchy.