The nature of Ontological Pluralism

According to Kris McDaniel (Reference McDaniel, Chalmers, Manley and Wasserman2009, Reference McDaniel2010, Reference McDaniel2017) and Jason Turner (Reference Turner2010, Reference Turner2012, Reference Turner, Bliss and Miller2020), Ontological Pluralism is the view that there are different fundamental and irreducible ways, kinds, or modes of being.10 That is, entities can (and do) exist in different ways from one another, which are represented by different existential quantifiers, without the denial of the fact of these entities existing in the univocal category of being – namely, these entities also possess generic existence. More specifically, the central tenets of Ontological Pluralism (hereafter, OP), according to McDaniel (Reference McDaniel, Chalmers, Manley and Wasserman2009) and Turner (Reference Turner, Bliss and Miller2020), can be stated as follows:

For (a), the notion of a ‘way of being’ finds its primary use in enabling one to account for the fact that the specific ontological kind (or category) that an entity is an instance of determines the specific manner in which that entity exists. For example, numbers are of a different ontological kind (or category) than tables – the former is of the kind (or category) abstracta, and the latter is of the kind (or category) concreta – and thus, these entities exist in a different manner from one another. An adherent of OP thus posits the existence of multiple ways of being in order to account for the different types of entities that display distinct features from one another. In positing the existence of multiple ways of being, OP is to be contrasted with the standard view in contemporary metaphysics of Ontological Monism (hereafter, OM), which posits the existence of solely one way of being. The notion of a way of being, posited by OM and OP, corresponds to the notion of an ontological structure. Following Turner (Reference Turner2010, 6–7), we can further elucidate the notion of an ontological structure by utilizing an analogy of a pegboard, which can be understood as follows: at a general level, an ontological structure is represented by a pegboard covered with rubber bands. For the adherent of OM, the correct understanding of ontological structure is that of a large pegboard, where pegs represent entities, and rubber bands of various colours represent objects instantiating different properties and objects standing in different relations to one another (picture, for the former, a band wrapped around a peg, and, for the latter, a band stretching from one object to another). For the adherent of OP, the view of ontological structure that is proposed by the thesis of OM is taken to be misleading in that reality is instead best represented by multiple pegboards – with each pegboard representing a distinct kind of entity with their associated ways of being. In short, proponents of OM conceive of reality as having a single ontological structure – represented by a single pegboard – for example, abstract and concrete entities existing together on one pegboard. However, for the proponent of OP, reality has multiple ontological structures – represented by multiple, independent pegboards – with, for example, abstract entities existing on one and concrete entities existing on another (Turner, Reference Turner2010). We can illustrate the multiple pegboards featured in OP as follows through Figure 1 (where, in the left image, ‘Abstract’ stands for ‘abstract ontological structure’ and ‘S_n’ stands for a ‘particular set peg’, whereas, in the right image, ‘Concrete’ stands for ‘concrete ontological structure’, ‘O_n’ stands for a ‘particular object peg’, and the different colours represent the different properties that are instantiated by each peg).

Figure 1.

Ontological Structure: Pegboard (i).

Thus, as is expressed by this particular analogy, the different ways of being featured within the framework of OP correspond to different structures or domains of reality – one can thus say that reality is indeed multifaceted.

For (b), the notion of an ‘elite quantifier’ is grounded upon the Quinean association between existence and existential quantification – where ontology concerns what existential quantifiers range over. Given this association, the proponent of OP takes there to be several semantically primitive existential quantifiers that range over distinct domains of reality (where a quantifier is semantically primitive in the sense that it is not reducible to the unrestricted quantifier and a restricting predicate). More specifically, a central aspect of the contemporary iteration of OP, as expressed by McDaniel and Turner, is that of the denial of the fact of there being solely one existential quantifier. Rather, there are many – where, for example, there is one, ‘∃_a’, which ranges over the domain of abstract entities, and another, ‘∃_c’, which ranges over the domain of concrete entities (Turner Reference Turner2010, 8). The contemporary project of OP is thus linked with quantificational pluralism – the view that there are multiple existential quantifiers, rather than a single generic quantifier (Turner, Reference Turner, Bliss and Miller2020). However, multiple existential quantifiers can come on the cheap (i.e. one solely needs to introduce an existential quantifier and a restricting predicate to formulate more than one (restricted) existential quantifier). Hence, Caplan (2011, 95–97), McDaniel (Reference McDaniel, Chalmers, Manley and Wasserman2009, 305–10) and Turner (Reference Turner, Bliss and Miller2020, 185) have emphasized the fact that, for the thesis of OP, only certain types of quantifiers are of concern to pluralists: elite quantifiers. Now, defining the notion of eliteness is indeed a challenging task, given that the notion seems to come in degrees. However, as noted by McDaniel (Reference McDaniel2017, 27–28) and Turner (Reference Turner, Bliss and Miller2020, 185), one can proceed to further elucidate the nature of this notion by adopting Sider's (Reference Sider2011) extension of David Lewis's (Reference Lewis1983) notion of perfect naturalness, which centres on the notion of ‘carving nature at its joints’. Existential quantifier expressions that ‘carve nature at its joints’ are thus to be taken as elite (or ‘more elite’ than others that do not). So, taking into account the distinction between abstract and concrete entities, proponents of OP take these two kinds of entities to have different ways of being. These ways can be expressed, as noted previously, by two elite quantifiers: ‘∃_a’ meaning existing abstractly (i.e. the quantifier ranging over the domain of abstract entities) and ‘∃_c’ meaning existing concretely (i.e. the quantifier ranging over the domain of concrete entities). These two existential quantifiers (and the other multiple existential quantifiers posited by pluralists) are thus, as noted previously, taken as semantically primitive – through the notions that they express being irreducible – and elite, where these quantifiers (‘∃_a’ and ‘∃_c’) seem to be ‘fine-grained’ and deeply ‘joint carving’. Thus, taking all this into account, as McDaniel (Reference McDaniel2010, 635) writes, OP is the view that there are possible languages with elite quantifiers ‘that are at least as natural as the unrestricted quantifier’. At the heart of OP is thus the (surprising) claim that there are multiple ways of being and structures of reality and, most importantly, that there are multiple elite existential quantifiers that express these ways of being and structures of reality (Turner, Reference Turner, Bliss and Miller2020). In other words, entities such as abstract entities and concrete entities are thus taken to have different fundamental ways of being – and are part of distinct fundamental structures of reality – that are ranged over by different elite existential quantifiers (e.g., ‘∃a’ and ‘∃c’). In short, one must thus use more than one existential quantifier to represent the extra ways of being and structures of reality.

For (c), the notion of ‘generic existence’ expresses the fact that all entities share in the univocal category of being. Thus, in affirming the veracity of OP – the existence of multiple ways of being that are expressed by multiple elite existential quantifiers – one is not (necessarily) negating an entity's possession of generic existence. An adherent of OP is simply committed to the fact, as noted by McDaniel (Reference McDaniel, Chalmers, Manley and Wasserman2009, 305–10), that the multiple elite quantifiers, which are taken to express the different ways of being of an entity (or entities), are more natural than the generic unrestricted quantifier, in the sense that they express the various fundamental facets of reality in a more accurate manner. Thus, in continuing with our paradigm examples of abstract and concrete entities, the distinction made between the modes of being of abstract entities and concrete entities – with the elite quantifiers of ∃_a and ∃_c – is simply to be taken to be more natural than the generic unrestricted existential quantifier: ∃. That is, as Bernstein (Reference Bernstein, Bernstein and Goldschmidt2021, p. 2), in emphasizing this point, writes:

OP thus affirms the fact that every entity – in addition to them having multiple ways of being – also enjoys the generic and univocal way of being that is expressed by the single, generic, unrestricted quantifier. Thus, what is disaffirmed by the thesis of OP is solely that of the latter quantifier being perfectly natural – in short, it does not ‘carve nature at its joints’.Footnote ³ This disaffirmation, however, does not mean that the single, generic, unrestricted quantifier is to be conceived of as a mere disjunction of the multiple elite existential quantifiers – given that, as McDaniel (Reference McDaniel2010) has shown, the domain that is ranged over by the former quantifier is unified by analogy. That is, as McDaniel (Reference McDaniel2010, 696) notes, we are aware of ‘something akin to disjunctive properties, but they aren't merely disjunctive. Analogous features enjoy a kind of unity that merely disjunctive features lack: they are, to put it in medieval terms, unified by analogy.’ This fact is evident, for example, in the concept of being healthy – which does not seem to be disjunctive, given the different ways of being healthy – as McDaniel writes (Reference McDaniel2010, 695), ‘I am healthy, my circulatory system is healthy, and broccoli is healthy.’ In each of these cases provided by McDaniel, there is a sense in which the generic ways of being healthy correspond to the particular ways of being healthy – that is, we are presented with a concept of generic healthiness by analogy with the particular ways of being healthy (Builes (Reference Builes2019), 4). Existence in its many particular forms and its singular generic form is akin to this, because, for the adherent of OP, there is a fundamental (i.e. perfectly natural) way in which certain entities exist and a non-fundamental (i.e. non-natural) and a non-disjunctive manner in which every entity generically exists, each of which is represented by (a modified form) of Quinean quantification.

The central components of the thesis of OP, and the manner in which these components are interconnected with one another, have been laid out. We will now turn our attention to applying the thesis of OP to the task at hand so as to provide a further metaphysical elucidation of the qua-clauses.

Pluralistic reduplicative predication

According to Conciliar Christology, Christ has two natures: a divine nature and a human nature. In having a divine nature, Christ has certain predicates that are apt of him, such as him being ‘impassible’. And, in having a human nature, Christ has certain other predicates that are apt of him as well, such as him being ‘passible’. Now, given the fact that these apt predicates are inconsistent with each other, the Conciliar Christologist faces a problem – the LPI – as no entity can have inconsistent predicates true of it, and thus Conciliar Christology must be false. As previously noted, a way to ward off this conclusion is to adopt the reduplication predication strategy, which gets one out of the issue raised by the LPI by ascribing each of the inconsistent predications to the particular nature that is possessed by Christ – such that Christ is passible qua his human nature and is impassible qua his divine nature. This method does clearly ward off any charge of inconsistency; however, according to the detractors of this approach, it does this at a purely linguistic level and thus is not, in itself, a metaphysical strategy that can tell us how and why Christ avoids having inconsistent attributes being predicated of him. So, the question that an adherent of the method of reduplicative predication faces is that of providing a further metaphysical elucidation of this approach, which can indeed show how the inconsistency can be avoided at a level that is deeper than the linguistic level. We can proceed to do this by employing the notion of OP that was detailed in the previous section.

Now, in the application of the thesis of OP within a Christological context, we take it to be the case that in our spatiotemporal reality, among the various ontological structures, there are the two ontological categories that are representative of our world: a human ontological structure and a divine ontological structure, each of which can be represented by a specific pegboard – with each pegboard having pegs that represent the entities that exist within that given ontological structure. We can illustrate these two pegboards as follows through Figure 2 (where, in the left image, ‘Human’ stands for ‘human ontological structure’, ‘S_n’ stands for a ‘particular human object peg’, and ‘C’ for ‘Christ peg’, and the different colours represent the different properties that are instantiated by each peg), and, in the right image, ‘Divine’ stands for ‘divine ontological structure’, ‘D_n’ stands for a ‘particular divine object peg’, ‘C’ for ‘Christ peg’, and the different colours represent the different properties that are instantiated by each peg).

Figure 2.

Ontological Structure: Pegboard (ii).

Each structure (and pegboard) would include within it a distinct kind of entity with a distinct way of being (or mode of existence): human entities that have a human way of being and divine entities that have a divine way of being. More precisely, human and divine entities – though they are each a part of the univocal category of being, and thus possess generic existence (which is expressed by the single, generic, unrestricted existential quantifier ∃) – are taken to have different fundamental ways of being that correspond to distinct fundamental structures of reality.Footnote ⁴ Given the Quinean association between existence and existential quantification – where ontology concerns what existential quantifiers range over – these structures or domains, as noted previously, are taken to be ranged over by two different elite existential quantifiers: ‘∃_h’ meaning existing humanly and ‘∃_d’ meaning existing divinely, each of which is perfectly natural by ‘carving nature at its joints’, and thus represent the distinct ways of being and structures of reality that are possessed by human entities and divine entities. Within the framework provided by OP, we take Christ to be an entity that exists within two ontological structures: the human structure and the divine structure. Christ is thus an entity that has two ways of being (or manners of existence), on the basis of him having two natures: a human nature that allows him to exist in the human ontological structure and a divine nature that allows him to exist within the divine ontological structure. Now, by existing in the human structure, Christ has a human way of being, represented by the quantifier ‘∃_h’, and by Christ existing in the divine structure, Christ has a divine way of being, represented by the quantifier ‘∃_d’. Christ is thus an entity that has two natures and thus exists within (or overlaps) two ontological structures and domains of reality – which then enables him to have two ways of being that correspond to these two structures and domains.

So, on the basis of the different ways of being that are possessed by Christ, we take the qua-clauses utilized by the method of reduplicative predication to pick out these two ways of being, which allows us to reconstrue (S) as follows:

Applying this to the inconsistent candidate predicates noted above, we thus can now affirm the existence of two subjects of the inconsistent predicates that are said of Christ – that is, our candidate predications are now: ‘Christ-qua-divine way of being is impassible’ and ‘Christ-qua-human way of being is passible’ – which is clearly not contradictory. More fully, in the human structure (or domain of reality), Christ's manner of existence is that of being an entity that is passible. Yet, in the divine structure (or domain of reality), Christ's manner of existence is that of being an entity that is impassible. Thus, given the different ways of being that Christ has, there is no absurdity in the Conciliar Christologist affirming these candidate predicates (and others like them) – as the attributes expressed by these predicates are possessed by Christ relative to a specific way of being. One can thus take the contradiction that is inherent within the LPI to be produced by a false assumption that Christ only has generic existence (i.e. he is solely part of the univocal category of being). However, as Christ is taken here to have generic existence and different ways of being, one can relativize the apparently problematic predicates to the latter, rather than making the assumption that they are possessed by Christ in a singular and generic fashion. That is, the mistake that was made, and which gave rise to the LPI, is that of one assuming a position of OM, with a single ontological structure, domain of reality and way of being that is expressed by the single, generic, unrestricted quantifier. Doing this is clearly problematic, because it leads a Conciliar Christologist, who affirms (1), to assent to the fact that – within one ontological structure, domain of reality, and way of being – Christ exists (∃) as a passible and impassible entity, which is clearly contradictory. However, by assuming the position of OP, which takes Christ to exist within multiple ontological structures (and domains of reality), and for him to have more than one way of being (i.e. a divine way of being and a human way of being) – with these ways being more natural than the generic way of being (which Christ does indeed possess) – the Conciliar Christologist is thus not led to affirm a contradiction, as they are simply affirming the more ‘fine-grained’ and ‘joint-carving’ state of affairs that takes into account the multiple structures, domains of reality, and ways of being, in which Christ exists (∃_h) as a passible entity and Christ exists (∃_d) as an impassible entity. Hence, it is due to this relativization of the attributes of the candidate predicates under question to two distinct subjects – namely, the two aforementioned ways of being – that we do not have a contradiction being affirmed by the Conciliar Christologist. One can affirm (1) – and affirm the fact of Christ having a dual nature: a divine and human nature – without falling into absurdity. The Conciliar Christologist can thus escape the LPI by adopting the method of reduplicative predication that is grounded on the metaphysical thesis of OP. Reduplicative predication is now not only a linguistic strategy but a metaphysical one as well. The LPI is not problematic for one who assumes the metaphysically developed method of reduplicative predication. However, by adopting this position, which is a form of the (S) method, we thus have one escaping the LPI and underdevelopment issue, but in doing this one also lands square in the face of the correspondence issue – as there seems to be a lack of correspondence with (S₁) and the Conciliar position that takes the predicates that are aptly made of Christ to be predicated of one and the same thing – given the fact that Christ-qua-human way of being and Christ-qua-divine way of being are distinct subjects. Hence, by adopting the method proposed here, as with the previously adduced (S) method, one has not shown the Conciliar position to be free of the LPI, but another distinct position. The question now presented to the Conciliar Christologist is: is there a way to further precisify the method proposed here so as to bring it into line with the Conciliar position? I believe that there is, through detailing the nature of an ‘aspect’ and applying it within a Christological context, which will help to deal with the correspondence issue, and, therefore, allow us to reaffirm the conclusion that the LPI is not problematic for Conciliar Christology. To this task, we now turn.

The nature of aspects

Donald L. M. Baxter (Reference Baxter1999, Reference Baxter2016, Reference Baxter2018a, Reference Baxter, Ivanhoe, Flanagan, Harrison, Sarkissian and Schwitzgebel2018b, Reference Baxter2018c) introduced the concept of an ‘aspect’ into the contemporary metaphysical literature in order to provide a coherent conceptual foundation for the notion of qualitative self-differing (hereafter, self-differing). Self-differing is the qualitative differing of some entity in one way (or respect) from itself in another (Baxter, Reference Baxter1999). To help motivate the existence of aspects within this context, we can consider a case in which an individual is torn about what to do (or how to feel) in a certain situation:

In this specific scenario, David is in a situation of self-differing as he knows that he has an important keynote speech that he needs to prepare. David being an ardent philosophy professor results in him wanting 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. This, 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. And for it to be a case of self-differing, the aspects must be numerically identical to the individual who bears them (Baxter (Reference Baxter2018a), 907).Footnote ⁶ From this introduction to the notion of an aspect, we can further elucidate this notion at two levels: the semantic level and the ontological level.

At the semantic level, the aspects in these cases of self-differing, as seen above, are expressed through ‘nominal qualifiers’ such as ‘insofar as’ (or ‘in some respect’ and to a lesser extent ‘as’ and ‘qua’) – which serve a special role of referring to aspects, as they are specifically present within self-differing cases, where the same entity can be discernible from itself. Furthermore, following Jason Turner (Reference Turner, Baxter and Cotnoir2014, 227), the use of a nominal qualifier in these cases (and other cases like them) can be further precisified via formalization where one takes ‘a’ as a regular term and ‘φ(y)’ as any formula open in y, which allows us to introduce a term to refer to aspects (i.e. an aspect term) written as such: ‘a_y[φ(y)]’. From this semantic basis, 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 (Reference Baxter2018a, 914), aspects are difficult to distinguish from other entities.Footnote ⁷ 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 particular way or manner in which that individual exists. However, as ways of being of an individual, aspects are not qualities (or properties) as they, themselves, possess qualities (or properties) due to their numerical identity to the individuals that bear them.Footnote ⁸ Aspects, however, do not possess all of the qualities that the particular individuals of which they are aspects have. Moreover, in a similar manner to their bearers, they are particular entities – rather than universals – through Leibniz's Law failing to hold for them.Footnote ⁹ Second, 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 (Reference Baxter2018a, 916), aspects are ‘incomplete entities’ due to them ‘having fewer properties than it takes to exist on one's own’. Aspects are thus incomplete in the sense of them being dependent upon the complete individuals to which they are numerically identical. The nature of a complete individual determines the aspects that it has, in that they depend entirely upon how that individual entity is – once we have the individual, we also have its ways of being (Giannotti (Reference Giannotti2021), 2). Third, 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 (Reference Baxter1999), 2). 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 (entity) that they are aspects of), which can be considered by means of abstraction – where one abstracts a way that an individual is – it is important to note, as Baxter (Reference Baxter2016, 104) 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’.Footnote ¹⁰ 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 on the basis of 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 (Reference Baxter2016), 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 more precisely as follows:

From this basic construal of an aspect, we can now return to our example of self-differing and reconstrue the notion of self-differing to be that of the qualitative differing of numerically identical aspects possessed by an individual (Baxter (Reference Baxter, Ivanhoe, Flanagan, Harrison, Sarkissian and Schwitzgebel2018b), 92). So, for example, ‘David insofar as he is a philosopher’ refers to one, numerically identical aspect of David and ‘David insofar as he is a father’ refers to another, numerically identical aspect of him. Aspects can thus differ in their qualities without the resultant differences indicating numerically distinct individuals (Baxter (Reference Baxter2016), 175). More fully, we can apply some aspect terms to our self-differing example, where one aspect term of David would be: David_y[y is a father], which is a name for ‘David insofar as he is a father’. And another aspect term of David would be David_y[y is a philosopher] which is a name for ‘David insofar he is a philosopher’. Thus, reconstruing the above situation as such:

1. (7) David_y[y is a philosopher] does not want to take his children on a camping trip this weekend.

and

1. (8) ~David_y[y is a father] does not want to take his children on a camping trip this weekend.

It would seem as if one is affirming a contradiction. However, through the use of nominal qualifiers such as ‘insofar as’ (i.e. formally a_y[φ(y)]), it removes any explicit contradiction, as the above case does not say that it is David, unqualified, that does and does not want to take his children on a camping trip this weekend. Nor does it say that David, in one ‘part’, does not want to take his children on a camping trip this weekend. Either of those, as Baxter (Reference Baxter, Ivanhoe, Flanagan, Harrison, Sarkissian and Schwitzgebel2018b, 908) notes, would indeed be contradictory. Rather it is simply David_y[y is a father] (i.e. David insofar as he is a father) who wants to take his children on a camping trip this weekend, and David_y[y is a philosopher] (i.e. David insofar he is a philosopher) who does not want to take his children on a camping trip this weekend. So, at a ‘coarse-grained’ level, in our example, we have David being in a self-differing situation in which he has two aspects that qualitatively differ: David_y[y is philosopher] and David_y[y is a father]. Thus, what we have with the aspects of an individual is that of the negation, as Baxter (Reference Baxter2016, 104) writes, being internal ‘that is, has short-scope relative to the nominal qualifier and so there is no contradiction’.Footnote ¹¹ Thus, it is the aspects of David that have the conflicting qualities noted above, but not David (unqualified). That is, one can block the secundum quid ad simpliciter inference, which, following Baxter (Reference Baxter2018a, 913), can be written formally as such:

1. (9) (Block) ~(∀x)(F(x_y[φ(y)]) → Fx).

2. Informally: It doesn't follow from the fact that an aspect of a complete individual x is F that x is F.

So, according to Baxter (Reference Baxter2018a, 913), by the above being true, an individual insofar as they are a particular way bearing a particular quality does not entail that the individual unqualifiedly bears that same quality. Thus, in our case, supposing David insofar as he is a philosopher does not want to go on a camping trip, it also does not follow that David does not want to go on a camping trip – as David might, in fact, mostly want to go on the camping trip rather than not, so that ‘David does want to go on a camping trip’ is what is overall true. Yet, David_y[y is a philosopher] and David_y[y is a father] – as aspects of David – are identical to him. Thus, as Baxter (Reference Baxter2018a, 911) notes, the following principle holds within an aspectival context:

1. (10) (Aspect Identity) (∀x)(x = x_y[φ(y)] → (∃z)(x_y[φ(y)] = z)).

2. Informally: Every aspect is numerically identical with a complete individual z.

In reality, David is David_y[y is a philosopher], and David is David_y[y is a father] – David insofar as he is a particular way (i.e. as philosopher or father) is still David.Footnote ¹² Moreover, taking into account the characteristics of the numerical identity relation – specifically the transitivity of identity – will result in:

1. (11) David_y[y is a philosopher] = David_y[y is a father]

which is that of David's aspects each being numerically identical to one another. 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. David is numerically identical to the two above aspects (and a near-infinite amount 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 – namely, the potential transgression of Leibniz's Law (i.e. the Indiscernibility of Identicals), which can be construed formally (and informally) as such:

1. (12) (Leibniz's Law) ∀x∀y(x = y → (F(x) ↔ F(y)).

2. Informally: For any things x and y, if x is numerically identical with y, then for any quality F, F is possessed by x if and only if F is possessed by y.

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, because, according to Baxter (Reference Baxter2016, 172, emphasis in text), 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,Footnote ¹³ that a relation that is not characterized by Leibniz's Law is not identity.Footnote ¹⁴ However, Baxter (Reference Baxter2016, 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 (Reference Baxter2018a, 907) 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’. 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. However, following Aristotle, Baxter (Reference Baxter2018a, 908) 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 manoeuvre, because it opens up the possibility that, as Baxter (Reference Baxter, Ivanhoe, Flanagan, Harrison, Sarkissian and Schwitzgebel2018b, 105) writes, ‘something in one respect has a property that it in another respect lacks’. 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 it possesses in no respect. Baxter's non-contradictory claim is thus simply that something in one respect is numerically identical with itself in another respect.Footnote ¹⁵ Thus, based on this claim, some numerically identical things can qualitatively differ without an entailment of a contradiction. Baxter (Reference Baxter2018a, 907) 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’. Rather it is important to consider the domain of quantification for Leibniz's Law. That is, according to Baxter, Leibniz's Law solely applies to individuals (i.e. complete/independent entities) and thus does not generalize to aspects (i.e. incomplete/dependent entities). The non-applicability of Leibniz's Law here leads Baxter (Reference Baxter2018a, 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):

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.Footnote ¹⁶ 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 qualitatively 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, Reference Baxter2018a). 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, but identicals that are considered qualifiedly may be discernible – that is, something may qualitatively differ from itself (Baxter, Reference Baxter1999). The non-contradictory internal negation in specific self-differing claims, such as David'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 (Baxter, Reference Baxter2018a, 908). Yet, phrases such as ‘David insofar as he is a father’ refer to aspects, which are incomplete entities, and not the complete individual with which the aspect is numerically identical. Thus, as Baxter (Reference Baxter2018a, 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, while the former is. And once we are sensitive to this distinction, we can realize that the domain of quantification for Leibniz's Law, in its original sense, as Baxter (Reference Baxter, Ivanhoe, Flanagan, Harrison, Sarkissian and Schwitzgebel2018b, 104) writes, ‘includes all the complete entities, but does not include the incomplete entities numerically identical to some of them’. 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.Footnote ¹⁷ 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. 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. 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 (properly so called) does not apply to aspects, and thus it is coherent to posit the existence of qualitatively differing, yet numerically identical aspects. We can now turn our attention to applying the notion of an aspect within a Christological context so as to deal with the LPI in a manner that does not transgress the Conciliar boundaries.

Aspectival reduplicative predication

According to the metaphysically developed reduplicative strategy, by Christ having two natures (a divine and human nature), he exists within distinct ontological structures and has distinct ways of being. Given this, one can thus ascribe the apt candidate predicate of ‘is impassible’ to one subject: Christ-qua-divine way of being, and the other incompatible apt candidate predicates of ‘is passible’ to another, distinct subject: Christ- qua-human way of being, which deals with the contradiction at hand. Yet, as the apt predicates are not ascribed to one and the same thing, there seems to be a lack of correspondence between this approach and the position of Conciliar Christology. However, one can proceed to deal with this issue by further reconstruing the (S₁) method within an aspectival framework as follows:

This reconstrual of the method of reduplicative predication is grounded on the notion of an aspect – that is, Christ is taken here to not only have distinct ways of being but also distinct aspects as well. We can begin to understand the nature of the aspects of Christ by focusing on their functional role and the relationship that they have to him – which allows us to say that they are not properties, complete entities, or mereological parts of him. Rather, they are taken to be incomplete abstract particular entities that are numerically identical to Christ and function as his ways of being. More fully, each of Christ's aspects is numerically identical to him, yet they do not possess all of the same characteristics as he does. Lacking these characteristics, Christ's aspects are thus incomplete entities, in that they are dependent on him – with Christ existing as a complete entity (i.e. an independently existing entity). These aspects of Christ do not exhaust the content or plime (location) that they are aspects of (i.e. they each do not exhaust Christ), and – in line with the thesis of OP – they each function as particular ways in which Christ exists, which we can consider through a process of abstraction. That is, as noted previously, by Christ having two natures, he would exist in two particular ontological structures (human and divine ontological structures), each of which has corresponding ways of being (human and divine ways of being). Given that Christ would exist in two distinct manners, he would also have certain abilities corresponding to each way of being that enable him to fulfil different roles. These functional roles fulfilled by Christ allows one to establish an aspectival distinction that takes these ways to be aspects of him. Therefore, as was seen with our previous example, we have a case of self-differing here. The subjects of this differing would be the aspects of Christ, with each aspect possessing a ‘quality’ that each of the other aspects lacks. That is, we can focus on our candidate predicates and reconstrue them within this aspectival framework as follows: ‘Christ_y[y is divine] is impassible (i.e. Christ insofar as he has a divine way of being is impassible)’ and ‘Christ_y[y is human] is passible (i.e. Christ insofar as he has a human way of being is passible)’. The contradiction highlighted by the LPI is reached by one claiming that Christ is simultaneously impassable and passible (by him occupying a single, generic ontological structure). However, with the notion of OP in hand and now also the notion of an aspect, one can ward off this contradiction by reduplicating the apt predicates by qualifying each predicate in respect to the distinct aspects of Christ (his aspectival ways of being) – namely, Christ_y[y is divine] and Christ_y[y is human].

More precisely, through the use of nominal qualifiers such as ‘insofar as’ for Christ (i.e. Christ_y[φ(y)]), there is no explicit contradiction, as the apt candidate predicates do not say that Christ, unqualified, is and is not impassible (or passible) – which would indeed be an explicit contradiction. Rather it is simply Christ_y[y is divine] (i.e. Christ insofar as he has a divine way of being) who is impassible, and Christ_y[y is human] (i.e. Christ insofar as he has a human way of being) who is passible – in short, one can block the secundum quid ad simpliciter inference within an aspectival framework. Thus, we have Christ being in a self-differing situation in which he has two aspects that qualitatively differ: Christ_y[y is divine] and Christ_y[y is human]. Hence, it is the aspects of Christ that are the subjects of incompatible predicates, but not Christ (unqualified). Thus, within the aspectival framework, to say that ‘Christ is passible qua human’ we are, at a more specific level, saying that there is a subject: Christ_y[y is divine], and that subject is aptly predicated by the predicate ‘passible’. Likewise, when we say ‘Christ is impassible qua divine’ again, at a more specific level, we are saying that there is a subject: Christ_y[y is human], and that subject is aptly predicated by the predicate ‘impassible’. Interestingly, by one using the (S₂) strategy proposed here to ward off the LPI – unlike that of the (S) and (S₁) strategies – we are not saddled with the correspondence issue. This is primarily due to the fact that both of the aspects of Christ – though qualitatively distinct – are each numerically identical to Christ. That is, as aspects are qualitatively differing entities that are numerically identical to their bearers, we can indeed proceed to posit that there is a numerical identity between Christ and the various aspects of Christ:

1. (15) Christ = Christ_y[y is divine] and Christ_y[y is human].

Christ insofar as he is a certain way (i.e. a divine way and a human way) is still Christ. Yet, due to the formal characteristics of the numerical identity relation – namely, the transitivity of identity – both of the aspects of Christ are also numerically identical to each other:

1. (16) Christ_y[y is divine] = Christ_y[y is human].

Thus, within an aspectival context, the same thing, Christ, is discerned in multiple ways without absurdity. That is, there is one particular object, Christ, who is identical to two aspects, which are, in turn, identical to one another. In short, Christ is the qualitatively differing aspects of Christ, and the qualitatively differing aspects of Christ are one another.Footnote ¹⁸ The understanding of the possession of two ways of being by Christ, which grounds his possession of the predicates that are aptly ascribed to him, is thus now further conceived of as the possession of two qualitatively differing, yet numerically identical aspects. Thus, by utilizing an aspectival distinction here, in a ‘loose’ sense, focused on qualitative distinctiveness, we can indeed count two aspects within Christ. Yet, in a strict sense, focused on numerical distinctiveness, there is solely one particular object, Christ, who is differently considered.Footnote ¹⁹ Hence, in line with Conciliar Christology, the predicates that are aptly predicated of Christ according to his human nature (e.g. ‘is passible’) and his divine nature (e.g. ‘is impassible’) are indeed predicated to one and the same thing (i.e. Christ_y[y is divine] and Christ_y[y is human]) – without, however, one having to face the inconsistency highlighted by the LPI. The aspectival reduplication strategy can thus enable a Conciliar Christologist to ward off the LPI, without, however, needing to disaffirm the Conciliar position as well.