1 The Logical Problem of the Doctrine of the Trinity

“We believe in one God, the Father Almighty.” So begins the Nicene Creed, a core statement of the Christian faith for many Christians. Monotheism, the belief in one and only one God, is a central tenet of Christianity. Yet it may seem that Christians are poor at counting, for they are frequently found affirming that Jesus Christ, the Son of the Father Almighty, is God and that the Holy Spirit is God. Doesn’t that obviously make three Gods? Commitment to the divinity of Christ and the divinity of the Spirit appears to threaten monotheism. It may seem that Christians are trying to have their cake and eat it too.

Much ink has been spilt regarding the historical development of the doctrine of the Trinity and the way in which it relates to Christology. The story is fairly complicated and convoluted, especially since the players in the debates and the discussions did not always have a univocal or uniform way of using some of the relevant terms. The misunderstandings related to terms such as ousia or hypostasis (in Greek) or essentia or substantia (in Latin) had exacerbated some of the historical disputes concerning the doctrine of the Trinity. As is commonly considered, an ecumenical expression began to take significant shape at the Council of Nicaea in 325 and the Council of Constantinople in 380/381, the latter providing the Niceno-Constantinopolitan Creed. According to what we now call “the Nicene Creed,” Jesus Christ is “God from God … true God from true God … consubstantial with the Father.” It also states that the Holy Spirit is “the Lord and giver of life … who with the Father and the Son is worshiped and glorified.”

When discussing the doctrine of the Trinity, early Christian theologians sometimes focused on issues that may appear irrelevant or perhaps even odd when considered in the light of contemporary reflections on the doctrine. This is not surprising when we become aware of the contexts surrounding much of the theological investigation, analysis, and presentation of such reflections. Many of the claims and discussions were polemical, often addressing a specific charge or problem raised against trinitarian beliefs.Footnote ¹ Sometimes the debates were primarily exegetical, disputing interpretations of biblical texts or whether certain claims concerning the Trinity fit with particular scriptural passages or come into conflict with them. Other disputes seemed to be over practical outcomes, including political navigation within the church and between church and state relations, and so some pronouncements appear to be made out of a practical compromise rather than seeking a systematic analysis of some doctrinal expression. While contemporary reflections on the doctrine of the Trinity typically highlight the claim that the divine persons (Father, Son, and Holy Spirit) have the same substance or nature or essence, historical reflections often involved considerable examination into the indivisible operations (ad extra opera sunt indivisa) of the divine persons and into the origination relations (e.g., unbegotten, begotten, spiration, and procession) that hold between the divine persons or the relational properties (e.g., paternity, filiation) that distinguish the divine persons.

Despite the concerns or the manner of presentation in which the doctrine of the Trinity was expressed by earlier Christians, the way in which the doctrine of the Trinity is typically presented today does seem to wear a logical problem on its sleeve. This is apparent when we try to state the doctrine of the Trinity as commonly formulated:

1. (1) The Father is God, the Son is God, and the Holy Spirit is God.

2. (2) The Father is not the Son, the Son is not the Holy Spirit, and the Holy Spirit is not the Father.

3. (3) There is exactly one God.Footnote ²

Some may be disappointed with the conjunction of (1)–(3) as being the referent of “the doctrine of the Trinity,” especially given the richness of the historical development of the trinitarian doctrine, which often include statements pertaining to the divine relations, the personal properties, or the unity of the divine actions.Footnote ³ However, it is not entirely unfair to maintain that these three claims are, at bare minimum, the central tenets of trinitarian teaching. For example, the twentieth-century theologian B. B. Warfield takes these three propositions as an adequate statement of the doctrine, for he states that “[w]hen we have said these three things … we have enunciated the doctrine of the Trinity in its completeness” (Warfield Reference Warfield and Orr1915, 3016).Footnote ⁴ Yet even if (1)–(3) do not capture the full scope of early Christian teaching concerning the doctrine of the Trinity, these statements (or similar ones) are the primary claims involved when discussing concerns about logical inconsistency related to the doctrine of the Trinity. And given that this Element is primarily concerned with the logical problem of the doctrine of the Trinity (where the positing of three divine persons threatens monotheism), for the sake of simplicity, I will from here on out use “the doctrine of the Trinity” to refer to (1)–(3), even if the official doctrine includes more statements.

While (1)–(3) may not capture the fullness of the doctrine, these statements serve an important function, which is to rule out particular theological errors or specific heresies (cf. Brower and Rea Reference Brower and Rea2005, 58–59). During the trinitarian debates from the third- to the fifth-century CE, declarations and pronouncements were formulated that led to the rejection (and condemnation) of views deemed heretical, the oft-discussed ones being (ontological) subordinationism and modalism. As the story goes, some influential thinkers and leaders in the early church – such as Arius, Aetius, and Eunomius – claimed that the Son and the Spirit were not divine in the same way or in the same sense as the Father. The Father is God, but the Son does not share the exact same divine nature. So an Arian might agree with the claims that the “the Father is God” and the “the Son is God,” but only if it is interpreted as “the Father is God₁ and the Son is God₂” (where God₁ ≠ God₂, and where the ontological status of God₂ is inferior to the status of being God₁). In order to rule out subordinationism, we must take (1) to mean that the Father is God₁, the Son is God₁, and the Spirit is God₁ (i.e., that they are of the same substance or nature or essence), which thereby rules out subordinationism. As the story goes, other thinkers – such as Sabellius, Noetus, and Praxeus – appear to have endorsed a kind of modalism whereby the Father, the Son, and the Spirit were modes of the same divine person or individual, where it was common to construe these modes as temporary and sequential (i.e., God put on the persona of the Father, later the Son, and then later the Spirit). Now modalism may be regarded as being compatible with (2) by reading it as claiming that “the mode of the Father is not the same as the mode of the Son” (and mutatis mutandis for the other divine persons). However, (2) is, at minimum, intended to convey that the person of the Father is not the person of the Son, and so the Father and the Son (and the Spirit) cannot be understood as modes, or at least not as temporary and sequential modes. Understood this way, (2) then rules out modalism. And while polytheism or tritheism was not a major temptation for early Christians, the claim in (3) ensures ruling out positions that would steer away from the Christian commitment to monotheism. At minimum, then, (1)–(3) have the constraints of being interpreted in such a way so as to rule out at least (ontological) subordinationism, (temporary and sequential) modalism, and polytheism (Rea Reference Rea and Rea2009a, 3–4).

Yet even with this bare-bones statement of the Trinitarian doctrine, some may take (1)–(3) as obviously entailing a contradiction. But its obviousness is only in the way that one interprets these statements. For some, there may be a natural tendency toward interpreting the claims in (1) and (2) as identity statements, where the kind of sameness relation is understood to be strict identity, a relation that has the formal features of being reflexive (a is strictly identical to a), symmetric (if a is strictly identical to b, then b is strictly identical to a), and transitive (if a is strictly identical to b and b is strictly identical to c, then a is strictly identical to c). Using “=” to represent strict identity, we can derive the following claims from (1): the Father = God and the Son = God. Given the symmetry of strict identity, it follows that God = the Son. And from the transitivity of strict identity, we can derive that the Father = the Son, which contradicts with what is said in (2) if we interpret the first clause as stating that the Father ≠ the Son.

Rather than taking the relation between God and the divine persons to be strict identity, another way of interpreting (1) and (2) is in terms of the exemplification of a certain collection of properties or the instantiation of a certain kind. However, even this way of construing (1)–(3) may yield a contradiction. For example, suppose we treat “God” in (1) not as a singular term but rather as a term that refers to a kind or property – and for ease, let us use “is divine” to denote that kind or property. So by (1), we have the claim that the Father is divine, the Son is divine, and the Holy Spirit is divine. Let us take (2) as involving strict distinctness (i.e., the negation of strict identity). Thus, the Father ≠ the Son, the Son ≠ the Spirit, and the Spirit ≠ the Father. Finally, (3) can be understood along familiar lines within first-order predicate logic. For example, if we state that there is exactly one dog, then a typical way of interpreting that is as follows: (∃x)(x is canine & (∀y)[y is canine → y = x]). Now suppose we interpret (3) along these lines, such that it is translated as (∃x)(x is divine & (∀y)[y is divine → y = x]). Interpreting (1)–(3) in this fashion, we can deduce the contradictory claim that the Father = the Son and the Father ≠ the Son, and so this interpretation does not resolve the worry of logical inconsistency.

Philosophers and theologians often use the label of “the logical problem of the Trinity” or the “threeness-oneness problem” to refer to the worry that (1)–(3) appear to be inconsistent, though as we’ll see, some use these labels to identify distinct but related problems. That said, I will typically use the expression “the logical problem of the doctrine of the Trinity” (rather than “the logical problem of the Trinity”) since the problem (as I see it) is de dicto and not de re.Footnote ⁵

Perhaps one mistake in formulating the doctrine of the Trinity as (1)–(3) is that it does not specify who the one God is in (3). Yet when we look at creedal formulations, such as the Apostles’ Creed and the Nicene Creed, they explicitly state that the one God is the Father Almighty. Maintaining orthodoxy, however, requires that we regard the Son and the Spirit as truly divine (“true God from true God”). This was so even though many early Christian thinkers accepted the claim that the Son is generated or produced or caused by the Father, which generated (pun intended!) controversy over the true divinity of the Son. If the Son had been generated/produced/caused to exist by the Father, then some averred that there had to be a time in which the Son did not exist, or that the Son could not be truly divine. Nevertheless, many early Christian theologians argued that the Son was truly divine and existed from all eternity even while being generated, produced, or caused by the Father. Moreover, some of these thinkers claimed that the Son’s true divinity was explicable by the Son’s generation from the Father – the Son’s generation is the grounds for why the Son shares the same divine essence as the Father and so is truly divine. If this is right, then identifying the one God as the Father or claiming that the Father is the source of the Son (and the Spirit) need not threaten the true divinity of the Son (and the Spirit).Footnote ⁶

Yet even with a formulation of the doctrine of the Trinity that clearly identifies the one God with the Father, a logical worry may still arise. For example, Michael Rea formulates the logical problem as follows, where his version explicitly identifies the one God with the Father (Reference Rea, Flint and Rea2009b, 406; McCall and Rea Reference McCall and Rea2009, 1):

1. (LPT1) There is exactly one God, the Father Almighty.

2. (LPT2) The Father is a God.

3. (LPT3) The Son is consubstantial with the Father but not identical to the Father.

4. (LPT4) If there are x and y such that x is a God, x is not identical to y, and y is consubstantial with x, then it is not the case that there is exactly one God.

5. (LPT5) Therefore, it is not the case that there is exactly one God.

Rea asserts that (LPT1), (LPT2), and (LPT3) are or follow from central Christian tenets, and thus the only way to avoid the logical problem is to deny (LPT4), and this must be done while avoiding the pitfalls of either incoherence or heterodoxy. Given this way of formulating the problem, Rea rejects certain solutions to the logical problem of the doctrine of the Trinity because they fail to offer a way of denying (LPT4).Footnote ⁷ Claiming that there is a trio of consubstantially divine persons, then, appears to conflict with monotheism such that a contradiction seems to be looming for those who hold to the divinity and distinctness of the Father, Son, and Holy Spirit – and this is so even if we take the one God to be identified as the Father.

As will be discussed later, some have argued that contradictions need not be avoided, and where the doctrine of the Trinity involves a contradiction. The most notable proponent of this approach is Jc Beall. While his view does not seek to avoid a contradiction, he does acknowledge that there is a logical problem, but it is a problem of identifying the exact identity relation being employed in the doctrine and of offering a characterization of that relation (Beall Reference Beall2023). Moreover, Beall distinguishes what he calls “the logical problem” from the “threeness-oneness problem.” It is not uncommon to use these expressions as denoting the same problem (cf. Rea Reference Rea, Flint and Rea2009b, 403–404; McCall and Rea Reference McCall and Rea2009, 1). However, Beall takes the threeness-oneness problem to be a problem regarding counting-conventions – it asks how God (or the divine nature) and the divine persons are to be counted given the identity relation specified in the answer to the logical problem (Beall Reference Beall2023, 16). So worries about contradictions aside, there may still be logical or logic-adjacent problems that need to be addressed. I will say more about the identification of the target identity relation and the counting-convention later, but until then, I will continue to use “the logical problem of the doctrine of the Trinity” to refer either to the worry of inconsistency in (1)–(3) or to the worry raised in (LPT1)–(LPT5).

When pressed with the logical problem of the doctrine of the Trinity, some people may be quick to point out that the Christian claim is that there are three divine persons and one God (or one divine substance or essence), not that there are three divine persons and one divine person, and not that there are three Gods and one God. However, (1)–(3) represent at bare minimum what must be accepted in the doctrine of the Trinity. And this simple maneuver does not help address the logical problem, as some straightforward ways of interpreting (1)–(3) appear to yield that there are three Gods and one God. Moreover, this simplistic solution does nothing to explain how to deny (LPT4) or to offer another explanation of how to avoid the conclusion in (LPT5). So even if (1)–(3) do not make the simple mistake of stating that there is one God and three Gods or that there is one divine person and three divine persons explicitly, it appears that one can derive a contradiction when adopting what may be regarded as typical interpretations of the statements and employing standard logical inferences.

Before examining some of the main approaches that have been offered as solutions to the logical problem of the doctrine of the Trinity, we may pause to ask whether a putative conflict between positing a trio of divine persons and monotheism arises on account of one’s conception of monotheism. We have been understanding monotheism as the claim that there is exactly one God. Yet careful consideration may open up space for different conceptions. Identifying a traditional conception of monotheism may be even harder to do, as some have claimed that the concept of monotheism (as now understood) is a relatively recent concept, perhaps an Enlightenment or post-Enlightenment invention (cf. Tracy Reference 67Tracy, Davis, Kendall and O’Collins1999, 280). And it is unclear how widely or narrowly we should take the concept, whether to exclude or include henotheism, divine councils, or views that permit other deities. It is beyond the scope of this Element to adjudicate this issue here, but it may be worth considering whether a more precise understanding of monotheism may help in our reflection on the logical problem of the doctrine of the Trinity.

One notable and influential account of monotheism has been advanced and defended by Richard Bauckham. To summarize it in an overly simplistic and sloganeering way (and without the appropriate nuance), monotheism is to be understood in terms of monolatry. The one God is the one to be worshiped. The Father is worshiped and so is the one God. The Son is also worshiped (as evinced in the New Testament and in church practice), and so the Son is to be regarded as “being in the identity of God” (Bauckham Reference Bauckham1998). Monolatry as such does not rule out that there is more than one divine individual or hypostasis, for what is worshiped will be in the identity of the one God. So if the Son and the Spirit are worshiped, then they are in the identity of God. Thus, monotheism is (allegedly) preserved.

What is the correct conception of monotheism? Some have claimed that a constraint on the kind of monotheism that must be accepted within Christian theology “should be a monotheism a Jew could accept as monotheistic” (Leftow Reference Leftow, Davis, Kendall and O’Collins1999, 235), or perhaps better that it must be acceptable for other Abrahamic traditions. There is some appeal to this, as the God that Christians worship is the same as the God of Abraham, Isaac, and Jacob. Bauckham’s conception of monotheism might then be criticized for having a poor fit with other monotheistic religions and so may be regarded as a form of special pleading for Christians inclined to accept the doctrine of the Trinity. Perhaps Christians should say “so much the worse for other religions.” But this may lead to an excessively complicated way of carving out various theistic categories, perhaps distinguishing between (to use terms typical in philosophy for distinguishing subgroups) hard monotheism versus soft monotheism, where hard monotheism rules out there being more than one divine individual, whereas soft monotheism allows for more than one divine individual (and so Christianity would count as soft monotheism), and where both types are distinct from polytheism. But even if that is a way to go, some may worry over soft monotheism as an option for Christians given the history of Christianity as developing from within (second Temple) Judaism, and hence there may be some pressure that the kind of monotheism acceptable for Christians would have to be compatible with a construal of monotheism for (second Temple) Judaism (or a construal of monotheism that is compatible with any of the Abrahamic faith traditions). To adjudicate this would be outside the boundaries of this Element, though for full disclosure I am sympathetic with embracing or subscribing to a distinctive form of monotheism and specifically to a monolatry-based account.Footnote ⁸

Nevertheless, it should be evident that soft monotheism, such as a monolatry-based view, does not by itself help with the worry of logical inconsistency given the way that the doctrine of the Trinity was formulated above. Even if the Son (and the Spirit) are to be regarded as being in the identity of the one God, how do we interpret (1)–(3) in a way that avoids logical inconsistency? If “being in the identity of God” means strict identity such that the Son = God (and we use that identity relation in the other claims), then we appear to run straight into a contradiction. Given Bauckham’s own theological proclivities, it is unlikely he means strict identity. But the “identity” in that expression is ambiguous, and as we will see, there are several ways that such an identity claim may be understood.Footnote ⁹ Without additional explanation of what the expression “being in the identity of God” means, the logical problem is not resolved merely by adopting this conception of monotheism. So the problem remains whether one has a more rigid notion of monotheism or a more lax (“soft”) view of the number of divine individuals that monotheism permits.

2 Standard Solutions

Early Christian thinkers considered and addressed several challenges raised against the doctrine of the Trinity, many of the debates being over Scriptural texts or theological tensions with some of the claims, though there were philosophical or logical worries that were also being discussed. These early Christian thinkers offered resolutions that are sometimes taken to be solutions to the logical problem of the doctrine of the Trinity as formulated in terms of (1)–(3) or (LPT1)–(LPT5), even though many of the contemporary formulations do not map on exactly to the kinds of concerns these earlier thinkers raised. Moreover, some of these early views are taken as predecessors to some of the contemporary solutions that have been offered to the logical problem of the doctrine of the Trinity.

At the more popular level, it is common to address the logical problem of the doctrine of the Trinity by presenting an example that serves as an analogy of the Trinity. Some analogies are regarded as outright problematic, as they appear to explain the doctrine in a way that would have been ruled out as heretical (e.g., sequential and temporary modalism, polytheism, ontological subordinationism). There are even pithy and humorous social media videos that describe, and in some cases parody or mock, these particularly problematic analogies.

It may be tempting to consider (most of) the philosophical solutions to the logical problem of the Trinity as no more than giving better analogies than the ones provided at the popular level. However, analogies or illustrations are not by themselves helpful in addressing the appearance of logical inconsistency, at least not without further elaboration. That further elaboration typically comes by way of offering an interpretation of the claims in (1)–(3), whether explicitly or implicitly (since someone may offer an account that does not state directly how to interpret those claims, but one may reasonably infer how to interpret them based on the account at hand).

In the contemporary philosophical literature, a dominant approach to addressing the logical problem of the Trinity has been to offer a paraphrase of (1)–(3), showing how the more precise and perspicuous propositions in the paraphrase do not yield a contradiction. Offering paraphrases is a common strategy in philosophy. For example, if someone claims “there is a hole in the paper,” someone might interpret it in such a way that the utterance is ontologically committed to the existence of holes. However, one may use a paraphrase such as “the paper is perforated,” which does not involve an ontological commitment to holes. The paraphrase, then, is taken to be the more precise and accurate statement, or the paraphrase is taken as what is meant when one utters the first sentence.

These paraphrases may be regarded as offering a prescriptive interpretation (“this is how you should interpret these claims”). However, the paraphrases may also be offered as a descriptive interpretation, perhaps one endorsed by a historical Christian thinker or at least inspired by a past Christian theologian (“this is how so-and-so interpreted these claims” or “this is how so-and-so would have interpreted these claims if so-and-so considered the logical problem of the doctrine of the Trinity”). What the conditions or constraints are for an adequate paraphrase may depend on one’s view of theological authority or one’s commitment to particular creedal or conciliar pronouncements, or even on the particular Christian tradition to which one belongs.

It is somewhat common to categorize the solutions to the logical problem of the doctrine of the Trinity along two different family of approaches, a taxonomy that appears to be influenced by Theodore de Regnon (Reference de Regnon1892–1898).Footnote ¹⁰ One approach – often labeled “social trinitarianism” – is supposedly based on eastern and Greek-speaking Christian theologians such as the Cappadocian fathers (viz., Gregory of Nyssa, Basil of Caesarea, and Gregory of Nazianzus). As the story goes, this approach begins with an emphasis on the distinctness or individuality of the divine persons, followed by an attempt at explaining the unity or the oneness of God, often by appealing to social analogies (e.g., family, community). The other way – often labeled “Latin trinitarianism” – is allegedly based on western and Latin-speaking Christian theologians such as Augustine and Thomas Aquinas. As the story goes, this way of addressing the logical problem begins with an emphasis on divine unity or divine oneness, followed by an attempt to explain how there are or can be distinct divine persons, often by appealing to psychological analogies (e.g., the mind’s faculties of memory, understanding, and the will).

As several scholars have pointed out, this story is quite inaccurate and overly simplistic, misrepresenting some of the similarities and differences between the theological approaches and claims by these early Christian theologians (Ayres Reference Ayres2004, Barnes Reference Barnes1995 and Reference Barnes, Davis, Kendall and O’Collins1999, Coakley Reference Coakley, Davis, Kendall and O’Collins1999, Cross Reference Cross2002). When reading the works of these Christian thinkers, there is not a clear sense that these Latin-speaking Christian theologians are “starting” with the oneness of God or that the Greek-speaking Christians are “starting” with the threeness of the divine persons. Additionally, some Latin theologians offered trinitarian models that seem to be either compatible with a social approach or can be suitably amended so as to count as a social approach (cf. Cross Reference Cross2002, 288).Footnote ¹¹ And some common representatives of social trinitarianism, such as Gregory of Nyssa, may agree enough with their Latin counterparts (such as Augustine and Aquinas) so as to count as a Latin trinitarian (Cross Reference Cross, McCall and Rea2009, 206ff.).

The overlap between early Christian theologians from these different traditions should not be overlooked. Both the Cappadocian fathers and Augustine emphasized the indivisible operations of the divine persons, and their appeal to such operations has been regarded by some interpreters as their primary way of addressing the concern of oneness or unity among the divine persons (Barnes Reference Barnes, Davis, Kendall and O’Collins1999, Ayres Reference Ayres2010). More than consubstantiality, the indivisible operations arguably play a more crucial role in addressing the challenges to divine unity that some of these thinkers faced in their time.Footnote ¹² And while some contemporary social trinitarians de-emphasize or outright reject the origination relations among the divine persons, the Cappadocian fathers and Augustine both regard the unbegottenness of the Father, the begottenness of the Son, and the spiration of the Spirit as key ingredients when expounding upon the individuation of the divine persons.

There are genuine differences that hold between those who are regarded as representing a more eastern view from those who are regarded as representing a more western view, as Gregory of Nyssa seems to have taken the divine nature as a universal, whereas Augustine takes the divine nature as a concrete particular (cf. Cross Reference Cross2002, 275). However, some of the differences between these approaches may have also been differences about points of emphasis, and some of the differences may have been exaggerated. Additionally, many of the writings that involve their reflections on the doctrine of the Trinity are polemical (and embedded within a political context, where some of the notable players in the debate had considerable political and ecclesial stakes in the matter). To understand and appreciate the claims and approaches requires awareness and careful attention to the details of the questions and issues being raised within the particular circumstances and contexts of these thinkers (a story that is extremely complicated, which is sometimes neglected in some of the hurried summaries that paint a picture of uniform or near-uniform agreement on many matters that were in fact contentious and hotly debated). Suggesting that Latin-speaking theologians focused on psychological analogies also narrows the attention to a handful of theologians who did utilize such illustrations for various purposes, but it neglects many other western and Latin-speaking theologians who employed other concepts and approaches in their theological investigation into the doctrine of the Trinity (cf. Friedman Reference Friedman2010, Paasch Reference Paasch2012). And suggesting that Greek theologians focused on social analogies also downplays the other conceptual tools and approaches that were employed in their trinitarian reflections (cf. Marmodoro Reference Marmodoro, Marmodoro and McLynn2018, Barnes Reference Barnes1995). Moreover, social trinitarianism and Latin trinitarianism do not exhaust the historical options, as there are other ways that historical Christian theologians had reflected upon the doctrine of the Trinity that do not neatly fit into either approach.

The conceptual landscape between social trinitarianism and Latin trinitarianism in contemporary approaches is also messy. For example, Brian Leftow characterizes Latin trinitarianism as including the claim that “while Father and Son instance the divine nature (deity), they have but one trope of deity between them, which is God’s … [such that] the Father’s deity = the Son’s deity = God’s deity” (Leftow Reference Leftow, Davis, Kendall and O’Collins1999, 204). For social trinitarianism, “Father, Son, and Spirit are three individual cases of deity … they are in the Trinity three tropes of deity, not one … [l]ike three humans, [social trinitarianism’s] Persons make up a community” (ibid., 204–205). Accordingly, Latin trinitarianism allegedly posits a single trope of deity and social trinitarianism allegedly posits three tropes of deity. However, some recent proponents of social trinitarianism claim that the divine persons “share between them a single trope of deity” (Hasker Reference Hasker2013, 226). Moreover, some take Latin trinitarianism as involving the claim that the divine nature is concrete, whereas social trinitarianism implies that the divine nature is abstract. However, some social trinitarians maintain that the divine nature is concrete (ibid.).

Another way of characterizing the difference between these approaches is to regard Latin trinitarianism as a “one-self” approach and social trinitarianism as a “three-selves” approach (Tuggy Reference Tuggy2020). This may be regarded as unproblematic for some in the debate, as some social trinitarians aver that the divine persons are “individual centers of consciousness,” which may sound to some like a self. But others would balk at understanding the divine persons as selves. Additionally, this characterization may be charged with being anachronistic and ambiguous. While the concept of a trope (or an instance of deity) appears to be understood by early Christian thinkers, it is not obvious that the concept of a self (at least understood in some robust sense, one that has been influenced by recent psychological categories) ever appears in the historical discussion. But whether it does or not may also depend on what we mean by “self,” and unfortunately that term is notoriously ambiguous and used in a multiplicity of ways.Footnote ¹³

While problems remain in attempting to categorize these two types of solutions to the logical problem of the doctrine of the Trinity, it remains typical for contemporary presentations of the logical problem and its solutions to distinguish social trinitarianism and Latin trinitarianism. Setting aside these criticisms related to this categorization of solutions, many contemporary philosophers and theologians present views that seem to fall under a social approach or a Latin approach, and it is worth considering some of the specific proposals under these approaches – even if they differ significantly from the historical positions from which they purport to inherit their view.

Beginning with Latin trinitarianism, Brian Leftow (Reference Leftow2004) has presented what is likely the most well-known and discussed contemporary proposal belonging to this approach, whereby he employs a case involving time travel. Imagine a scenario where a dancer for the Rockettes named “Jane” performs a dance routine, enters into a time travel machine set to go back in time right before the routine, and then stands to the left of her past self to perform the routine. Imagine she does it one more time but this time stands to the right of her past (initial) self when performing. From the audience’s perspective, there would appear to be three dancers: Left Rockette, Middle Rockette, and Right Rockette. Yet there is a single Jane living her life along these different streams.

From this example, Leftow appears to claim that Jane is strictly identical to the Left Rockette and that Jane is strictly identical to the Right Rockette. And by the symmetry and transitivity of strict identity, it would follow that the Left Rockette is strictly identical to the Right Rockette. However, it seems that we should say that the Left Rockette is not strictly identical to the Right Rockette. According to Leftow, the logical problem can be avoided when we distinguish how we are interpreting some of these claims. Take the claim that “the Left Rockette is strictly identical to the Right Rockette.” If we take the terms “the Left Rockette” and “the Right Rockette” to function as definite descriptions (or if we interpret them non-rigidly), then the statement would turn out to be false (since one is characterized as being on the left and the other is characterized as being on the right). If we take these terms to function rigidly, then the statement is true and unproblematic, as it would be tantamount to claiming that “Jane who is on the left side is strictly identical to Jane who is on the right side.”

To apply this to the doctrine of the Trinity, suppose we take the claims from (1) that “the Father is God” and “the Son is God” to mean that the Father is strictly identical to God and that the Son is strictly identical to God. It would follow by the symmetry and transitivity of strict identity that the Father is strictly identical to the Son. But by (2), we might also interpret “the Father is not the Son” as meaning that the Father is not strictly identical to the Son. However, if we take “the Father” and “the Son” as definite descriptions, then it is false to state the Father is strictly identical to the Son (since one is unbegotten and the other is begotten). But if we take those terms to function rigidly, then we should interpret “the Father is strictly identical to the Son” as “God in the Father stream is strictly identical to God in the Son stream,” which is true but unproblematic since God is strictly identical to God. Moreover, God is never Father in the Son stream, and God is never Son in the Father stream (just as Jane is never the Right Rockette in the first adventure out of the time travel machine where she stands to the left of Middle Rockette, and Jane is never the Left Rockette in the second adventure where she stands to the right of Middle Rockette). And so we can maintain the claim that the Father is not the Son.

Leftow does not take the analogy with the time-travel case as a description of what God is actually like. Rather, he wants “to suggest by analogy with a time-travel case that it is possible that God be a Latin Trinity … that for all we know, this is how it is with God in some metaphysically possible world” (Reference Leftow2004, 309). Whether this avoids logical inconsistency for the doctrine of the Trinity or not, the glaring concern for many is that it seems to veer too close to modalism. However, there is modalism and then there’s (bad) modalism. Talk of modes has been employed in Christian theology (cf. Barth Reference Barth, Thomson, Knight, Bromiley and Torrance1956, Rahner Reference Rahner1967), and there are trinitarian views that employ notions that are quite similar to modes, such as aspects or forms of being (Ward Reference Ward2015). Elsewhere, Leftow explicitly defends an understanding of divine persons as modes in terms of Lockean persons that are event-based (Leftow Reference Leftow, van Inwagen and Zimmerman2007). As we look at the historical debates, the kind of modalism that was condemned in the early church seems to have been the sort associated with Sabellianism, in which the modes are temporary and sequential. However, God lives God’s life in the Father mode, Son mode, and Spirit mode simultaneously (not sequentially) and from all eternity (and not temporarily). Leftow’s view should not be conflated with Sabellian modalism. This is not to conclude that Leftow’s Latin trinitarianism avoids charges of heresy or a collapse into other problematic forms of modalism. Rather, it shows that attention to the history of heresies is needed, as it may not be obvious that every kind of modalism should be regarded as heretical (or as conflicting with either Scriptural or creedal pronouncements).

Other views that fall within the family of Latin approaches have been offered, some formulating positions that appeal to metaphysical concepts such as extended simples (Pickup Reference Pickup2016), (mental) episodes and identity under a sortal (Mooney Reference Mooney2021), multilocation (Effingham Reference Effingham2015), indexicals and numerical sameness without identity (Williams Reference Williams2013), powers (Page Reference Page2017), improper parthood (Molto Reference Molto2018), or proper parthood (Cotnoir and Bacon Reference Cotnoir and Bacon2012). These views may bear enough similarity so as to count as being part of the same family of solutions (though it remains difficult how to characterize Latin trinitarianism in a way that makes it exclusive from social trinitarianism or in a way that makes Latin and social trinitarianism exhaustive). Yet one way in which they may be regarded as falling under the same umbrella is the fact that if there is a heresy that Latin trinitarianism leans toward or is at least accused of doing so, it would be modalism (and not polytheism or subordinationism).

Similar to Latin trinitarianism, social trinitarianism also includes a variety of views such that a general characterization is difficult to provide, at least in a way that captures all of the positions that are deemed as belonging in that camp.Footnote ¹⁴ Despite the difficulty, Thomas McCall and Michael Rea have offered a general characterization that does capture many of the extant positions within social trinitarianism:

• (ST1) The Father, the Son, and the Holy Spirit are “of one essence,” but are not numerically the same substance. Rather, the divine persons are consubstantial only in the sense that they share the divine nature in common. Furthermore, this sharing of a common nature can be understood in a fairly straightforward sense via the “social analogy” in which Peter, James, and John share human nature.

• (ST2) … the central claim of monotheism that there is but one God is to be understood as the claim that there is one divine nature – not as the claim that there is exactly one divine substance.

• (ST3) The divine persons must each be in full possession of the divine nature and in some particular relation R to one another for Trinitarianism to count as monotheism (McCall and Rea Reference McCall and Rea2009, 3; cf. Rea Reference Rea, Flint and Rea2009b, 413–414).Footnote ¹⁵

Not all who regard themselves as social trinitarians would accept this characterization (cf. Hasker Reference Hasker2013, 22). But (ST1)–(ST3) do accurately capture what seems to be core in several views that are identified as belonging within the camp of social trinitarianism. Additionally, it is common to find proponents of social trinitarianism claiming that the Father, Son, and Spirit are three individual centers of consciousness or distinct centers of knowledge, will, and action (Davis Reference Davis2006, Hasker Reference Hasker2013, Plantinga Jr. Reference Plantinga, Feenstra and Plantinga1989, Moreland and Craig Reference 65Moreland and Lane Craig2003, Brown Reference Brown, Feenstra and Plantinga1989, Morris Reference Morris1986). That is, social trinitarians typically construe the Father, Son, and Spirit as persons in some modern, robust sense informed by contemporary psychology (though not every social trinitarian will agree). Against such an understanding of the divine persons, some may aver that such a concept of personhood was either unavailable or not employed in the early development of the trinitarian doctrine, whereas others claim that the concept of persons utilized by social trinitarians is familiar or pre-theoretical enough so as to be compatible with the historical understanding of the divine hypostases/persons (though even the term “person” was sometimes a vexed one in early trinitarian discourse).

With three centers of consciousness who share a common divine nature, social analogies are often provided whereby they depict the three divine persons as forming a community (Plantinga Jr. Reference Plantinga, Feenstra and Plantinga1989, 28) or something like a community (Davis Reference Davis2006, 69). The trick is positing some feature or relation that the three divine persons bear to each other that will secure monotheism. Some social trinitarians claim that the three divine persons are the only individuals that instantiate divinity or possess all of the essential divine attributes, or that they are the only members of a divine family or community. Others posit that they are mutually interdependent such that one cannot exist without the others (some citing the origination relations among the divine persons). Richard Swinburne (Reference Swinburne1994) has advanced one of the more well-known versions of social trinitarianism, and he maintains that the divine persons are the only individuals to possess all of the essential divine attributes and are mutually interdependent on each other for their existence (and in a way that allows the Father to be the source of the other divine persons). Agreeing with many early Christian thinkers, Swinburne also holds that the divine persons have perfect unity of wills. From this, he construes monotheism as the claim that there is only one independent divine being, whereas polytheism would be understood as claiming that there is more than one independent divine being (Swinburne Reference Swinburne1994, 180). Since the divine persons are dependent on each other, monotheism is putatively secured.

In order to secure monotheism, other social trinitarians have appealed to various concepts such as perichoresis or the mutual indwellingFootnote ¹⁶ of the divine persons (Davis Reference Davis2006), a constitution relation (Hasker Reference Hasker2013), group agency (McIntosh Reference McIntosh2016), divine fissioning (Forrest Reference Forrest1998), embedded properties (Yandell Reference Yandell, McCall and Rea2009), or parthood relations – whether illustratively (Moreland & Craig Reference 65Moreland and Lane Craig2003) or analytically (Spencer Reference Spencer2019). These various relations and features can be mixed and matched into other social-trinitarian-friendly combinations.

The depiction of God as being a community or being like a community is a shared feature of many of the views within social trinitarianism. Accordingly, a common objection to social trinitarianism is that it collapses into polytheism (Howard-Snyder Reference 63Howard-Snyder2016). For example, Rea (Reference Rea2006) offers one such critique of this kind, raising a parallel case with the pantheon of Greek gods, a religious tradition that is evidently polytheistic. And yet if we were to suppose that some of these gods (say, Zeus, Hera, and Athena) were to bear these candidate relations proposed by social trinitarians that can serve as a substitute for R in (ST3), nevertheless it seems that the group of gods would still count as polytheistic, and hence none of these relations proposed by social trinitarians are adequate in securing monotheism (cf. Leftow Reference Leftow, Davis, Kendall and O’Collins1999, 232f.).

Other critics of social trinitarianism worry that this view renders God as a deceiver, since Scripture (especially in the Old Testament) does not appear to be using “God” or “YHWH” to refer to a group of individuals, and so divine revelation appears to involve a problematic form of divine deception (Tuggy Reference Tuggy2004).Footnote ¹⁷ Additionally, some critics have challenged the historical merits of social trinitarianism. While some social trinitarians claim that their view enjoys some historical precedence (Swinburne Reference Swinburne2018, Plantinga Jr. Reference Plantinga, Feenstra and Plantinga1989, Hasker Reference Hasker2013), others have argued that the alleged forebears, such as Gregory of Nyssa, should not count as being a social trinitarian nor even close enough even to count as a proto-social trinitarian (cf. Coakley Reference Coakley, Davis, Kendall and O’Collins1999, 131ff.; Cross Reference Cross, McCall and Rea2009). Other objections have also been raised that are either directed at specific versions of social trinitarianism or against social trinitarianism more generally (Brower Reference Brower2004a, Clark Reference Clark1996, Feser Reference Feser1997, Leftow Reference Leftow, Davis, Kendall and O’Collins1999, Mosser Reference Mosser, McCall and Rea2009).

As already explained, the contemporary taxonomy has been shown to have some serious flaws with its classification and characterization of social trinitarianism and Latin Trinitarianism. Since the taxonomy is not exhaustive, there are attempts to resolve the logical problem of the doctrine of the Trinity that do not fit into either approach. For example, Trenton Merricks (Reference Merricks, Crisp, Davidson and Vander Laan2006) employs a case of split brains, which seems to utilize a psychological analogy (which is typically associated with Latin trinitarianism), but there are features of his case that construe the divine persons in a manner similar to how it is understood by social trinitarians, specifically in terms of centers of consciousness. Moreover, there are other non-social and non-Latin views, some of which appeal to a variety of concepts such as one-many identity (Bøhn Reference Bøhn2011), feature-placing sentences (Kleinschmidt Reference Kleinschmidt2016), empty names in Free Logic (Kleinschmidt Reference Kleinschmidt2018), truthmakers (Byerly Reference Byerly2019), or supervenience (Fisher Reference Fisher2016).Footnote ¹⁸

There are other non-social and non-Latin trinitarian solutions that proceed by positing a sameness relation aside from strict identity. As noted earlier, strict identity has the properties of being reflexive, symmetrical, and transitive. It is also common to take such a relation as obeying Leibniz’s Law, or at least the indiscernibility of identicals (such that if x = y, then for any property F, x is F just in case y is F). Moreover, strict identity is commonly taken to be absolute. For example, when we claim that “Cicero is the same person as Tully,” what is meant is that Cicero is a person, Tully is a person, and Cicero = Tully. The identity relation is the same no matter what kind of thing we are talking about.

Rather than strict identity, some have suggested employing relative identity when interpreting the doctrine of the Trinity, in particular the statements in (1) and (2) (van Inwagen Reference van Inwagen and Morris1988, Cain Reference Cain1989, Martinich Reference Martinich1978 and Reference Martinich1979, Baber Reference Baber2015).Footnote ¹⁹ Proponents of relative identity posit fundamental sameness relations that are relative to a kind or sortal. That is, “Cicero is the same person as Tully” would not be reduced to the translation in the previous paragraph since being the same person may be regarded as not being further analyzable. Now some proponents of relative identity maintain that there is no absolute identity (such that every statement involving absolute identity is either non-fundamental or incomplete). Others, however, make room for both relative identity and absolute identity such that there is more than one fundamental identity relation.

By using relative identity, there is a possible way of satisfying the following schema: x is F and G, y is F and G, x is the same F as y, and x is not the same G as y. If so, then it is possible that the Father is God and a person, the Son is God and a person, the Father is the same God as the Son, and the Father is not the same person as the Son (and mutatis mutandis, for the Son and the Spirit and for the Father and the Spirit). Despite this fairly clean way of resolving the logical problem, some worry that the appeal to relative identity is ad hoc since such an appeal may only be usefully posited when seeking to avoid a contradiction in the doctrine of the Trinity. Against that, others have defended relative identity as an ideological primitive that should be accepted because of its utility in solving other metaphysical paradoxes such as the problem of material constitution, for example, Ship of Theseus, Tib/Tibbles, Growing Paradox, statue/lump, and so on (cf. Geach Reference Geach1967, Reference Geach1980).Footnote ²⁰

Some proponents of a relative identity approach have pressed harder into the comparison between the logical problem of the doctrine of the Trinity and the problem of material constitution (Brower and Rea Reference Brower and Rea2005). Regarding the latter, some are inclined to believe that when a statue is made from a lump of clay, the statue is strictly identical to the lump of clay. That may be because when we count the number of objects, an intuitive or pre-theoretical answer to the question of how many objects there are (when we are pointing at the clay statue) is that there is one material object. However, the statue and the lump of clay appear to have distinct modal profiles and persistence conditions; for example, the lump of clay can survive being smashed whereas the statue cannot, and the statue can survive proper part replacement whereas the lump of clay cannot. One way of explaining the difference is by positing distinct forms or structures for the lump of clay and the statue. However, both the lump of clay and the statue share all of the same matter. Taking a form-matter or hylomorphic framework, the lump of clay is a material object (i.e., it is made up of matter) and a hylomorphic compound, the statue is a material object and a hylomorphic compound, the lump of clay is the same material object as the statue (since they are both made up of the same matter), yet the lump of clay is not the same hylomorphic compound as the statue (because they have distinct forms).

Similarly, the Father and the Son can be construed as distinct hylomorphic compounds. They share the same matter, where “matter” can be understood functionally, and where the divine nature in this case plays the role of matter. The Father and the Son are taken as having distinct forms, where the forms may be understood in terms of their unique relational property (e.g., paternity, filiation). Accordingly, the Father is the same divine being as the Son in virtue of having the same matter, viz., the divine nature. And the Father is not the same hylomorphic compound as the Son in virtue of having distinct forms. The way we count Gods, then, is by counting divine natures, and since the Father and the Son have the same divine nature (since they share the same matter), we count only one God. But since the divine persons are hylomorphic compounds, we count the number of divine persons by counting hylomorphic compounds, which in this case are three (and they are strictly distinct because they have distinct forms).

In their hylomorphic approach, Brower and Rea appeal to a sameness relation aside from strict identity, viz., numerical sameness without identity.Footnote ²¹ The divine persons are numerically the same and yet they are not strictly identical to each other. This may be a difficult pill to swallow for contemporary philosophers who learned to count by studying first-order predicate logic with (strict) identity. However, there may be other plausible counting conventions, ones that do not require counting in terms of strict identity. Indeed, the appeal to numerical sameness without identity may have some historical precedent, as it appears to have been adopted and utilized by Peter Abelard (Brower Reference Brower, Brower and Guilfoy2004b) and by Henry of Ghent (Williams Reference Williams2012). Moreover, Scott Williams (Reference Williams2013, Reference Williams2017) utilizes numerical sameness without identity in his account of the doctrine of the Trinity (which, as noted earlier, arguably counts as both Latin and social).

Several objections have been raised against Brower and Rea’s hylomorphic approach. For example, counting material objects in terms of their matter may be regarded as an implausible counting convention (Hughes Reference Hughes, McCall and Rea2009), and problems may arise regardless of how one understands the constituting matter (Leftow Reference Leftow2018). Others have charged this approach as failing to illuminate the trinitarian doctrine, especially since it is unclear how colocated hylomorphic compounds can in any significant way be like three divine persons who engage in acts of love and communication to each other (Craig Reference Craig, McCall and Rea2009, 288–291). Additionally, Brower and Rea’s approach may also lead to a proliferation of other hylomorphic compounds, such as “God-judging” or “God-forgiving” – or at least there may need to be some explanation for when a form (plus the matter in which it inheres) is person-constituting and when it is not, otherwise we will end up with many more hylomorphic compounds than three, and therefore many more divine persons than we should have (Pruss Reference 66Pruss, McCall and Rea2009, 320–321).

Aside from relative identity, other sameness relations have been utilized in the construction of solutions to the logical problem of doctrine of the Trinity. For example, there have been appeals to virtual identity (Ott Reference Ott1960), formal identity (Blander Reference Blander2020), or real identity (Koons Reference Koons2018). These other sameness relations may yield different counting conventions that purport to uphold three divine persons and one God. And some of these sameness relations are employed as a way to avoid contradiction in the doctrine of the Trinity given that some of these sameness relations have different formal features than strict identity. For example, Koons suggests that the Father is not really distinct (i.e., is really the same) from the divine nature, the Son is not really distinct from the divine nature, but the Father is really distinct from the Son.Footnote ²² Accordingly, real sameness is not transitive, or at least it cannot be both symmetrical and transitive (cf. Spencer Reference Spencer2017, Pawl Reference Pawl2020). There are other ways of understanding real sameness. Cross, for instance, interprets real identity between a divine person and the divine essence as “the fact that the essence is the only real constituent of each divine person” (Cross Reference Cross, McCall and Rea2009, 204). Now these ways of addressing the logical problem have an obvious cost, viz., the ideological commitment to another primitive instead of strict identity or alongside of strict identity. Some may be willing to pay the price, but others may not be so willing, especially if one regards appealing to these ideological primitives as ad hoc or metaphysically bloating.

A common feature with all of these solutions discussed so far is that they are seeking to provide a logically consistent account of the doctrine of the Trinity such that no contradiction can be derived from an interpretation of the claims in (1)–(3) (or by providing an account that denies (LPT4)). However, some solutions do not attempt to avoid the appearance of a contradiction and we will consider two such approaches. The first approach does not attempt to avoid the appearance of a contradiction because it does not regard the appearance as misleading. Rather, the doctrine of the Trinity is contradictory, but that does not suggest that it is just false or that it is not true. Indeed, according to this approach, there can be true contradictions (in the sense of there being true sentences of the form “it is true that P and it is false that P”), and the doctrine of the Trinity contains such true contradictions. Jc Beall (Reference Beall2023) has offered the most developed and ardent defense of this approach, initially defending (true) contradictions related to Christology (that it is true of Christ that he is omnipotent and that it is false of Christ that he is omnipotent) but later applying the same approach to the doctrine of the Trinity.

Contradictions are a tough pill to swallow – they cannot be swallowed at all if one accepts classical logic. According to classical logic, propositions must have a truth value, the only truth values are truth and falsity, and no proposition can have both. However, classical logic is not the only (logical) game in town. Some theories of logical consequence allow for a statement to have neither truth value – that is, they allow for gaps in their logic. Other theories of logical consequence allow for a statement to have both truth values – that is, they allow for gluts in their logic. And some theories allow for more than two truth values. Beall embraces a logic (First Degree Entailment) that permits both gaps and gluts, but it is gluts that are salient for his approach to the doctrine of the Trinity (and to his approach to Christology), and it is typical to call such logics that allow for gluts as “paraconsistent.”

Beall avers that (1)–(3) employ a relation of identity, but he is skeptical that it is strict identity, or at least any identity relation that includes the formal property of being transitive (Beall Reference Beall2023, 15). However, he does take the identity relation to obey what he calls the “Leibnizian recipe,” that is, the indiscernibility of identicals. So we can come up with a predicate that is true of the Father, for example, the Father begets the Son. Since the Father is identical to God, it is true of God that God begets the Son. However, it is false of the Son that he has the property of begetting the Son, and since the Son is identical to God, it is false of God that God begets the Son. Thus, it is true of God that God begets the Son and it is false of God that God begets the Son. Contradiction! (Beall Reference Beall2023, 38f.).Footnote ²³ Yet this contradiction is not supposed to be problematic since they do not have absurd consequences. In classical logic, contradictions are indeed problematic since they license explosion, such that any proposition (in the relevant language) can be derived from a contradiction. With paraconsistent logic, however, explosion is not licensed, and so the primary concern with contradictions is removed. Accordingly, there can be true contradictions, and Beall takes the doctrine of the Trinity (and the doctrine of the incarnation where Christ is truly divine and truly human) as involving such true contradictions. On the one hand, a purported advantage of a contradictory approach to the doctrine of the Trinity is its simplicity, for it appears to take the statements in (1)–(3) at face value. They say what they say, and no interpretation involving an elaborate paraphrase or the tacking on of metaphysically substantive assumptions is required to make sense of them. On the other hand, where it is metaphysically-lite, it is logically heavy. Which account of logic or logical consequence is the true or correct one is undoubtedly contentious, and there are substantive defenses of classical logic (cf. Burgis Reference Burgis2022). That the doctrine of the Trinity depends on accepting a particular logic may place more theoretical demand than desired.

The second way of embracing the appearance of a contradiction in the doctrine of the Trinity has been developed by James Anderson (Reference Anderson2007), whose view is sometimes labeled as “mysterianism.” According to this approach, there is no way to state the doctrine of the Trinity in an orthodox way while avoiding the appearance of inconsistency. Unlike the previous approach, however, the mysterian does not accept that there is a genuine contradiction lurking in the doctrine, only that the appearance of a contradiction cannot be removed – at least not without sacrificing orthodoxy or intelligibility. According to Anderson (Reference Anderson2007, 222ff.), the apparent contradiction arises on account of an unarticulated equivocation. Since we cannot ascertain where in the doctrine an equivocation is occurring, we cannot dispel the appearance of a contradiction without falling into heterodoxy or unintelligibility. Now one might take even the appearance of a contradiction as providing sufficient reason for rejecting the set of beliefs whose members apparently yield a contradiction; however, Anderson employs Plantinga’s account of rationality and properly basic beliefs as a way of defending the rationality in believing in the doctrine of the Trinity, even if we are unable to eliminate the appearance of a contradiction (Reference Anderson2007, chs. 5–6).

But the appearance of a contradiction for which there is no adequate explanation may serve as a defeater for the rationality of such a set of beliefs, for in some cases it may not be reasonable to believe that there is an unarticulated equivocation. Compare this with philosophical paradoxes wherein the appearance of a contradiction is reason for rejecting a particular view (e.g., the Liar Paradox may be taken as a reason for rejecting the Principle of Bivalence, the Grandfather Paradox may be taken as a reason for rejecting the possibility of time travel into the past, etc.). In these cases, stating that there is an unarticulated equivocation is not generally regarded as an adequate solution. Additionally, some criticize Anderson’s form of mysterianism as lacking clarity of what the theory is even supposed to be, or at least of failing to provide sufficient specification of the theory, including specifying the relevant logical or extra-logical entailment relation in the theory (Beall Reference Beall2023, 123). While I will argue later that a satisfactory solution need not provide an account of the (logical or extra-logical) entailment relation being employed, mysterianism as presented does little to explain why the apparent contradiction is an unproblematic one, or at least it does not adequately explain how to discern between unproblematic appearances of a contradiction from problematic appearances of a contradiction.Footnote ²⁴

We have so far considered Latin trinitarianism, social trinitarianism, and some views that fit with neither or count as both, utilizing different sameness relations or other ideological primitives. We have also seen solutions to the logical problem of the doctrine of the Trinity that seek to keep the appearance of contradiction, either because they take the contradiction to be genuine or because the appearance of a contradiction cannot be avoided even if they are not to be regarded as genuine. Worries for each of these solutions have been briefly considered, and no doubt proponents of these solutions are likely to have a ready response. While I have not sought to present every solution that has ever been offered, the positions and solutions discussed here do represent many of the main approaches to the logical problem of the doctrine of the Trinity, especially by contemporary philosophers and theologians who have attempted directly to address the problem.

3 A Minimalist Approach

Given the solutions to the logical problem of the doctrine of the Trinity presented thus far, the typical approaches assume that (1)–(3) need to be suitably interpreted or paraphrased in order to avoid inconsistency. That is, the content of (1)–(3) needs to be more precisely stated to evince that a contradiction can be avoided. A contradictory approach embraces the inconsistency, whereas a mysterian approach embraces the appearance of inconsistency (due to some unarticulated equivocation). If either a genuine contradiction or the appearance of a contradiction is to be avoided, it may seem as though we are left with the strategy of paraphrasing (1)–(3).

An interpretation or paraphrase of (1)–(3) seems especially urgent if we read them in a way that may be customary for contemporary analytic philosophers and theologians. Utilizing first-order predicate logic with strict identity, Jedwab and Keller take the following statements to be a standard regimentation of the doctrine (Jedwab and Keller Reference Jedwab and Keller2019, 187):Footnote ²⁵

• (1N) ∀x (x is a divine person → x is a God).

• (2N) ∃x∃y∃z (x is a divine person & y is a divine person & z is a divine person & x≠ y & x≠ z & y≠ z & ∀w (w is a divine person → (w = x v w = y v w = z))).

• (3N) ∃x (x is a God & ∀y (y is a God → y = x)).

Using standard inference rules (and using “f” to stand for the Father and “s” to stand for the Son), we can plainly derive a contradiction (e.g., f = s & f ≠ s). The solutions from Latin trinitarianism and social trinitarianism discussed in the previous section thereby offer paraphrases or a “nonstandard regimentation” of the relevant statements in the doctrine of the Trinity in order to avoid inconsistency (ibid.).

For a paraphrase or reinterpretation to succeed, the newly formulated statements should offer logically equivalent alternatives, ones that are more precise or perspicuous than the original statements in (1)–(3).Footnote ²⁶ As Jedwab and Keller note, there are different types of paraphrasing strategies that are employed in philosophical discussions, and the views that seek to offer a paraphrase as a solution to the logical problem of the Trinity typically offer reconciling paraphrases that are “intended to preserve what is said: their purpose is to clarify the contents of the originals … [and] are meant to be more perspicuous, then, in the sense of being more clear than the originals” (Jedwab and Keller Reference Jedwab and Keller2019, 174–175). An obvious reason for requiring logically equivalent paraphrases is that the solutions are aiming to demonstrate that the doctrine of the Trinity as stated in (1)–(3) is not logically inconsistent. However, if the paraphrases are not logically equivalent, then it may not matter that the paraphrases of each claim form a logically consistent set, for it does not show us that the doctrine of the Trinity is logically consistent – only that the new sentences taken together are. Thus, the paraphrases, according to these solutions, need to ensure that they are logically equivalent to the original statements. Therefore, adequate solutions that utilize a paraphrase technique will seek to preserve the content of the original pronouncements concerning the doctrine of the Trinity by offering logically equivalent propositions to (1)–(3) – or at least statements that entail (1)–(3) – and then show that these paraphrases are logically consistent.

For example, a social Trinitarian such as Richard Swinburne may paraphrase (1)–(3) as follows (Reference Swinburne1994, 180–181; cf. Jedwab and Keller Reference Jedwab and Keller2019, 183):

1. (S1) The Father is a divine being, the Son is a divine being, and the Holy Spirit is a divine being.

2. (S2) The Father is not strictly identical to the Son, the Son is not strictly identical to the Spirit, and the Father is not strictly identical to the Spirit.

3. (S3) There is exactly one independent divine being.

That there are three divine beings who are not strictly identical to each other does not conflict with (S3) since the divine persons are not independent divine beings. Given their causal relations or their mutual interdependence to each other, each divine person is a dependent being. For another example, a social trinitarian such as William Lane Craig may offer the following paraphrase (Moreland and Craig Reference 65Moreland and Lane Craig2003):

1. (S1*) The Father is divine₂, the Son is divine₂, and the Holy Spirit is divine₂.

2. (S2) The Father is not strictly identical to the Son, the Son is not strictly identical to the Spirit, and the Father is not strictly identical to the Spirit.

3. (S3*) There is exactly one divine₁ being.

Accordingly, there is more than one way to be divine, such that God is divine in one way and the persons are divine in another way (where God is divine by being strictly identical to the one divine nature, whereas the divine persons are divine by being a proper part of the one divine nature or by instantiating the one divine nature).

While the paraphrasing approach to solving the logical problem of the doctrine of the Trinity has able defenders, I aim to offer another solution to the problem, one that seeks to reframe the debate between these putatively competing accounts of the doctrine of the Trinity. The strategy here is similar to the mysterian and contradictory approach insofar as it wants to read (1)–(3) straightforwardly. That is, no (reconciling) paraphrase or reinterpretation is required. Unlike the contradictory approach, it does not claim that (1)–(3) yield a genuine contradiction. And unlike the mysterian approach (at least the version discussed in the previous section), it does not assume that there is an unarticulated equivocation in the doctrine. Rather, the solution here claims that the doctrine of the Trinity as stated in (1)–(3) have minimal (semantic or propositional) content such that a contradiction cannot be derived from them. I will label this view as “minimalism” about the doctrine of the Trinity. Before stating the view more precisely and how it avoids the logical problem, I will begin with some motivations for taking this approach.

First, consider the horos-based framework concerning conciliar pronouncements, such as the kind advanced by Sarah Coakley (Reference 61Coakley, Davis, Kendall and O’Collins2002). Focusing on the Council of Chalcedon in 451, Coakley avers that the Chalcedonian definition should be construed as a horos or boundary in the sense that it plays a regulatory role in our understanding of Christ. The conciliar claims are not merely linguistic regulations – that is, they do not merely restrict how it is that Christians can or should talk about Christ. Nor does a horos-based approach take these pronouncements to be metaphorical. Although what is provided may aptly be called a “definition,” it is not of the kind that one commonly finds in analytic philosophical discussions, whereby one seeks to provide necessary and sufficient conditions of a definiendum. Rather, the regulatory role of the conciliar pronouncement provides the limits or boundaries of orthodox Christology, especially since one of the main purposes of formulating the Chalcedonian definition was polemical, targeting various heretical positions (Reference 61Coakley, Davis, Kendall and O’Collins2002, 161f.). Imperial or political pressure toward more precise statements appears to have been placed on some of the early bishops in Chalcedon, and yet some of these Christian leaders did not capitulate to such demands. A similar view has been suggested by Oliver Crisp, who regards the Chalcedonian definition as offering a dogmatic minimalism such that the pronouncements say “as little as doctrinally possible about hypostatic union while making clear that certain ways of thinking about the person of Christ are off-limits or unorthodox” (Reference Crisp2016, 80). Accordingly, dogmatic minimalism allows for “many different Christologies that are consistent with the canons of Chalcedon” (ibid., 81).Footnote ²⁷

Tensions and disputes concerning the divinity of the Son were erupting in the third- and fourth-century CE, leading to theological controversies by various groups identifying as Christians and eventually culminating in the Council of Nicaea in 325 and the Council of Constantinople (I) in 380/1. It would be historically naïve to assume that these meetings were devoid of political motivations and influence; however, it would be cynical to assume that these meetings were solely about politics, power, and influence. The statements formulated in the creeds and conciliar pronouncements and the theological disputes happening in and around that time need to be understood within the polemical context in which they originated. It is tempting for some to assume that some of the Cappadocian Fathers were developing a social or proto-social approach to the doctrine of the Trinity, though we have already cited some thinkers who are skeptical of that view. Of course, some take it as significant that they use examples such as three human persons possessing or instantiating the same human nature.Footnote ²⁸ However, these examples were often proffered in response to some challenge or (what was deemed as a) heretical claim. For example, while the analogy of three men employed by Gregory of Nyssa is often cited by social trinitarians, it is worth noting that Gregory’s interlocutor Ablabius (whose argument is summarized by Gregory) is the one who introduces the example of three individual men, whereby Gregory utilizes that example in his response given the dialectical context (cf. Coakley Reference Coakley, Davis, Kendall and O’Collins1999, 132). As such, one may need to pause before taking these examples as saying more than what they were intended to do. What we do find explicitly is the ruling out of particular positions and claims that were regarded as heretical or theologically unacceptable, and so it seems appropriate to read the creeds and conciliar pronouncements from the fourth century concerning the Trinity in that spirit.

Second, while there were differences and disagreements by early Christian thinkers – even notable differences by Greek-speaking, eastern theologians and Latin-speaking, western theologians (though, as stated earlier, the differences are sometimes exaggerated or inaccurately presented) – one typical area of overlap for many early Christian thinkers was in the acceptance of divine ineffability or a commitment to apophaticism (though not always in the same sense or to the same degree). For example, while Gregory of Nyssa is thought by some as advancing a social or proto-social trinitarian view (though we mentioned earlier why this may be suspect), he does appear to appeal to divine ineffability to render invalid the inferences that move from there being three divine hypostases to three Gods (cf. Moreland and Craig Reference 65Moreland and Lane Craig2003, 584). Divine ineffability implies that God transcends our categories, and yet some who held to divine ineffability such as Augustine did not regard it as leading to our lack of knowledge of God but rather as being “part and parcel of the particular intelligible structure of the creation as revealing of its Creator” (Ayres Reference Ayres2010, 262). Divine ineffability, then, should not yield an inability to talk about God or to acquire knowledge of God, but it may severely constrain how it is that we can come to know God and what it is about God that we can know.

There is not an agreed upon sense of apophaticism in these early years (nor even today). While it is typical to characterize apophaticism as a kind of negative theology whereby only negative attributions about God can be made, not everyone held to such a strict criterion. Some Christian thinkers who were deeply influenced by apophatic theology made room for some positive attributions about God’s nature. While extreme versions do not allow us to make any positive attribution about God (though they usually permitted making positive attributions about God’s actions in the world), less extreme versions only ruled out making positive attributions about the intrinsic properties of God’s nature. There were even less extreme versions that allowed for some positive attributions, though we are barred from knowing God’s essence or where our language for God needs to be understood analogically rather than univocally.

More recently, Jonathan Jacobs (Reference Jacobs2015) offers a version of apophaticism that holds to our inability to utter anything about God’s (intrinsic) nature that is both true and fundamental, where fundamentality is understood as carving nature at the joints (so to speak). So while it is true to say that “God is good” or “God is powerful,” these statements would not be fundamental. Moreover, the kind of apophaticism that is in the spirit of early Christian thinkers should not be limited to focusing on predications or statements about God, as Sameer Yadav has argued that the aim of apophatic theology includes attention to mystical experiences that yield a direct and immediate apprehension or union with God (Yadav Reference Yadav2016). The mode of presentation by which we experience God will be, in one sense, manufactured, as it is a “gerrymandered mode of presentation which is recognized by the mystic as an indicator of God’s ineffability” (ibid., 34–35). Thus, our speaking of God may not provide an accurate representation of God but it can make us relationally closer to God.

To be clear, I am not endorsing any specific account of apophaticism here. However, the general commitment to some form of apophaticism by these early Christian theologians who were integral in the development of the doctrine of the Trinity or who were involved in the formulation of the conciliar and creedal pronouncements needs to be taken seriously. Many of these statements about God, the divine persons, the divine nature, the hypostatic union, and the like need to be understood in light of the constraints on our knowledge of God, especially since many early Christian thinkers who played a central role in our early theological reflections on Christology and the doctrine of the Trinity were committed to divine transcendence and divine ineffability.Footnote ²⁹

Given the historical context surrounding the development of the doctrine of the Trinity as well as the widespread acceptance of some form of apophaticism by early Christian thinkers, we may need to be cautious importing content into trinitarian claims that may not have been there. Consider the so-called “standard regimentation” of (1)–(3) that Jedwab and Keller (Reference Jedwab and Keller2019, 187) formulated in (1N)–(3N). The regimentation involved using “=” (i.e., strict identity). But why suppose this is the way we should interpret them? One might take it as obvious that when we say “the Father is not the Son” or that “the Father is God,” these statements are employing strict identity. But we have reason to be suspicious of that claim. As Jc Beall states:

Indeed, the fact that the doctrine of the Trinity accepts that the Father is God, the Son is God, and the Father is not the Son gives the appearance that whatever relation it is that is being denoted in the copula (assuming that the copula has a denotation at all), it is not both symmetrical and transitive. Other scholars have pointed out the same worry of assuming that the identity relation (if it is even identity at all) is strict identity. For example, William Lane Craig states that “it is an anachronistic hermeneutical error to import the modern identity relation into these authors’ statements” (Craig Reference Craig and McIntosh2024, 53). To be sure, I am not suggesting that ancient thinkers lacked the concept of strict identity. Rather, those who make claims of sameness or identity may not be employing strict identity, and to utilize strict identity as a default when interpreting the doctrine of the Trinity may not be advisable. Indeed, when considering the councils and creeds, Tim Pawl claims that strict identity cannot be the relevant identity relation that is being employed in these statements since it is inconsistent with conciliar trinitarianism (Reference Pawl2020, 109). Moreover, the relation may not be a sameness or identity relation at all, as some have interpreted the claims as involving predication (e.g., Wierenga Reference Wierenga2004). But if we understand predication in terms of instantiation (or exemplification) of a property or kind, then that too may be inconsistent with conciliar trinitarianism (Pawl Reference Pawl2020, 112–114).

Furthermore, why suppose that there is a univocal notion of existence in the doctrine of the Trinity? Some thinkers both historically and now have adopted ontological pluralism such that there are different ways of being or different ways of existing. One way of developing this is by positing more than one fundamental existential quantifier. Perhaps there is one way for things in the created order to exist and another way for God to exist. As some classical theists state (sometimes in sloganeering fashion): “God is beyond being.” Now the doctrine of the Trinity does not by itself commit us to how many fundamental existential quantifiers there are. But if (2N) and (3N) employ more than one fundamental existential quantifier,Footnote ³⁰ then a contradiction does not straightforwardly follow from (1N)–(3N). This is not to claim that we ought to interpret (1)–(3) in terms of ontological pluralism. If we are assuming that (1)–(3) are employing strict identity or a single way of existing, then perhaps we need a paraphrase or reinterpretation in order to avoid logical inconsistency. But it is not obvious that we should interpret the doctrine as requiring strict identity or a single fundamental existential quantifier, and there is no compelling reason to make those assumptions when considering the historical development of the doctrine (and perhaps some compelling reason against making some of these assumptions, especially given an apophatic or horos-based framework).

Additionally, minimalism does not require that we interpret (1)–(3) while upholding many of the ontological or ideological commitments made by most of the solutions in the previous section, nor does it require adopting a particular theory of logical consequence. This is because the doctrine of the Trinity is not presenting content that includes such notions, otherwise acceptance of these ontological entities or ideological primitives would be required for those adhering to Scriptural teaching or to orthodox tradition. By having faith in the doctrine of the Trinity, it would be odd to demand that these believers accept some of these ontological commitments or ideological primitives, or to be required to endorse a particular theory of logical consequence. Moreover, one may have belief in the doctrine of the Trinity and reject some of these notions (e.g., numerical sameness without identity, immanent universals, etc.). Faith in the doctrine of the Trinity should not require one to take a stand on particular metaphysical debates (though it may on some of them), some of which were not even being considered by the early Christians who were formulating these doctrinal claims.

Minimalism, then, does not require any of these additional metaphysical or logical additions that are attached to the doctrine when constructing a solution to the logical problem of the doctrine of the Trinity, such as the ones surveyed in the previous section. The doctrine of the Trinity does indeed have substantive ontological commitments, for example, the existence of a deity and the existence of more than one divine hypostases or divine person.Footnote ³¹ Nevertheless, minimalism does seek to be minimal both metaphysically and logically.

First, it seeks to be metaphysically minimal by being both ontologically minimal and ideologically minimal. One’s ontology states what one takes to exist or what kinds of things one takes to exist. One’s ideology states what primitive predicates or operators are required for explaining the metaphysical structure of (some part of) the world. To illustrate this, take a Platonic realist about universals. Such a realist would include universals in their ontology, and they would include “instantiation” or “exemplification” (or “… instantiates …” or “… exemplifies …”) in their ideology. According to minimalism about the doctrine of the Trinity, there need be no ontological commitment to the existence of properties, tropes, centers of consciousness, and so on. There need also be no ideological commitment to strict identity, relative identity, real identity, formal identity, numerical sameness without identity, a single existential quantifier, and so on.Footnote ³²

Some of the solutions presented in the previous section are much more ontologically and ideologically committing. For example, several social trinitarians appear to be committed to universals or properties. Some Latin trinitarians appear to be committed to Lockean (event-based) persons or extended simples. And some of these solutions are ideologically committed to parthood (or associated concepts such as overlap, disjointedness, etc.) or to a specific sameness relation – or if not committed in the strictest sense to these, at least committed to the possibility of some of these items (e.g., the possibility of extended simples). Minimalism, however, is neither ontologically or ideologically committed to any of these nor to the possibility thereof (e.g., it is open to the minimalist that time travel or extended simples be impossible, as some metaphysicians have argued). And some social trinitarians are committed to construing the divine persons as centers of consciousness or as persons in some robust, psychological sense that corresponds with the understanding of personhood in contemporary psychology (or at least from the early modern period). However, minimalism does not require any substantive metaphysical analysis of the three divine hypostases or persons. Indeed, it may not be treating the term “person” with much conceptual weight, taking a cue from Augustine:

And some take God or the divine nature in (1)–(3) as being concrete or abstract. But minimalism does not commit us to any particular analysis of the divine nature.Footnote ³³

Second, minimalism seeks to be logically minimal such that an acceptance of the doctrine of the Trinity as spelled out in (1)–(3) does not commit one to any particular view of logic or logical consequence. Minimalism is thereby compatible with classical logic, strong Kleene, First Degree Entailment, or whatever other view of logical consequence. Thus, a minimalist may embrace gaps or gluts, or they may embrace neither. So unlike Beall’s contradictory solution, acceptance of the doctrine of the Trinity does not require acceptance of a paraconsistent logic. One can accept a paraconsistent logic and the doctrine of the Trinity, but the former is not required as a way to resolve the logical problem for the latter. For minimalism, one does not have to settle which theory of logical consequence to endorse in order to accept the doctrine of the Trinity. That said, minimalists do not have to remain unsettled. They may choose classical logic or something else such as paraconsistent logic. They may accept a particular entailment relation whereby the truths of divine reality are closed.Footnote ³⁴

By characterizing minimalism in this way, it should be somewhat straightforward how it handles the logical problem of the doctrine of the Trinity. First, take (1)–(3). Since there are no substantive ontological or ideological commitments, there is no obvious way to generate a contradiction from the claims. Since the “is” in (1) and in (2) are not to be taken as strict identity, no contradiction such as “the Father = the Son & the Father ≠ the Son” can be derived. As noted earlier, Beall does not take the relation to be strict identity but some kind of identity relation that is not transitive. Nevertheless, he takes there to be a contradiction given the indiscernibility of identicals (what he calls the “Leibnizian recipe”), such that it is true that God begets the Son (since both the Father begets the Son and the Father is identical to God) and that it is false that God begets the Son (since both it is false that the Son begets the Son and the Son is identical to God). However, we have no compelling reason to think that the relation in (1) is a sameness or identity relation of any kind, as it may instead be a kind of predication relation, a mereological relation, or a constitution relation, and thus the “Leibnizian recipe” would be inapplicable. Therefore, no contradiction will be derived unless one tacks on an assumption beyond what the claim states (e.g., that it employs a sameness relation that obeys the Leibnizian recipe), but that assumption is not being made under minimalism.

Next, consider a minimalist response to the problem as laid out in (LPT1)–(LPT5). Some solutions to the logical problem will specify why we should deny (LPT4), perhaps because of adherence to a particular counting convention when we introduce a particular primitive, such as Brower and Rea’s hylomorphic solution that employs numerical sameness without identity (and where we specify whether we are counting by matter or by form-matter compounds). However, minimalism takes (LPT4) to be underspecified. Suppose that by the expression “is not identical to” in (LPT4) (and (LPT3)), the relation of strict identity holds as well as the typical counting convention that we learned in logic class when being introduced to first-order predicate logic with identity. If so, then (LPT4) is true, but it is irrelevant since minimalism does not commit one to any particular relation, and hence the minimalist will deny (LPT3) instead. Indeed, for any specific way of spelling out the identity relation in (LPT4), the minimalist will be inclined to deny (LPT3) if that relation is being employed in that proposition. However, if no particular sameness relation is being specified, then there is no reason to regard (LPT4) as true, since it is unclear in what way we ought to count Gods without some additional conceptual machinery. Absent such machinery, we have no reason to accept (LPT4) as being true. Thus, minimalism solves, or perhaps better, dissolves the logical problem of the doctrine of the Trinity because it shows that the content of the relevant claims in the doctrine of the Trinity is not substantive enough to derive a contradiction.Footnote ³⁵

What about other logical problems or the threeness-oneness problem? Some take “the logical problem of the Trinity” and “the threeness-oneness problem” to denote the same problem. However, Beall regards these as separate problems. Moreover, he does not take the logical problem of the Trinity to be merely concerned with the apparent inconsistency of the doctrine, which fits with the fact that he thinks the attempt to “consistentize” the doctrine is misguided. Rather, Beall understands the logical problem of the Trinity to be concerned with specifying what the identity relation is in the doctrine, and he takes the threeness-oneness problem to be about offering a counting convention – so as to end up with the right count of divine natures and divine persons, viz., one and three, respectively (Beall Reference Beall2023, 16–17). However, minimalism regards the attempt to answer Beall’s logical problem as misguided, as it would be a mistake to try and provide what that exact sameness relation is – and it also takes it to be misguided because the relation may not even be a sameness or identity relation but rather something else, such as exemplification/instantiation, composition, constitution, or some other relation. The more we embrace apophaticism, the more we are likely to take this to be an impossible task for us (at least in this life, but perhaps always). Moreover, given the minimalist approach that is ontology-lite and ideology-lite, a counting convention will not be able to be established.Footnote ³⁶ Yet not being able to provide a counting-convention is a feature of the view, not a bug; a benefit, not a defect. For by being metaphysically minimal, we have no way of deriving a contradiction from (1)–(3) nor do we have any reason for accepting (LPT4). Failing to provide a counting convention would be problematic only if our account of the doctrine of the Trinity needs to provide some analysis of what God is actually like.Footnote ³⁷ But minimalism offers no such account. This does not leave us totally in the dark, as we do know what the count is even without a counting convention, for we must wind up with three divine persons and one divine nature (or essence or substance). But we get to that via revelation (at least for those of us who do not believe we can reason our way to the doctrine of the Trinity, pace Richard of St. Victor, Swinburne Reference Swinburne1994, or Davis Reference Davis2006). We do not need to provide an account that gets us to the right count – we already had the right count before creating any specific model.

While the content of the claims involved in the doctrine of the Trinity – at least as stated in (1)–(3) – is understood to have minimal content so as not to rise to the level where a contradiction can be derived, the minimal content of these propositions nevertheless provides enough information to rule out particular views that have been regarded as out of the boundaries of orthodoxy. Thus, we need to assess whether the statements say enough so that non-trinitarians cannot accept these claims.

Take, for example, the claim that the Son is divine or that the Son is consubstantial with the Father. The content must be substantive enough to rule out Arianism or some heretical form of ontological subordinationism. The heretical view maintains that the Son is not divine or not divine with the same kind of divinity as the Father (i.e., that the Son possesses a lesser divinity). To reject that heresy, one must claim that the Son is divine or has the same kind of divinity as the Father. Start with the claim that the Son is divine. For simplicity, let us use “divine” or “divinity” (and its cognates) to refer to the substance or nature of the Father (and thus, we will not use that term to refer to any lesser divinity such as a created one). An Arian view suggests that whatever relation it is that the Son bears to divinity such that it would make it true that the Son is divine does not hold between the Son and divinity. So to deny that would be to accept that the Son does bear that very relation to divinity. Perhaps that relation is some kind of sameness relation (e.g., numerical identity, relative identity, real identity, formal identity, or whatever), or perhaps it is a relation of instantiation, constitution, or parthood. Whatever the relation is that the Father has to divinity, the heretical view would be that the Son does not bear that relation to divinity (though the Son may bear that relation to a lesser nature). Orthodoxy requires that the Son is related to divinity with the same kind of relation that the Father has to it. If the Father instantiates divinity, then the Son instantiates divinity. If the Father is really the same as divinity, then the Son is really the same as divinity. If the Father is strictly identical to divinity, then the Son is strictly identical to divinity. Neither the trinitarian doctrinal claims nor arguably even the conciliar pronouncements tell us what that relation is (nor does it tell us the exact nature of divinity, though there is a tendency to treat divinity as concrete rather than abstract within the conciliar framework). By claiming that “the Father is divine and the Son is divine,” what is required of orthodoxy is that we hold fixed the meaning of “divine” and the copula.Footnote ³⁸ And mutatis mutandis, the same goes for the Spirit’s relation to divinity. And thus, heresies involving the ontological subordination of either the Son or the Spirit are precluded by the doctrinal claims. Indeed, this seems to fit well with the way that the pro-Nicene theologians ruled out heretical views such as Arianism by introducing the term homoousios, even though “[n]either the council fathers of Nicaea nor Athanasius himself were working with any determinate technical sense of ousia or homoousios” (Anatolios Reference Anatolios2011, 128). Yet the term homoousios had sufficient semantic content to serve as a hermeneutical guide to Scripture and as a means to argue against the heretics.

Let us consider another key claim in the doctrine of the Trinity: the Father is not the Son. According to the Sabellian heresy, the Father is the Son such that one and the same individual is being presented under a different persona or guise sequentially (the one God presented as the Father, then the Son, and later the Spirit). The Father and Son would only be able to interact with each other in the way that Superman and Clark Kent can interact with each other. But the data of the New Testament implies or depicts interactions between the Father and the Son that involve more than that. Perhaps one way of explicating this is that each divine person needs to be able to use certain indexicals, such as the first-person pronoun, in a way that is self-referential and without referring to another divine person – and this is a relatively thin criterion that is compatible with denying that the divine persons are “centers of consciousness.” This explication also fits with the portrayals in Scripture of the divine persons and their relationship to each other (cf. McCall Reference McCall and Sexton2014, 117–118).Footnote ³⁹ So when the Son says, “My God, my God, why have you abandoned me?”, he uses “me” to refer to himself (viz., the Son) without referring to the Father (or to the Spirit). So the Father has to be distinct from the Son. But with what kind of distinctness? It cannot merely be distinctness of guises, personas, or modes of presentation, otherwise the indexicals would fail to be exclusively self-referential. Yet there are different ways for the Father and the Son to be distinct that would allow for the indexicals to function in the way required. One obvious way is by positing strict distinctness. However, it may be another kind of distinctness, such as relative distinction or real distinction.Footnote ⁴⁰ We may instead say the Father is not the same person as the Son or that the Father is really distinct from the Son (among other options). The formal properties of relative identity may be the same as strict identity, but it will be sortal bound. And the formal properties of real distinction are different from the formal properties of strict identity, as real distinction is not transitive, or at least not simultaneously symmetrical and transitive (Pawl Reference Pawl2020, 114–115; Ott Reference Ott1960, 75; Koon Reference Koons2018, 348). So given the possible options, the trinitarian claim that the Father is not the Son does not demand any specific kind of identity/distinction relation (though it may preclude some relations and some ways of analyzing the divine persons). Since the claims that the Father is not the Son, the Son is not the Spirit, and the Father is not Spirit are plausibly interpreted (in light of its historical development) so as to rule out that there is only a single divine hypostasis or person, the doctrinal claim has enough semantic content to play its role of eliminating a heterodox view such as Sabellianism.Footnote ⁴¹ To be sure, one need not interpret the requisite distinctness in the way that I have. I have stated it this way since it is my own preference and seems to me to be relatively neutral, though given the difficulties surrounding the first-person indexical, this may not be the case. However, there may be other ways of making the distinction in terms of haecceities, relational properties, and the like. Though these other ways require additional metaphysical baggage and minimalism’s approach seeks to be metaphysically-lite.Footnote ⁴²

For some Christians, minimalism may be too minimal. This may especially be true for those who take the creedal or conciliar pronouncements to be more restrictive in their understanding of some of the concepts employed in (1)–(3). Let us then use “minimalism+” to refer to a minimalist approach that includes whatever restrictions or additional content that one accepts on account of their authoritative sources or their theological traditions.

For example, someone who wants to take a conciliar approach to the doctrine of the Trinity (which we will label “conciliar trinitarianism”) may espouse minimalism+ and require that we construe the divine nature as concrete rather than abstract.Footnote ⁴³ A conciliar trinitarian form of minimalism+, then, will rule out certain interpretations of the doctrine of the Trinity, such as versions of social trinitarianism whereby the divine nature is understood as abstract (such as a universal or a collection of universals that the divine persons instantiate). Others argue that a conciliar approach to the doctrine of the Trinity requires positing only a single will or a single power rather than positing separate wills or powers for each divine person (Williams Reference Williams2017, Reference Williams2022). Some social trinitarians, such as Hasker (Reference Hasker2013), insist on there being three wills or three powers (though in perfect harmony with each other). These interpretations that posit a plurality of wills or powers in the doctrine of the Trinity would be ruled out by a conciliar trinitarian form of minimalism+. Yet even with these constraints or additional content in minimalism+, plenty of options remain for filling in the content of the doctrinal claims. Without them suitably filled in, a contradiction cannot be derived from them. Thus even minimalism+ avoids contradiction from (1) to (3). Additionally, minimalism+ does not tell us what the exact relation is that is used in (LPT3) or (LPT4), even if we take God or the divine nature as being concrete. So the same move can be made whether one endorses minimalism or minimalism+.

The benefit of minimalism is that it satisfies typical desiderata for an adequate solution to the logical problem of the doctrine of the Trinity. An obvious desideratum is that the view be orthodox (or consistent with orthodoxy), and minimalism easily checks that off. Another desideratum that is sometimes posited in these discussions is that a satisfactory solution should maintain the mystery of the doctrine of the Trinity. A common criticism against analytic theology is that it sees the doctrine of the Trinity as a puzzle to be solved, or that it removes the mystery in the doctrine. This may be true with some of the views or some of the proponents of those views that were mentioned in the previous section. However, minimalism retains the mystery of the trinitarian doctrine insofar as it does not offer an analysis of the divine persons or of the divine nature, nor can we precisely articulate the relation between the divine persons and the divine nature. It is utterly mysterious to us. It seems to respect the mystery more than contradictory approaches since it does not aim to identify or characterize the identity relation being employed in these doctrinal claims, nor does it require opting for a particular theory of logical consequence. Whatever the correct theory of logic, the doctrine of the Trinity remains mysterious.

Finally, any satisfactory solution should articulate why there is no logical inconsistency between (1) and (3). Mysterianism offers a partial diagnosis insofar as it states that there is an unarticulated equivocation. Yet it does not tell us where it is, and so the appearance of inconsistency is not completely dispelled. Moreover, it is unclear in mysterianism when such appearances of contradictions are problematic and when they are not. Minimalism, however, explains why there is no inconsistency, for a contradiction cannot be derived given the minimal content in (1)–(3). Any attempt to derive a contradiction will smuggle in content in the doctrine that we need not accept (and perhaps where we even have reasons to reject, especially as it applies to God).

Now there is some precedent to the view I am defending, where a similar view has been discussed and rejected by James Anderson (Reference Anderson2007) and Dale Tuggy (Reference Tuggy2011), a view they label as “semantic minimalism” or “negative mysterianism” (as opposed to Anderson’s “positive” mysterianism), respectively. Anderson rejects the view because either it is wed to an extreme form of apophaticism that is incompatible with what the trinitarian doctrine affirms (since the doctrine makes positive assertions and not just negative statements) or because it seems that every interpretation of the doctrine yields the appearance of a contradiction.Footnote ⁴⁴ However, we have already noted a variety of apophatic views that allow for positive assertions of the sort we find in the doctrine of the Trinity. And this section has sought to show that there are plausible interpretations of the doctrinal claims that remove the appearance of inconsistency (since no contradiction can be derived) and yet are semantically informative enough to rule out the relevant heresies. It has certainly not removed all mysteries, though minimalism does not seek to do that.

Tuggy characterizes negative mysterianism as being “not understandable because it is too poor in intelligible content for it to positively seem consistent (or not) to us” (Tuggy Reference Tuggy2011, 209). This is to be contrasted with positive mysterianism, where the doctrinal claims have too much content so as to contain putatively at least one contradiction (which is the view that Anderson defends and which was discussed in the previous section). Now Tuggy states that he finds adherence to negative mysterianism among “the catholic church fathers and the medieval traditions beholden to them” (ibid.), but he sets it aside given its lack of extant support. I would agree that there is something like negative mysterianism in the patristics and the medieval divines; however, I would aver that what they were supporting is more akin to minimalism as characterized earlier.

Indeed, minimalism should not be understood in precisely the terms that Tuggy uses to characterize negative mysterianism. Tuggy’s use of the expression “too poor in intelligible content” sounds as though the trinitarian claims are defective. Yet attending to the history of doctrinal development concerning the Trinity, these claims were not being offered as a systematic account or as an analytic definition. Rather, these claims were either received from revelation or formulated in response to views that were deemed out of bounds by the church creeds and councils. Thus, it would be anachronistic to suppose that there is some adequate criterion of informative characterization by which (1)–(3) fail to meet, especially if that criterion is one that is demanded by contemporary philosophers and theologians. The context of these formulations is crucial to remember, often being formulated within a polemical context or specific circumstances in which particular challenges to orthodox faith were being put forward. What the doctrinal statements in (1)–(3) were seeking to achieve in many contexts was the rejection of heretical teaching. As elaborated earlier, these statements are substantive enough to do that even if they do not specify particular ontological, ideological, or logical primitives in spelling out these claims. But they are informationally robust enough to do what they were intended to do. Hence, we ought not to regard minimalism as claiming that the propositional content of the doctrine of the Trinity is “too poor” in content. Rather, it says what it needed to say in order to rule out certain views, and as shown earlier, it can do at least that.Footnote ⁴⁵

While minimalism explains how contradiction is avoided, at surface level, the statements in the doctrine of the Trinity do have an initial appearance of being inconsistent, so a satisfactory solution should offer some explanation as to why the doctrine of the Trinity as stated in (1)–(3) appears that way. As we have seen, the appearance of inconsistency disappears once we discern what the claims are actually stating. However, the appearance of inconsistency arises only when we import more content in these claims than they originally had. If we read them and interpret them as utilizing strict identity, which is a very natural thing to do for those of us who were immersed in first-order predicate logic with identity during graduate school, then the claims will appear inconsistent using well-known logical rules. It also seems that strict identity, given its place in mathematics, is a common one for many people to use (including those who were not so immersed in the standard logic training that many philosophers receive), almost as a default (cf. Hawthorne Reference Hawthorne, Loux and Zimmerman2003), and so the almost automatic use of such a relation will make the doctrine appear inconsistent, at least when done without some nuance or additional (contentious) assumptions (cf. Tweedt Reference Tweedt2023). For many, the term “identity” virtually comes with the presumption that strict identity is what is meant. If so, that would explain why (1)–(3) smack as being inconsistent.

Additionally, the acceptance of some other sameness relation – such as accidental sameness (i.e., numerical sameness without strict identity) or real sameness/distinctness – is not as common among folks, especially those not well versed in Aristotelian philosophy or medieval theology. However, if operating with a sameness relation whose formal properties do not include transitivity (or do not include both symmetry and transitivity), then it is less likely that one would find these doctrinal claims inconsistent – at least not without additional assumptions. As some have averred, strict identity was not the common notion of sameness employed by ancient thinkers (Craig Reference Craig and McIntosh2024, 52–53). It is no surprise, then, that early discussions of logical challenges related to the doctrine of the Trinity seem neither to be stated with the same level of concern nor formulated in the same way as it is typically done in more contemporary discussions, and it may be due to the prevalence of different concepts of sameness operating at those times. But once strict identity dominates, especially given the success of mathematics and its relation to the development of logic in the nineteenth and twentieth centuries, an automatic tendency of reading sameness relations as strict identity gives rise to the appearance of inconsistency.Footnote ⁴⁶

4 Minimalism and Models: Reframing the Debate

Given that minimalism offers a solution to the logical problem of the doctrine of the Trinity, what are we to make of the solutions in section 2? Were they all wasted efforts? As I see it, minimalism can make room for many of the imaginative and creative insights into thinking about the doctrine of the Trinity by these various approaches. Doing so, however, requires reconceiving the aim of these approaches as well as reframing the debate between them.

Many of these solutions claim to be offering an analogy or a model of (the doctrine of) the Trinity. For example, Michael Rea characterizes analytic theologians writing about the Trinity as typically presenting “a model or analogy that helps us to see how it might be coherent to say that there is one god but three divine persons” (Rea Reference Rea and Rea2009a, 4; cf. Rea Reference Rea, Flint and Rea2009b, 408ff.). However, the use of the term “model” does not seem to be precise, as William Wood notes that many in theological discussions tend to use that term “loosely in academic writing to mean just ‘an account’ or ‘a way of understanding’” (Wood Reference Wood2016, 40). Terms such as “model,” “account,” “theory,” “view,” or “position” are commonly used as synonyms in these discussions. If models are understood to serve as an analysis or an explanation of the doctrine of the Trinity, it is not surprising that some theologians have criticized the use of models in expounding the doctrine of Trinity as being idolatrous or treating the doctrine of the Trinity as a problem to be solved rather than a mystery to be appreciated (Weinandy Reference Weinandy2000).Footnote ⁴⁷ Getting a better sense of the nature, function, or role of models may yield a theological method that can ward off some of these criticisms, whereby the models of the doctrine of the Trinity need not be regarded as merely “logic-chopping” solutions or as an attempt to demystify the doctrine.

Recently, some analytic theologians and philosophers have been utilizing a more technical and precise conception of models, one that overlaps with an understanding of models as they are employed in the sciences (Wood Reference Wood2016, Crisp Reference Crisp, Arcadi and Turner2021).Footnote ⁴⁸ Stating what models are can be a tricky endeavor since scientists and philosophers of science do not all operate with the same definition or characterization of models. Following the philosopher of science Michael Weisberg, who offers an in-depth and careful treatment, modeling is characterized as “a form of surrogate reasoning, a practice in which one constructs and analyzes a model in order to learn, indirectly, about something else” (Weisberg Reference Weisberg, Cappelen, Gendler and Hawthorne2016, 264). Models, then, are representations of some target or target domain, which is some phenomena or portion of reality (Elliott-Graves and Weisberg Reference Elliott-Graves and Weisberg2014, 180–181).Footnote ⁴⁹ This would involve indirect representation, whereby the model is what is analyzed rather than the target, yet we can learn things about the target by studying the model. In some cases, models are hypothetical or targetless, whereby we would not include in our ontology that which the modeler is trying to represent.

As Catherine Elgin has put it succinctly, “Models simplify and often distort … The models that scientists work with often fail to match the facts they are adduced to account for” (Elgin Reference 62Elgin and Suarez2009, 77). Because of such simplifications, models often involve idealization – they are not meant to be “maximally realistic” (Weisberg Reference 68Weisberg2013, 98). Idealizations commonly introduce intentional distortions in the representation of the target. The idealized model is constructed so that in some ways it does not match a feature of the target. In doing so, the model may use false assumptions or false elements, and hence some philosophers of science use the label “false idealizations” or “false models” when describing these types of models (Bokulich Reference Bokulich and Suarez2009 and Reference Bokulich2011, Maki Reference Maki, Humphreys and Imbert2011). This distortion is not regarded as a defect but rather as a means of better understanding the target or yielding some theoretical benefit that cannot be acquired without the distortion in the model (cf. Cartwright Reference Cartwright1983). Thus, idealization “involves lowering one’s standards of fidelity explicitly, perhaps because such an action can promote some other desirable theoretical virtue” (Weisberg Reference Weisberg2007a, 229). Elsewhere, Weisberg states that an idealization is a “departure from complete, veridical representation of real-world phenomena … we distort or misrepresent our target by representing it having properties that it does not have” (Reference 68Weisberg2013, 98; cf. Jones Reference Jones, Jones and Cartwright2005). By introducing distortions in the model, this may allow us to investigate or consider the target “in a new and fruitful way by focusing on the features that the model draws attention to” (Elgin Reference 62Elgin and Suarez2009, 85). And while it does sacrifice some truths for falsehoods, there are other epistemic benefits that the inclusion of falsehoods can provide, such as understanding (Elgin Reference Elgin and Hetherinton2006, Zagzebski Reference Zagzebski and Steup2001). Indeed, a completely accurate representation may hinder understanding because of the complexity of the target, whereas a simplified and distorted model may allow someone to understand the target in a better way because of the simplifications and distortions. For example, a map may be a model of some geographical region, where the simplifications and the distortions allow us to comprehend the terrain or to navigate certain paths, whereas a more accurate map that included the complexity of the region may make it more difficult to understand how to find one’s way.

Weisberg categorizes idealizations into three types: Galilean idealization, minimalist idealization, and multiple-models idealization. Regarding Galilean idealization, he states that it is the “practice of introducing distortions into models with the goal of simplifying, in order to make them more mathematically or computationally tractable” (Weisberg Reference 68Weisberg2013, 99; cf. McMullin Reference McMullin1985). The goal with Galilean idealization is eventually to de-idealize the model in order to acquire more useful information about the target domain or to achieve a more accurate representation (Elliott-Graves and Weisberg Reference Elliott-Graves and Weisberg2014, 177; Weisberg Reference Weisberg2007b, 642). Next, minimalist idealization seeks to incorporate “only the core causal factors which give rise to the phenomenon … [and] contains only those factors that make a difference to the occurrence and essential character of the phenomenon in question” (Weisberg Reference 68Weisberg2013, 100). A common way of engaging in minimalist idealization is abstraction (and this is sometimes labeled “Aristotelian idealization”), which is a “mental operation, where we ‘strip away’ – in our imagination – all that is irrelevant to the concerns of the moment to focus on some single property or set of properties, ‘as if they were separate’” (Cartwright Reference Cartwright1989, 187). By leaving out details, there is less noise, and so one can better focus on the salient (causal) features (Elliott-Graves and Weisberg Reference Elliott-Graves and Weisberg2014, 178). Finally, multiple-models idealization involves the “practice of building multiple related but incompatible models, each of which makes distinct claims about the nature and causal structure giving rise to the phenomenon” (Weisberg Reference 68Weisberg2013, 103; cf. Elgin Reference 62Elgin and Suarez2009, 77). Models may have several goals in representing their target domain, goals such as accuracy, precision, generality, simplicity, and so on. Providing a plurality of models is sometimes best suited in cases where there is no “single best model” when representing a target, and especially when there is no expectation of constructing a single model that is better at meeting every one of these goals than other models (Weisberg Reference Weisberg2007b, 645f.). For example, model A may be more accurate than model B and model C, model B may be more precise than A and C, and C may be simpler than A and B. In such a case, including A, B, and C offers the best way of representing their target rather than providing only a single model. These models, although related insofar as they seek to represent the target domain, may be and often are incompatible with each other, especially since they may emphasize certain features more than another or introduce different types of distortions into their models. But unlike Galilean idealization, multiple-models idealization does not expect to de-idealize, as doing so may lead to a single best model, of which there is no expectation with this kind of idealization (ibid., 646). Moreover, if the target is extremely complex (at least to us), then it is common to find the utilization of multiple-models idealization since it would be difficult to construct a single model that satisfies all the goals or criteria of adequacy that may render one model better than the others. Therefore, a complex system may be best captured by a plurality of models, where some models highlight features that other models downplay, whereas these latter models emphasize other features neglected or diminished in the former models.

Models, then, do not need to strive to be accurate depictions of their target – they should not be understood as “true descriptions of their targets” (Elliott-Graves and Weisberg Reference Elliott-Graves and Weisberg2014, 181) – as they may involve false assumptions given that a model will introduce (or eliminate) features that the target does not have (or does have). The model and the target will have to be appropriately related, and there is a large literature and debate regarding that relationship, a common position being the semantic view whereby models are related to their targets by structure-mapping relations (Suppes Reference Suppes1960, van Fraassen Reference van Fraassen1980, Elliott-Graves and Weisberg Reference Elliott-Graves and Weisberg2014, 181). Whatever the correct view (which won’t be adjudicated here), the relationship between a model and the target cannot be simply based on similarity. A picture being similar to an object does not entail that the picture is a representation of that object, as Hilary Putnam provided a somewhat well-known example of markings created by ants that wind up resembling Winston Churchill (Putnam Reference Putnam1981). Those markings, though looking to us as being similar to Churchill, do not constitute a representation of Churchill. So similarity does not entail representation. And representation need not involve similarity, as the word “table” can represent an actual table and a block of marble (as an abstract sculpture) can represent a famous person. The formal properties of representation and similarity also distinguish the two, as representation is asymmetric and irreflexive (if x represents y, then y does not represent x; and x does not represent x), whereas similarity is both symmetrical and reflexive (Elgin Reference 62Elgin and Suarez2009, 79).

Models, then, need not be evaluated in terms of whether they are true or whether they are accurate or not, for models may introduce distortions that attribute features that are not possessed by the target object. While some models may be more representationally accurate than another, that does not entail that the more accurate model is somehow better than the less accurate one. Rather, a model is evaluated in terms of whether it is adequate for a purpose, where the purpose should be evident either explicitly by the modeler or at least implicitly understood given the aims of the modeler (cf. Parker Reference Parker2020, Bokulich Reference Bokulich2021). To recall an earlier example, a map can be constructed as a model that represents some geographical region. Whether the map is a “good” representation depends on the purpose for which the map was constructed. If someone is seeking to lay out the various freeways, a map that distorts many of the features (by making the freeways look more parallel or perpendicular than they really are) can serve the purpose of navigating the roads. Another map may be created that seeks to represent the districts within a city for schooling or voting purposes. Such a map may be more precise as to the boundaries of some of the features it represents, but it would be odd to say the districts map is better than the freeway map. Whether a map does what it is supposed to do depends on what in fact the map was constructed to do. Now a map may be intended to represent the freeway structure and fail to do it adequately and thereby function as a “poor” map. But these two kinds of maps (the freeway map and the districts map) are not competing models with each other since they are offered to satisfy different purposes. Their evaluation, then, is not in terms of accuracy but in terms of adequacy (for a specified purpose).

Not only have philosophers of science paid attention to models, but recently other philosophers have taken notice of the theoretical strategy of model-building to understand or explain various phenomena (Williamson Reference Williamson, Blackford and Broderick2017). For example, L. A. Paul has argued that while metaphysics has a distinctive subject matter from the sciences, it does not have a distinctive methodology (Paul Reference Paul2012, 3). Metaphysicians sometimes propose theories to explain some puzzling feature, or they engage in conceptual analysis. However, some metaphysical views can instead be understood as models akin to scientific models. Paul suggests understanding some of the thought experiments that metaphysicians have offered as models of hypothetical situations, where such models utilize idealization (Paul Reference Paul2012, 13–14). For another example, Joe Roussos (Reference Roussos2022) suggests that we take normative ethics to involve models and the practice of model-building. Some of the normative theories may be better understood as a model of (normative) reality, whereby these normative theories involve simplifications and other forms of idealization when seeking to represent (normative) reality. Sometimes classical utilitarianism and Kantian deontological ethics are criticized for offering counterintuitive judgments in some scenarios. But if we take these normative theories to be models, then these alleged counterexamples will not automatically refute the theories since models would be understood as involving simplifications and distortions, and so they should not be regarded as having to provide the correct judgment in every case. A model is to be evaluated not in terms of being counterexample-free but rather whether it is adequate for a purpose, where one model may be superior to another by being more useful for the stated purpose. To be sure, I am not endorsing that we take normative ethical theories as models (though I am very sympathetic with taking metaphysical accounts or thought experiments as models of reality or possible reality). I simply note here that the utilization of models and model-building has been growing given the way it can help situate certain philosophical debates and reframe certain philosophical positions.

As we consider the use of models in theology, and particularly as it is applied to the doctrine of the Trinity, some of the solutions in section 2 appear to have been offered as theological models that aim at representational accuracy or approximations to the truth. Under this way of treating theological models, a model of the Trinity may be typically evaluated or assessed in terms of whether it is similar to or like the (tri-personal) God.Footnote ⁵⁰ A model that is a closer approximation than another is supposed to be reason for preferring the former model over the latter. But given the way that models are understood and evaluated in the earlier discussion, this is not the only way to evaluate models. Moreover, given the typical use of idealization in models, emphasis on accuracy or approximations to the truth may not fit well with the standard way of utilizing models.

Additionally, there are theological motivations for eschewing attempts at offering models that are supposed to approximate the truth, especially for those who endorse apophaticism. Indeed, an apophatic approach to God may even render it impossible (or at least extremely unlikely) that one model approximates the truth more than another model.Footnote ⁵¹ For example, take the apophatic view that what we utter about God cannot be both true and fundamental. What we say about God can be true, but it will not carve God at its joints (so to speak). If this is correct, then none of the models of the doctrine of the Trinity will be closer to approximating the structure of God (and that may be especially so if God has no structure, say because of the doctrine of divine simplicity). While models sometimes do employ analogical reasoning, the emphasis on resemblance or similarity or the emphasis on accuracy or approximations to the truth offered in some solutions to the logical problem of the doctrine of the Trinity seems to fit poorly with an apophatic framework. If God is transcendent, ineffable, or wholly other, then focusing on the similarities between the model and the target may lead one astray in seeking to understand God.Footnote ⁵²

With regards to theological models in contemporary debates over the logical problem of the doctrine of the Trinity, the common strategy is to offer models or analogies to show that the doctrine of the Trinity is not inconsistent (cf. Padgett Reference Padgett, McCall and Rea2009, 334).Footnote ⁵³ And the way the debate sometimes proceeds is in terms of whether one model provides a more accurate representation of God than another, or whether one more closely approximates what we take God to be like. And these models or analogies are commonly criticized by way of a counterexample or a disanalogy. If there’s some relevant and significant way in which the model or analogy is unlike God, then we have reason to reject that model.

Yet taking minimalism as our solution to the logical problem of the doctrine of the Trinity, these models are no longer needed for that purpose since a contradiction cannot be derived from (1) to (3), as was argued in the previous section. Minimalism, then, does not require adopting any model or even using the method of model-building to address the logical problem. This may seem to render models as otiose, though that is true only if the singular purpose for these models of the doctrine of the Trinity is to show that the doctrine is logically consistent. But these models can be repurposed in such a way that allows them to provide some benefit or utility in theology and Christian practice. Since models are to be evaluated in terms of adequacy for a purpose (rather than accuracy), we need to specify what it is that a model is seeking to do in order to assess whether it has satisfied that aim. The doctrine of the Trinity is mysterious and difficult to comprehend, even if it does not entail a contradiction. Moreover, it is difficult, if not impossible, to contemplate some of these truths simultaneously. What a model can do, however, is to draw attention to particular features of the Trinity that are worth our reflection and meditation. But it does so by introducing a deliberate distortion via simplification or idealization. Approaching it this way, we would not take the posited features as being applied to God, viz., the target (or being applied to the doctrine of the Trinity, if that is what is taken to be the target).

To make this purpose of models a bit more perspicuous, let us use a contemporary theological model of the Trinity, such as Leftow’s Latin trinitarian model that utilized the time travel case. For Leftow, he uses strict identity in the relevant claims in (1)–(3) as well as the predicates “is a mode” or “is a Lockean (event-based) person” (Leftow Reference Leftow, van Inwagen and Zimmerman2007). Now the doctrine of the Trinity does not demand that we use strict identity or that we analyze divine persons as Lockean persons (otherwise, the doctrine of the Trinity would be too metaphysically demanding). Indeed, we may go even further and say that it is false that the divine persons are Lockean persons. However, Leftow’s model allows us to appreciate the unity or oneness of God. While the model is logically consistent, it does not show us that the doctrine is logically consistent (for given minimalism, we would not take Leftow’s paraphrase as being logically equivalent to the original claims). This distortion, however, affords contemplation and reflection on what divine unity might look like, and we can imagine a story about God as having that kind of unity via the model that Leftow proposes.

Consider another model of the Trinity, such as Hasker’s social trinitarianism (Reference Hasker2013). He analyzes the divine nature as being concrete, posits three separate wills and powers (or the persons as centers of consciousness), and employs the predicate “is constituted by” in his model. We can repurpose this model such that we need not take it to be the case that in God there really is a constitution relation or that there really are three separate wills and powers. Rather, we may take these as false assumptions or as deliberate distortions. Yet doing so may help us appreciate and reflect on the threeness of the divine persons and their relationship to each other. Accepting the doctrine of the Trinity should not demand that we accept the existence of a constitution relation, especially given how contentious such a relation is (cf. van Inwagen Reference van Inwagen2002).Footnote ⁵⁴

A common criticism of these two models in the extant literature is that Leftow’s view veers too closely to problematic forms of modalism (Hasker Reference Hasker2009b), whereas Hasker’s view leans too closely to tritheism (Tuggy Reference Tuggy2013b). But if we are not taking these models to be approximations of what God is actually like but rather treating them as deliberate distortions or idealizations in order to represent God in a way that helps us appreciate or meditate on a certain aspect of God, then we do not have to worry whether they collapse into heresy, since we are not taking God to be exactly like the model. Such criticisms are not apt since the modeler can agree that this is not what God is actually like, and the model is not suggesting that God is actually like that. Moreover, both models afford the opportunity to reflect on God, but they emphasize or spotlight different features. These models may include metaphysical and logical commitments, some of which end up attributing some object (e.g., God, the divine nature, and the divine persons) in the target domain as having features that it does not really have. For example, we can imagine God as consisting of three divine persons with three different powers or wills, which may help us conceive of the interpersonal dynamics between the divine persons. But we may take it to be strictly speaking false that God has three different powers or wills. Yet reflecting on this model allows us to appreciate the distinctness in God, even if we cannot specify what kind of distinctness – whether strict, real, formal, relative to a particular sortal, and so on – is actually at play between the divine persons.

Moreover, I propose that we understand modeling the doctrine of the Trinity as utilizing a multiple-models approach to idealization. We will not be able to regard these models as Galilean models, even though they do introduce distortions and simplicity, since there is no intent of de-idealizing these models. Nor should we take these models as minimalist idealizations or abstractions, since we are not seeking to remove features from the target to get to an underlying (causal) core. With multiple-models idealization, however, we do not expect there to be a single best model of the doctrine of the Trinity. Some models may be better at capturing the threeness of God (such as Hasker’s), and other models may be better at capturing the unity or oneness of God (such as Leftow’s). Some models may be better at representing how the divine persons share the same nature, whereas other models may be better at representing how a divine person possesses a distinguishing feature such as a personal (relational) property. And some models may be better at representing the divine nature as concrete, whereas other models may be better at representing the divine nature as abstract.Footnote ⁵⁵ Rather than seeking to adjudicate and single out a victor among the models, we might prefer a plurality of models, each of which helps represent some aspect of God such that having multiple models provides a better (collective) representation of God than a single model would.

By construing these solutions, thought experiments, illustrations, analogies, and the like as models in the technical sense, the nature of the debate between the various approaches to the doctrine of the Trinity will be significantly altered. As noted, criticizing a view for falling into a heresy may not apply since the model need not attribute a genuine feature onto God nor import a metaphysical or logical commitment onto the believer of the doctrine of the Trinity. Moreover, sometimes a counterexample is provided against one of the solutions, which is a typical move to make in philosophical debates. But those philosophical frameworks that focus on models and model-building change the nature of the discussion and debates. As Timothy Williamson states with regards to model-building more generally in philosophy:

In metaphysics and normative ethics (and other philosophical areas), it is common to offer counterexamples to conceptual analyses or (metaphysical or ethical) theories; but as mentioned earlier, the reframing of those debates in terms of models and modeling makes the proposals less susceptible to counterexamples (Roussos Reference Roussos2022, 3). Similarly, an alleged counterexample to a trinitarian model, then, is not by itself a reason to think that the model is a failure, for the counterexample is usually offered to show that the proposal does not accurately represent the target. But the criteria of success for models depend on the purpose for which they are being constructed. And if the aim is to spotlight or draw attention to a particular feature of God, even if it involves some distortion and idealization, then the presence of a counterexample as such does not provide a reason for rejecting the model. Indeed, the project of theological modeling will eschew the program of providing counterexamples but rather emphasize the activity of constructing models that do a better job of satisfying the purpose for which the model was intended.Footnote ⁵⁶

By adopting multiple-models idealization (such that there is no single best model), the minimalist can retain many (if not all) of the extant models – appreciating the different ways they represent God, whereby we may come upon some insight or expand our theological imagination by having more than one model. This reframing does allow for some competition between these theological models, as some models may be better than others at satisfying the purpose for which they were constructed.Footnote ⁵⁷

Moreover, the theological debates may not be over whether a counterexample can be raised but perhaps shifted over to disputes concerning which theological sources we ought to take as authoritative. For those who reject the authority of the ecumenical councils, it may not be off-putting to deny the eternal processions or to deny that the divine nature is concrete (if that is indeed a commitment from the conciliar pronouncements). The theological debates may also be over whether to prefer minimalism or minimalism+, or over which version of minimalism+ we ought to embrace. Hence, there is plenty of theological debate left to have.

Understanding the solutions as model-building reframes the extant debate between the different solutions to the logical problem of the doctrine of the Trinity. We do not need to take these views as competing with each other. Rather, we can understand them as serving different but related purposes, such as representing God but spotlighting or drawing attention to a certain feature in the doctrine of the Trinity. Moreover, the purposes may not be solely for epistemic goals such as understanding or insight. Another goal may be for contemplative or devotional purposes. For those of us who believe in the doctrine of the Trinity and who actually worship the God that the doctrine is about, we do not take the doctrine in a detached, disinterested way. As Thomas McCall states regarding the task of trinitarian theology, “the doctrine of the Trinity is about so much more than [solving the logical problem] – it is about contemplation, personal communion, transformation … Trinitarian theology is not about solving a problem – it is about worship” (McCall Reference McCall, McCall and Rea2009, 347). William Wood has also addressed charges against analytic theology more generally, and he has proposed the practice of analytic theology as involving reflection and meditation, as well as awe and wonder at the God we worship (Reference Williams2021, 122). Attending to different models of God can involve such awe and wonder, as we realize that even our attempts to represent God demonstrate the uniqueness and radical otherness of God.

As I have suggested elsewhere, we can take these models to be akin to icons – artworks that are constructed for devotional purposes (Yang Reference Yang and Rutledge2023). But unlike physical icons, these models of the doctrine of the Trinity are conceptual icons. Both in the making of and in the appreciation of these conceptual icons, we can marvel at the God who has revealed things about God’s self – viz., (1)–(3) – truths that are mysterious to us since there is still so much we do not know, such as how to analyze the divine nature, the divine persons, or what the relation is between a divine person and the divine nature. These models make the mystery more pronounced while also allowing us to imagine creatively what God may be like – all the while fully aware that God is not like the way we are picturing God.

By framing the project in this way, we avoid these worries that analytic theology involves either demystifying the doctrine of the Trinity or simply conceiving of it as a problem to be solved. Since minimalism provides reason for not regarding (1)–(3) as being logically inconsistent, the purpose of constructing theological models is not to solve the problem via “logic-chopping” but to allow us to appreciate certain aspects of God, allowing us to marvel and wonder at the mystery of God. This framing also helps us avoid another concern about the philosophical discussion over the doctrine of the Trinity as articulated by Beau Branson:

If the models seek to be paraphrases of (1)–(3), then Branson’s charge applies to many extant solutions and the models they employ (consider the variety of metaphysical tools brought into the discussion to address the issue: relative identity, hylomorphism, constitution, immanent universals, event-based persons, extended simples, parthood, powers, etc.). However, if the models are offered to draw attention to certain features for devotional purposes, then we can welcome more models that employ various ontological or ideological tools. We do not typically object when someone creates another painting of an object for which there are already many paintings. Similarly, by taking models as conceptual icons or artworks, we can welcome other theological models that help us appreciate and stand in awe of the God Christians worship. Moreover, minimalism does not succumb to Branson’s charge because no metaphysical innovation or novel concept is being introduced into the doctrine, for no paraphrase or additional metaphysical or logical commitment is being foisted onto the claims.

Some may worry that by creating models that distort the target such that it represents it as having features that it in fact does not have, we may be forced into an anti-realist position concerning God. Some may not balk at that suggestion, and some may be willing to take theological models as being hypothetical or targetless (cf. Wood Reference Wood2016, 56). My own proclivities are strongly within a realist camp. God is not merely my conception or representation of God. There is something actually out there, independent of my conception of it. However, our representation of God via a model will involve distortion and idealization. Yet even within the sciences, idealization does not imply anti-realism (Weisberg Reference Weisberg2007b, 657; Elliott-Graves and Weisberg Reference Elliott-Graves and Weisberg2014, 182; Elgin Reference 62Elgin and Suarez2009, 88). Scientists offer false models that seek to represent some actually existing object, which has some characteristics independent of the scientists’ conception of it. And it should be made clear that the believer in the doctrine of the Trinity believes in (1)–(3), and those statements (for realists) do make substantive metaphysical claims that have to be believed. It is true that there is one God, and it is true that there are three divine persons. But it is not true (or need not be true) that the divine persons are constituted by the divine nature, that the divine persons are Lockean-persons, that the one God is composed of the divine persons, that the divine persons are numerically the same but not identical to the divine nature, that the divine persons are really distinct from each other, or whatever other claim that is being made in some theological model. So one can maintain a realist framework in theology without taking the models as approximations to the truth of the matter.

In this Element, I have offered minimalism as a way of addressing the logical problem of the doctrine of the Trinity. It also allows us to read the doctrine of the Trinity in a straightforward way – there is no tricky paraphrase or reinterpretation that is required to understand (1)–(3). A nonacademic believer in the doctrine of the Trinity can believe in it coherently without learning metaphysics or advanced logic. And the solution retains mystery in the doctrine – we still do not know what the divine nature is, how to analyze the divine persons, or how to understand the relation between the divine persons and the divine nature. Yet the doctrine says just enough to rule out those positions that have been deemed as out of bounds by Scripture or church tradition (and for those who put more authoritative weight on some of the creeds and councils, we can opt for minimalism+, which offers the same type of solution in avoiding contradiction).

Moreover, by taking a more precise approach to models and model-building as advanced in this section, minimalism need not eschew all of the models that have been developed in the extant discussion. Rather, it can retain many (if not all) of the models proposed so far, repurposing them to help us gain some theological insight or deeper appreciation of certain aspects of the Trinity. While many in these debates reject rival models to their own, the minimalist can incorporate these various models, especially given a multiple-models approach where no single model will be the best. Taking all of them together helps us appreciate the target more. Thus, minimalism does not have to close the discussion on offering theological models of the Trinity but can invite further models, especially those that highlight some feature which may lead us to stand in awe of the God that our model represents. God is much more awesome and much more mysterious than our models can show.