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Metaphysics and Logic of the Trinity

Abstract and Keywords Recent work by analytic philosophers on the Trinity takes a mysterious 5th-century document as its starting point, accepting widespread but inaccurate narratives about the history of Trinity theories. This article summarizes the Platonic influence on ancient theologies and describes the rise of transcendent triads, and eventually the idea of a tripersonal God. Recent Trinity theories (positive mysterianism, Trinity monotheism, relative-identity approaches, and “social” theories) are explained as built to respond in various ways to a type of anti-trinitarian argument. But since each recent application of logic and metaphysics to the theology of the Trinity is problematic, it is argued that another look at the minority unitarian report is warranted. Keywords: Trinity, God, metaphysics, logic, monotheism, theology, trinitarian, unitarian, relative identity

1. A Mid-5th-Century Starting Point Recent analytic philosophers and theologians have in almost all cases approached the Trinity as a problem defined by the so-called “Athanasian” creed. This famous statement is now believed to be by an unknown mid-5th-century clerical author who had been influenced by the writings of Augustine of Hippo (354‒430 a.d.). Pleasantly short and bracingly paradoxical, it cries out for logical and/or metaphysical clarification.1 This focus has caused several blind spots in the recent literature of analytic theology. For one, it is not clear that this creed accurately summarizes the statements from the officially recognized councils at Nicea (325 a.d.) and Constantinople (381 a.d.). These are puzzling but not as immediately paradoxical. If the Son and Spirit are “one substance” or “one essence” (Greek, homoousion) with God the Father, making each of them “true God,” that is interesting to be sure, but it does not immediately seem inconsistent with the traditional monotheistic declaration that each creed begins with: “We believe in one God the Father all powerful.”2 The claim seems to be about the origin and consequent qualities of the Son and Spirit; these creeds do not clearly imply the numerical identity of Son and Spirit with the “one God the Father,” and so do not generate incoherence from the evident assumption that Son and Spirit are numerically distinct, both from the Father and from one another. It would seem that in addition to the one god, there are two others who can be called “God” and even “true God” because, it would seem, of their origin in and similarity to the one god, the Father. In contrast, the “Athanasian” creed seems to assert unique qualities of each of the Three, and also that each is (among other things) eternal, and then asserts that “there are not three eternals, but one eternal.”3 It thereby seems to assert both that there are three eternal (etc.) beings (because each is eternal and also has a quality which nothing else has), and also that there is exactly one. Hence, the famous put-down by the Anglican minister Stephen Nye (1647/8‒1719) that this “is an error in counting or numbering, which, when stood in, is of all others the most brutal and inexcusable; and not to discern it, is not to be a man.”4 Second, analytic philosophers neglect both the content of those councils’ creeds and the processes of reasoning and controversy which led up to them. Their formulas are merely accepted as a majority report, hoped to be well thought through and not unduly warped by merely cultural or political forces.5 Third, analytic philosophers nearly always neglect pre-Nicene catholic theologians. They simply have not spent the energy working through the arguments of Justin, Origen, Tertullian, or Novatian that they have spent on, for example, Hume, Descartes, or Aristotle. This is surprising, given the philosophical interests of these early catholic intellectuals, as well as their central concerns with God, Christ, and how they are related. Fourth, they unfortunately repeat the historical mistakes of Christian apologists and theologians. One recent treatment falsely asserts that “From the beginning, Christians have affirmed the claim that there is one God, and three persons—Father, Son, and Holy Spirit—each of whom is God.”6 This is an anachronism arising from the misguided narrative that mainstream Christianity has always been trinitarian (i.e., always believed in a tripersonal god), only developing in how (i.e., in what terms) it expressed this belief. Fifth, analytic theologians nearly always neglect how one might reason from the Bible to the Trinity. Although they would never trust, for example, historians to tell them what Aristotle or Aquinas really thought, in contrast, when it comes to the Bible, many Christian philosophers simply accept the authority of whoever they consider mainstream scholars. But such do not speak with one voice. Many conservative Protestant theologians hold the teachings of the Bible to logically imply the Trinity formulas. In contrast, many textual scholars, theologians, and historians deny this; it would, they are convinced, be an anachronism to read any occurrence of “God” in the Bible to refer to a triune deity composed of three co-equal, essence-sharing “Persons.” A more promising approach would be to argue that the Trinity formulas are not implied by, but nonetheless best explain what the Bible does and does not say. But many early modern and recent Roman Catholic scholars have thought it hopeless to argue for the Trinity from the Bible alone; this, in their view, shows the need for the authoritative teaching and post-biblical traditions of the Church. Against all of this, the unitarian Christian minority report has argued that the Bible doesn’t imply the Trinity formulas, nor do those formulas best explain the contents of the Bible, for the two are logically incompatible. The Bible, they argue, assumes and asserts the numerical identity of the Father of Jesus, and no one else, with the one true God.7 While the Bible, unitarians argue, is all about a unipersonal god or a perfect self, trinitarian traditions make God out to be tripersonal. Finally, recent analytic Christian philosophers usually uncritically assume that most opposition to Trinity doctrines arises from epistemic scruples and/or moral vices. A popular 4th-century catholic argument, revived in modern times by John Henry Newman (1801‒1890), is that non-trinitarians are proud, unspiritual “rationalists,” who arrogantly refuse to believe what they cannot understand, foolishly assuming that God can be understood, or fully understood, by puny human minds.8 But to the contrary, opposition to Trinity theories has always been primarily text-based, that is, based on convictions that what the Bible teaches is incompatible with Trinity theories and/or is better explained by some unitarian theology. A number of early modern sources address the “rationalist” accusation and reply that they will accept any “mystery” which divine revelation truly demands.9 A mystery, whether this be an apparent contradiction or a confusing and hard to understand claim, may be thrust upon the Christian by her sources, or by her own speculations. In the latter case, the obvious solution is to reconsider one’s theories. And they add that no scriptural author appeals to “mystery” to defend a problematic theoretical claim.10 One hardly has to be a “rationalist” to think it problematic for a theory to be apparently incoherent or inconsistent with what it purports to explain; any trinitarian analytic theologian always rejects rival Trinity theories on the grounds that they seem, in the end, incoherent and/or inconsistent with other traditional teachings or evident truths.

2. From Plato to the trinities The metaphysics of the Trinity traces ultimately back to Plato (424/3‒348/7 b.c.) and runs through various later trinities or triads. One of his most influential dialogues has been his Timaeus, which contains an original myth about the creation of the cosmos.11 This myth applies his famous theory of “ideas” or “forms” (what came to be called universals). In this “likely account” the eternal god who made the cosmos, the “Demiurge” or craftsman or maker (Greek, demiurgos) fashions a living, self-sufficient, spherical cosmos, consisting of body and soul, a “blessed god” which contains all other bodily life (the divine stars, the divine earth, and the inhabitants of air, earth, and sea) and the usually invisible living beings (the spiritual beings, Greek, daimones, the offspring of the gods). But he did not make the bodily creatures directly; rather, he charged these last, the gods, with making them, for “if these creatures came to be and came to share in life by my hand, they would rival the gods. It is you, then, who must [make them]…. This will assure their mortality.”12 This Craftsman, the “Father who had begotten the universe,” made it temporal, and in so doing created time, but he used a model which was itself a timeless “Living Thing,” which the reader surmises is supposed to be the totality of the forms, understood (or imagined) to be a single, eternal, living being. These forms the craftsman in some sense combines with a sort of featureless receptacle, something like matter, thereby imposing order and proportion on it.13 In later centuries, wherever platonic philosophy was influential, so was its assumption that the creator needed some sort of go-between to interact with his material creation, that an unmediated interaction between the creator and the cosmos is metaphysically impossible. This idea is prominent both in the Alexandrian Jewish thinker Philo, a contemporary of Jesus, and in the theology of the early Christian theologian Justin Martyr.14 Elaborating this scheme, in the 1st and 2nd centuries it became popular for platonic philosophers to posit some transcendent triad, three sources of the cosmos, the primary among which is always the ultimate source, with the other two standing between this and the cosmos.15 In the latter half of the 2nd century, philosophically minded Christians too started touting their own triad and coined the words we now translate as “Trinity” (Greek, trias; Latin, trinitas) to refer to it.16 But in light of later developments, this English translation “Trinity” is misleading. The famous Augustine, and many a later trinitarian theologian, uses “Trinity” as a singular referring term for the tripersonal God as expounded by catholic theologies from around 381 a.d. on. In contrast, all uses of trias and trinitas prior to just a few years before that council seem to be plural referring terms, picking out God, his unique Son, and his Spirit (or spirit), without implying these to be one being or one god. This ambiguity of “Trinity” continues to cause confusion today, and theologians often deploy both senses without discerning the ambiguity. This article, following some modern translators of early Christian theologians, uses “trinity” for the plural referring term, and “Trinity” for the singular referring term. Thus, in the late 2nd century, Christians too explicitly preached a trinity of their own, a transcendent triad, but this was not then supposed to be a Trinity (i.e., a god in some sense containing or composed by three equally divine “Persons”). This concern to insulate God from direct contact with the cosmos was also a primary motivation for seeing the pre-human Jesus as active throughout the theophanies of the Old Testament. Starting with Justin, many argued that any seen “God” or “Lord” in those times must have been not God himself, but rather the “Word” (Greek, logos) of John 1, the pre-human Jesus.17 Later catholic theology kept the resulting interpretations, but largely forgot the concern with shielding God from direct interaction with his creation.18 But given how the creeds evolved, property-theories such as the theory of forms (now called realism about universals) have remained relevant. The creeds, after all, claim that there is a property of divinity (godhead, being-a-god) which is shared by three somethings. Trinity theories differ significantly on what they take this shared nature to be, and on the status of the ones who share it.

3. From trinity to Trinity The Christian trinity was supposed to have as its members in some sense divine beings, deities. And yet, these trinity theologies did not depart from the monotheism of the Bible, on which Yahweh, the god of the Jews, and the one to whom Jesus prayed as “Father,” is the unique deity, the “one true God,” creator of the cosmos.19 Whereas the New Testament authors are reticent about applying god terms to anyone other than the Father, by the early 3rd century, mainstream Christians had become comfortable with referring to Jesus as “God,” “a god,” “our God,” and so on. But when challenged on how their theology could be legitimately viewed as monotheistic, early catholic authors always emphasize the unique status of the Father. Various authors of the 2nd and 3rd centuries assert the Father to be literally older than, and greater in knowledge and/or power and/or goodness than any other “god,” and to be the source of all else. The platonic theory of forms introduced another twist. A Christian monotheist must view the one God as the ultimate, so the ultimate reality can’t be any mere form (universal). And as ultimate, this God can’t “participate in” or in any way depend on some other reality, such as the universal divinity. Rather, he must be divinity. And other things which are to some degree divine must “participate in” or “imitate” God, who is the universal divinity, to various degrees. Thus, the Son and Spirit, as divine, get their degree of divinity ultimately from the Father, that is, from God himself. And for some, the Spirit gets his indirectly, by way of the Son. This transmission of divinity was first envisioned as occurring a finite time ago, before the creation of the cosmos, but starting with Origen of Alexandria (c. 186‒255 a.d.), the more popular view became that this divinity transmission is eternal, so that relative to any time (or timelessly) there is a triad of three divine beings, with the second and third ultimately depending on the first for their existence and divine nature/essence.20 In this way, the members of the trinity share the universal essence divinity. It is the result of God (either eternally or a long time ago) as it were producing inferior copies of himself, putting a degree or amount of his divinity into two others. Another major shift that occurred in much catholic theology of the 2nd and 3rd centuries is an intense focus on the pre-existent divine Logos, putting the historical man Jesus largely in the background. Arguments prevailed among many theologians that Jesus’s teaching, miracles, and role in salvation required that he had a divine nature in addition to his human nature. Any view on which Jesus is understood as a man, whether miraculously conceived by a virgin or begotten in the normal way, was polemicized against as making him a “mere man,” and as unspiritual and Jewish. And the primary locus of his saving work, for many, was shifted from his earthly life, death, and resurrection to the event of his incarnation, when this divine Logos somehow became unified with a man, a human nature, or a human body. Christological controversies continued to pop up in various forms through the 7th century, although a type of standard language was enforced from 451 a.d. on.21 This eternal Logos, based mostly on the first chapter of gospel according to John, was held to be the intermediary who was there with God at the time of creation, through whom God made the cosmos.22 This sort of “logos theology” or christology seems to have been controversial in the 2nd and early 3rd centuries.23 It must be remembered that most Christians at the time had little interest in Greek philosophy and did not see any need to shield God from direct interaction with creation. Several reactionary “monarchian” theories opposed these developments. Exactly what these were is obscure, but a main general thrust of them is that there is a divine nature or being at work in the teaching and miracles of Jesus—and this is just God himself, the Father.24 This opposition, for some decades centered in Rome, diminished as logos theologies came to dominate and was eventually outlawed in the Roman Empire from around 380 a.d. on (see below). Earlier logos theologians held to what one scholar calls a “two-stage” theory, on which God’s eternal “Word” (thought, reason, knowledge; Greek, logos) is so to speak externalized or spoken out, which results in the pre-human Jesus coming into existence in order be the direct agent of creation.25 After Origen “one-stage” theories became more popular, on which God somehow timelessly causes the existence of this second divine agent. These different approaches clashed in a controversy between the Alexandrian presbyter Arius (d. 336 a.d.) and his bishop Alexander (d. 328 a.d.), culminating in the first emperor-initiated universal council of bishops at Nicea in 325 a.d. This meeting introduced new and unfortunately vague language, the chief virtue of which was that Arius and his few supporters found it unacceptable. The controversy is often spun as the trinitarian mainstream merely clarifying its terminology in a defense against innovators who denied the full divinity of the Son and Spirit. But recent scholarship has corrected this narrative.26 A part of this is seeing that these bishops were not at all trying to “define the Christian God” or to “express how God is three and yet one.” Rather, they were emphasizing the similarity of Jesus to God, specifying that they shared a single ousia (essence, nature, substance), making them “true God from true God.” This was not then understood to imply that Jesus and the Father were the same god. Rather, they continued the tradition, dating from the 2nd century, of beginning their creed by confessing belief in “one God, the Father all powerful.”27 To many this new formula suggested that God had changed, sharing some of his material substance with the Son, or that the Father and Son were numerically the same being. It thus met with stiff resistance, and the years 325‒380 a.d. are filled with dueling polemical authors and councils of various sizes and degrees of geographical representation, some supporting the new Nicene language as helpful, and others opposing it. The discussion was forcibly ended by emperor Theodosius I, who in 380 a.d. issued a decree damning and declaring his official opposition to the non-Nicene catholics. This was followed by a series of laws that effectively criminalized non-Nicene Christianity. The actual events at the 381 a.d. council have been lost to history. But it is clear that this council, convened by Theodosius and presided over him in his capital city, obediently reaffirmed the 325 a.d. creed, effectively putting it beyond debate as a standard of catholic orthodoxy.28 While officially a reaffirmation, their version also revised it, by implication making the Holy Spirit also homoousion with the Father. In the course of the controversy in the mid-300s, Nicenes had argued from various scriptural and theological premises that the Son must be the same ousia as God, and eventually these sorts of arguments were reapplied to the Holy Spirit. And some began to assume that this equality of status made the three the same god. Jewish monotheism was denounced as an erroneous extreme, the opposite of the polytheistic error, with the new trinitarian theology a happy medium between them. From this time Trinity theories dominate the Christian mainstream; truly trinitarian theology (which affirms the one God to be the Trinity) dates from this time (the late 370s or early 380s). The unitarian minority report has repeatedly resurfaced, especially since the Protestant Reformation.29 But insistence on creedal Trinity language has mostly held firm, especially the creeds of 381 and 451 a.d., with another, less popular source being the aforementioned “Athanasian” creed. Most recent theologians, be they Roman Catholic, Eastern Orthodox, or Protestant have neither considered changing this traditional language nor much concerned themselves with clarifying its meaning, although individuals continue to speculate on the subject. It is only Christian analytic theology, employing logic, metaphysics, epistemology, and a sober, careful style of argumentation, which has carefully explored several ways in which this traditional language might be understood. The subject is thought to be intrinsically important, but apologetic aims have also loomed large, it being a commonplace of Christianity’s modern despisers that its trinitarian theology is patently incoherent and/or unintelligible. To explore some of these recent Trinity theories, we will consider a sort of argument which any Trinity theory constructed by a recent analytic theologian has been designed to survive. Like the writers in the literature, its jumping off point is the “Athanasian” creed.

4. An Argument against the Trinity This argument renders traditional trinitarian language into precise claims using the tools of logic, with an aim toward showing some central problems any Trinity theory must solve. Similar arguments have been used by analytic theologians as anvils on which to forge their own Trinity theories. We will use it as a way to explore a Christian’s options for understanding the Trinity in a self-consistent way (table 1). Table 1 An Argument Against the Trinity Claim Logical Translation Semi-Logical Translation Justification 1. The Father is divine. Df The Father is divine. premise 2. The Son is divine. Ds The Son is divine. premise 3. The Father and Son have differed. ƎP ((Pf ^ ¬Ps) v (¬Pf ^ Ps)) There’s some feature P such that either the Father has had it while the Son lacked it, or vice versa. premise 4. Things which have differed are non-identical. ∀x∀y(ƎP ((Px ^ ¬Py) v (¬Px ^ Py)) → ¬(x = y)) For any x and any y, if they’ve differed in some way, then x and y are distinct (non-identical). premise 5. Therefore, Father and Son are non-identical. ¬ (f = s) It is not the case that the Father just is the Son. 3, 4 6. For any two (or “two”) things, they are the same god only if each is divine, and they are identical. ∀x∀y (S(x,y) → (Dx ^ Dy ^ x = y)) For any x and any y, if x and y are the same god, then x is divine, y is divine, and x just is y. premise 7. Therefore, the Father and Son are not the same god. ¬S(f,s) It’s not the case that Father and Son are the same god. 5, 6 8. Therefore, there are at least two gods. Ǝx (Dx ^ Ǝy (Dy ^ ¬(y = x))) There is some x which is divine, and there is some y which is divine, and x and y are not numerically the same. 1, 2, 7 9. There is exactly one god. Ǝx (Dx ^ ¬Ǝy (Dy ^ ¬(y = x))) There’s some x which is divine, and there is no y which is divine and distinct from x. premise 10. But this is contradictory. 8, 9 11. Therefore, one or more of these is false: 1, 2, 3, 4, 6, 9. ¬1 v ¬2 v ¬3 v ¬4 v ¬6 v ¬9 1‒10 While a trinitarian may dispute what is in the second and third columns, nearly all will grant that this argument is valid. That is, if each premise is true, then the other steps must be true as well (5, 7‒8, 10‒11) But this arguably would imply the falsity of any trinitarian theory. Why accept each premise? Premises 1 and 2 are implied by the “Athanasian” creed, which seems to imply that the Father and the Son each have every attribute required for being divine, such as omnipotence, eternality, and being uncreated. Premises 1 and 2 are also implied by the central claims of the 325 and 381 creeds, that Father and Son are one ousia, making them one “true God” (Son) who is eternally from another who is “true God” (Father). Premise 3 is implied by the New Testament and by any trinitarian theology. The Father sends his unique Son to save the world, but Jesus does not do that; Jesus doesn’t send his own Son into the world. And for most trinitarians, the Son is, but the Father is not “eternally generated.” Again, the Son is incarnate and lives as a man, but the Father is not and does not, according to mainstream Christian theologies. Premise 9 is uncontroversially a part of trinitarian theology; trinitarianism is supposed to be the uniquely Christian variety of monotheism, the thesis that there is exactly one god.30 This leaves only premises 4 and 6. Each is plausibly thought to be self-evident, something that any normal adult human knows to be true immediately upon understanding the claim, and so something which is fair to include in any argument. Premise 4 is often called the indiscernibility of identicals or the difference of discernibles. It is based on the conviction that nothing of any possible sort can be and also not be some one way at a single time (or timelessly). Thus, if we’re discussing some a and some b and we don’t know whether they are two or one (so that “a” and “b” co-refer), we can decisively show them to be two by finding out that at any time a has been some way and b has not, or vice-versa. Even the mere metaphysical possibility of their differing implies that they are two, that a is not numerically the same as b and vice versa. It is difficult to argue for this principle using premises that are more evident, but the principle is widely employed in recent analytic metaphysics, and arguably enjoys an epistemic status comparable to “If a is larger than b and b is larger than c, then a is larger than c.” Premise 6 follows from a widely accepted analysis of statements of numerical sameness. The idea is that for any a and b, if they’re the same thing of some sort, then a is a thing of that sort, and b is a thing of that sort, and the one just is the other (a and b are numerically one). This analysis is accepted as obviously true by most analytic philosophers, but as we’ll see below, some deny it. About the words “god” and “divine,” this argument assumes it to be an analytic truth (something true by virtue of the meaning of the terms involved) that to be divine is to be a god, and to be a god is to be divine, just as to be human is to be a human being, and to be a human being is to be human. As we’ll see, some theorists deny this equivalence in the meanings of “god” and “being which is divine.” Here then, is the problem. Unaided human reason, quite apart from any theological concerns, seems to demand our assent to both 4 and 6. And trinitarian traditions seem to demand 1‒3 and 9. But the rest follows. This group of claims is self-contradictory, and they can’t all be true. And the principles based on reason (4, 6) seem innocent. But if they are, then some claim essential to trinitarian tradition must be denied; at least one of 1‒3, 9 is false. Either the Father is not divine (1 is false), or the Son is not divine (2 is false), or the Father and Son have never differed in any way (3 is false), or monotheism (9) is false, or more than one of these claims are false.

5. Analytic Trinity Theories as Refutations of the Argument All contemporary analytic Trinity theories are designed to show what is wrong with arguments like the one in section 4. We will sort them by which premise(s), if any, they deny. Outside the realm of analytic theology, these concerns are widely avoided and ignored. Or a theologian may gesture unclearly at one or more options. But the analytic theorists generally understand the price(s) they’re paying for a coherent Trinity theory, and generally own up to any difficulties the payment may produce. 5.1 Positive Mysterianism A clear if unpopular response is to affirm a subset of the argument in section 4, steps 1‒9, as a sound argument. It is admitted that the commitments of trinitarian theology appear to be incoherent (self-contradictory), but it is insisted that we are dealing with merely apparent contradictions. The idea is that God has revealed these truths, and knowing this, we ought to affirm them all, because they must be coherent after all, though we have no clue how.31 There must be in equivocation in the terms of the claims somewhere, an equivocation which if removed would reveal how the claims are mutually consistent after all. But we’re unable to determine what this equivocation is. What we would initially take as a sign of theoretical failure (apparent contradictions), we should instead take as a sign that we really are accessing a reality which far outstrips our mental abilities. Such confusions, when it comes to the case of God, are to be expected, and it would be proud or overconfident for us to suppose we can think about the transcendent God without being mired in apparent contradictions (paradoxes, mysteries). Further, don’t we employ this sort of reasoning in the case of physics? This proposal can be attacked on epistemic grounds.32 But we should reflect on why this strategy is so unpopular with analytic theologians. It is not because analytic philosophy makes people foolishly confident in human powers of speculation. Rather, analytic philosophy has many resources which can be deployed to remove apparent contradictions from a theory, and it seems premature to declare that any such will fail, leaving us only with a mysterian defense. While many an analytic theologian falls back eventually on the point that some element of “mystery” (apparent incoherence) seems unavoidable when it come to the Trinity, few make this the main thrust of their defense. In practice, this sort of mysterian defense arguably amounts to a counsel of serially inconsistent thinking. Is there only one god, or are there at least two? When reading biblical statements of monotheism, the mysterian will think there is exactly one. And then, he’ll note that both Father and Son are divine, and that they are numerically two, so that there are at least two gods, two divine beings. And then, eventually, we come back to monotheism, and the cycle begins again. The mysterian assurance that there must an equivocation somewhere in the terms of premises 1‒9 gives the Christian believer nowhere to rest her mind. Nor is the mysterian’s counsel to suspend judgment on the matter. So the believer is left to flap in the winds of confusion, now thinking P, and then thinking ¬P, and then back to P again. This confusion seems a high price to pay to “preserve the mystery” of the Trinity, and it seems an Achilles’ heel for trinitarian theology as it competes with its rivals. Further, many a traditional, non-pluralistic Christian must admit that she would wield an apparent contradiction like this as a bludgeon against theories in any other religion, such as Islam, Buddhism, Hinduism, Daoism, and so on, and even against “heretical” views in or near the Christian camp. Thus, the positive mysterian seems to be special pleading, claiming as a virtue for her own cherished theory what she would denounce as a deficiency in anyone else’s theory. 5.2 Denying Premises 1 and 2: Trinity Monotheism Recall that in our argument, to be “divine” just means to be a god. But a trinitarian by definition says that the one god is the Trinity; the only god is the tripersonal god. But neither the Father nor the Son is the Trinity. Thus, trinitarian theory points one in the direction of denying premises 1 and 2. And denying just one of those is sufficient to escape the incoherence; happily, one may then grant that premises 3, 4, 6, and 9 are obvious truths. If the creeds are insisting on the essential equality of Father and Son, then they must be essentially divine in the same sense. But this can’t be the same sense in which the one god is divine, otherwise there would be multiple gods. Thus, there are two senses of “divine,” one in which God is “divine,” and another sense in which the “Persons” of the Trinity are “divine,” and this latter sense doesn’t imply being (identical with) a god. This strategy of “Trinity monotheism” has been developed by William Lane Craig.33 This theory has the Father and Son being “divine” not in the sense of being a god, but rather in the sense of being something like parts of the one God, which is the Trinity. Only the Trinity is “divine” in the sense of being a god. The “Persons” of the Trinity are described as “minds” or “centers of consciousness” in the one soul which is the triune god. Craig discards the traditional claims that the Father “eternally generates” the Son, and that the Spirit eternally “proceeds” from the Father (or from him and the Son). He does this because such claims are arguably not at all supported by any biblical texts, and because they seem to compromise the equality of the Persons, as the Father but not the others, given generation and procession, exists a se, independently of anything else. While Father and Son are equal to one another on this scheme, neither is divine in the highest sense. Thus, the theory has been criticized as “Arian” because it requires levels or kinds of divinity.34 It is also hard to see how it can be consistent with the creedal claims that there is “one God the Father all-powerful,” or with the statements in the gospel of John that the one God is the Father, or with creedal statements that Father and Son are each “true God”—seemingly, god/divine in the highest sense of the terms.35 Further, the theory is not as developed as some of its rivals below. It is particularly hard to grasp just what the metaphysical status of the “Persons” is supposed to be. 5.3 Denying Premises 1 and 2: Concept-Relative Monotheism Einar Duenger Bøhn denies premises 1 and 2 on the grounds that “God is identical with the Father, the Son, and the Holy Spirit collectively, but not each one of them distributively.”36 The idea is that the same “portion of reality” can equally well be conceptualized as a single God, or as three divine persons, but due somehow to the objective structure of that portion, not as, say seventeen divine persons or two gods.37 This theory requires that the numerical identity relation can be one-many (e.g. your body just is the plurality of your head, torso, arms, and legs) and not only one-one (e.g., you just are you) or many-many (e.g., the four men who robbed the bank just are the four men now in that jail). The only obvious motivation for believing in one-many identity is the unpopular metaphysical thesis that the numerical identity relation just is the composition relation, the relation between parts and wholes.38 But the trinitarian tradition has always rejected the interpretation of the Trinity as the one God being a whole composed by three parts, the Persons. 5.4 Denying Premise 3: Oneness Theologies Premise 3 is implicitly denied by present-day “Oneness” Pentecostals, who collapse Father and Son into one self-identical (numerically one) being. But so far no analytic theologian has made this move, because the differences between Father and Son seem undeniable on any plausible Christian theology, and because the other solutions seem to exact a lower price. 5.5 Denying Premise 4: Geachian Relative Identity Theory Few analytic theologians have denied premise 4, recognizing that it is merely an application of a self-evident truth which is relied upon in other areas of philosophy, and arguably also in everyday life, and in other fields of inquiry. A few who have denied or not affirmed premise 4 have done so because they hold that statements involving numerical identity (or “absolute” or non-relative identity, expressed by the symbol “=” in our argument) are incomplete and unintelligible, and so are not capable of being either true or false. Their main idea is that it is not a complete thought that some a and b are “the same” (full stop). Rather, we can intelligibly ask whether or not a and b are the same man, the same planet, the same dog, the same god, and so on. Identity relations, they hold, must be understood as relative to a “sortal” term.39 Whether are not there are irreducible relative identity relations, most philosophers insist that it is intelligible to ask whether or not some a and some b are “the same,” that is, the same being or same thing, so that the terms “a” and “b” either do or don’t co-refer.40 Everyone admits that it is intelligible to ask, for instance, whether or not Paul and Saul are the same man. But most understand this to employ the concept of non-relative numerical identity, according to the analysis assumed in premise 6 and discussed in section 5.6. No philosopher has ever given an uncontroversial example of things which are the same F but different Gs; there are no uncontroversial or even widely accepted examples of things related by only relative identity and not also by absolute identity.41 5.6 Denying Premise 6: Constitution Trinitarianism Premise 6 follows from an analysis of numerical sameness statements that is widely accepted in philosophy: for any a and b, if they are the same F, then a is an F, and b is an F, and a = b. For example, Paul and Saul are the same apostle only if Paul is an apostle, Saul is an apostle, and Paul just is Saul (and vice versa). On this analysis, being the same F (being in an F-relative identity relation) just amounts to three facts: Fa, Fb, and a = b. And if a and b are different Fs, this means that a is an F, b is an F, and ¬ (a = b). Thus, sortal-relative sameness and difference really just turn out to be cases of absolute, non-relative numerical sameness and difference. If this is correct, then there can never be a case where some a and some b are the same F but different Gs, since their being the same F would imply a = b, and their being different Gs would imply that ¬(a = b). How, then, can anyone reasonably deny premise 6? Some admit that the only reason to deny premise 6 is to show how the sentences of the “Athanasian” creed may possibly be coherent.42 This strikes most people trained in philosophy as backwards. We should develop and defend our theology by using our most basic and unshakeable convictions. But it seems too much for a controversial theory to cause us to deny truths which seem obviously correct in any other context. It’s hard to imagine, for example, some alleged divine revelation making it reasonable for us to deny that 2 + 2 = 4, or that if a = b and b = c, then a = c. But as philosophers Michael Rea and Jeffrey Brower have shown, there is a realm of contemporary metaphysics which may be argued to motivate a denial of premise 6: the metaphysics of material constitution.43 They ask us to consider a statue which is also a load-bearing pillar in a building. They argue that the statue and pillar are non-identical, as they differ. (This is an application of our premise 4 above.) While they share their current properties such as mass and shape, arguably the pillar could, but the statue could not survive being sanded smooth. Again, the pillar might have come into existence before the statue was carved, or vice versa. But if it’s possible that one should exist without the other, they must be distinct (non-identical). Rea and Brower urge that the statue and pillar are nonetheless to be counted as one material object, although they are different form-matter compounds. This is to say that both statue and pillar are “constituted by” some portion of matter. Thus, it is argued that in the realm of material objects, some a and b can be the same F while being different Gs. Perhaps, then, we can doubt premise 6 in our argument. Perhaps the Father and Son are the same god, but different persons, if for each to be divine (as premises 1 and 2 assert) is for each to be constituted by something akin to matter. As a certain batch of matter simultaneously constitutes both the statue and the pillar, so similarly the divine nature eternally constitutes both Father and Son. Logically, the solution is neat: we’ve been given a non-theological reason for thinking that things can be the same F but different Gs, which may cast doubt on premise 6. Perhaps the Father and Son are related in a way that requires the falsity of premise 6. We’ve arguably been given an intelligible model or analogy to help us to think about the Trinity. Father and Son are to the divine nature as the statue and pillar are to that portion of matter which simultaneously constitutes both. The account has not been widely accepted, though. Many philosophers just do not grant that things may be “numerically one” without being identical. And it’s been objected against any claim that some a and b are the same F but different Gs that it is inconsistent with the truth of this general principle: If every F is a G, there are at least as many Gs as there are Fs.44 For example, if every one of Bob’s pets is a cat, then Bob has at least as many cats as pets. Thus, if every divine person is a god, then there are at least as many gods as divine persons. We are urged to deny this, as the case is similar to this one: if every form-matter compound (e.g., the statue, pillar) is a material object, then there are at least as many material objects here as there are form-matter compounds. This, it is urged, is false. But many will think that a metaphysical theory about material objects is producing an obvious error in counting. Rather than declaring them to be non-identical but “the same material object,” many philosophers think it preferable to deny the existence of the statue, the pillar, or both. Perhaps at least one of them is better understood to be reducible to particles in a certain configuration. The “constitution” relation, much more than identity, is controversial in recent metaphysics; many a metaphysician just denies that there is any such basic relation in reality as constitution. And some, even accepting this idea of constitution in a metaphysics of material objects, would resist any application to the wholly immaterial God. It is not obvious that in God there is something much like matter, something that as it were plays a role in the being of God similar to the role played by matter in a material form-matter compound such as a statue.45 It is also unclear whether this account really allows one to affirm premise 9. On this theory, we have three beings, three non-identical form-matter (or form-nature/essence) compounds, each of which is omniscient, omnipotent, omnibenevolent, uncreated, and eternal. Why isn’t this a scheme of three gods, papered over with the claim that they “are to be counted as one” because each is constituted by the same quasi-matter (“nature”)?46 Finally, any theory on which the Father and Son are the same god runs into a difficulty with the sources. Various New Testament books explicitly say that the Father is Jesus’s god, which arguably rules out their being the same god.47 5.7 Denying Premise 9: “Social” Trinitarians No recent analytic theologian explicitly denies premise 9, the thesis of monotheism. It is, however, frequently urged against various theories that they imply the falsity of 9. This is a main charge against the best-developed analytic “social” Trinity theories by philosophers Richard Swinburne and William Hasker.48 These seem to assume the truth of all the other premises in our argument. And they define a god as a being with the essential nature divinity, which implies the possession of attributes such as omnipotence, omniscience, perfect goodness, uncreatedness, and perfect freedom. So far, so good; these are arguably attributes of the biblical Yahweh. But then, as the creeds demand (“true God from true God”), they attribute divinity to each member of the Trinity. But this means that each is a god. And they seem to grant that, as none is identical with any other, the Father, Son, and Spirit are not the same god, but rather three different gods. Thus, they seem implicitly to deny premise 9. But this is arguably the ruin of any Trinity theory; both the Bible and later traditions demand monotheism. In response, each argues that those three gods function in such a unified manner that it makes sense to talk and to think about them as if they were a single god. Certainly, there has arisen a tradition of using “God” to refer to the Trinity, whether this in the end is a god-like thing composed of gods (Swinburne) or a god-like community or group of gods (Hasker).49 They insist on using “God” in that manner, while also using it to refer to various gods (i.e., to the Father, or the Son, or the Spirit). But as-if monotheism, or rather polytheism plus monotheistic-sounding talk, goes against both apostolic and later mainstream Christian traditions.50