Preamble

Readers familiar with recent work on the Trinity will quickly discover that the author is neither a scholar steeped in the history of discussions of the Trinity nor a regular contributor to the vast contemporary literature on the topic. I have read enough to have encountered a number of ingenious attempts to mine the resources of analytic metaphysics to provide a coherent account of the metaphysics of the Trinity. Too often, however, metaphysical theses appear to have been adopted, not because they have independent merit, but because they contribute to a solution to the puzzle of the Trinity. This kind of cherry-picking occurs also in the philosophy of mind when philosophers confront the problem of mental causation or the ‘hard problem’ of consciousness. I do not mean, of course, that everyone who writes on the Trinity, or mental causation, or consciousness is guilty of cooking the books, only that it does occur and is all too common. Indeed, it was the prevalence of what seemed to me the misuse of metaphysics that drove me in the late 1990s from the philosophy of mind to full-bore metaphysics.

In what follows I discuss an ontological picture that I believe is independently attractive; indeed it is one I myself find compelling (see Heil (Reference Heil2014)). As it happens, the ontology in question might possibly provide a way of understanding the metaphysics of the Trinity. Complications abound, of course, but I like to think that the position I describe at least departs from the usual fare and for that reason might inspire some more competent philosopher engaged with the Trinity to improve on it and iron out the wrinkles.

The dialectic

One unavoidable impression of an outsider encountering disputes concerning the metaphysics of the Trinity is that disputants appear to be trapped between Scylla – a robust account of the three Persons of the Trinity, which threatens polytheism – and Charybdis – minimizing threeness, which risks undercutting the idea that there really are three Persons. It is hard not to conclude that the situation is hopeless: the Trinity is a mystery not susceptible to metaphysical domestication. And, indeed, I think this is likely so. Nevertheless, I propose to sketch a line of inquiry that might, if nothing else, sharpen the difficulty. In doing so, I am going to appeal, not to the kinds of manoeuvre popular today with philosophers engaged in analytic metaphysics, but to metaphysical categories at home among the late scholastics and early moderns, in particular Suárez, Descartes, and especially Spinoza.

One aspect of discussions of the Trinity that I have been unable to master is the nature and extent of constraints on the metaphysical options. Thus Michael Rea, in a useful discussion of attempts of philosophers to explicate the Trinity, suggests that orthodoxy requires that the Persons of the Trinity are substances, not modes: ‘modalism is a heresy’, because modalism downgrades the Persons of the Trinity to ‘mere properties’ (Rea (Reference Rea, Flint and Rea2009), 407). More generally, in providing an account of the Trinity are we constrained by metaphysical positions held by, or at least available to, philosophers and theologians in the fourth or fifth century? Are we restricted to Aristotelianism as it was then understood or Aristotelianism supplemented by Neoplatonism? If these philosophers and theologians held that persons are substances, is this definitive of the Trinity (so that its rejection is heretical) or is this simply their attempt to provide an account of the metaphysics of a doctrine the metaphysics of which is dramatically underdetermined? And what of hylomorphism? Does hylomorphism enjoy a privileged position in discussions of the Trinity, or is it wholly optional?

I will assume, perhaps naively, that the metaphysics is more or less completely open. The goal is to provide an account of the metaphysics of the Trinity without cooking the books, without resorting to exotic metaphysical doctrines that lack independent motivation. And I will assume that this requires showing how you could have three Persons’ ‘being of one substance’, where ‘one substance’ is understood as ‘one and the same substance’, not ‘one and the same kind of substance’. I realize this is controversial, but in that case you could understand this article as an attempt simply to suggest that there is a plausible metaphysical story consistent with this interpretation of the Trinity, leaving open the question whether this interpretation is the correct one.

Finally, I should note that I will speak of the Persons of the Trinity as persons, not selves. I am aware that some distinguish selves and persons, and that this distinction could turn out to be momentous. But I myself am not sure what to make of it, so I will not invoke the distinction in what follows.

Substance, attribute, mode

My starting point will be Descartes's ontology of substances, attributes, and modes. Kinds of substance are distinguished by their respective attributes. Material substances are extended, for instance, and non-material substances think, where the attribute of thought is best understood as pertaining to conscious states generally. A substance is not simply extended or conscious, however; a substance must be extended or conscious in particular ways. These ways are modes. A material body's shape or size, for instance, are ways it is extended. Your thinking of Vienna or hoping for rain are modes of thought or consciousness, ways of being conscious.

Descartes holds that there are just these two kinds of substance: extended substances and thinking substances. You are a thinking substance intimately united with a particular extended substance, your body. In fact, it is possible that Descartes believed there is but one extended substance, space itself. What we regard as ordinary extended bodies are really ‘thickenings’ or eddies, wavelike disturbances of this extended substance. Although I am partial to this interpretation, I will not insist on it here.Footnote ³ For present purposes, the important point is that Descartes regards persons as individual substances: as he notes in the second Meditation, in response to the question ‘what am I?’, ‘I am a thing that thinks’. If three persons are thinking of Vienna, three distinct substances are doing the thinking; three distinct substances are entertaining thoughts of Vienna.

Extension and thought are attributes that demarcate kinds of substance. It is tempting to think of attributes as determinable properties belonging to substances and modes as determinates of these determinables, but this is not Descartes's view. A substance does not have or possess an attribute in the way a tomato might be said to have a colour or a shape. Attributes do not inhere in substances. A substance is – is strictly identical with – its attribute. If a substance is an it, its attribute is what it is. Thus, an extended body is its extension. But again, nothing can be extended simpliciter. An extended body must be extended in a definite way or ways: the spherical way, the fuzzy way. A thinking substance must think particular thoughts, must think in this or that way. These ways are modes, modes of extension, modes of thought.

So substances are their attributes and what we would think of as properties of substances are modes, ways of being thus attributed, ways of being extended, ways of thinking or being conscious. Substances, attributes, and modes alike are fully particular. Modes are abstract particulars, not abstract in the peculiar twentieth-century sense of being non-spatio-temporal, but in the less dramatic sense of being dependent for their identities on the substances of which they are modes, substances they modify. None of the philosophers I shall be discussing regarded properties as universals.

So modes are unsharable. If two tomatoes are red, their individual rednesses are ‘numerically distinct’. Nowadays properties thus regarded are labelled ‘tropes’, a term unleashed in the 1950s – not without irony – by D. C. Williams in the course of developing a ‘bundle theory’ of substances (see Heil (Reference Heil2012), 88–93, for an etymology). According to Williams, a substance's having a property is a matter of the property's being a part – a mereological part – of the substance. This makes substances dependent on their properties in the way collections or sums are dependent on their members.

Modes, in contrast, are not in any sense parts of substances. A simple substance, an entity lacking substantial parts – parts that are themselves substances – could possess many properties, could be many ways. And, again, modes depend for their identities on the substances they modify. One important motivation in the late mediaeval period for talk of modes as distinct from individual accidents stems from the role accidents were thought to play in the Eucharist when consecrated bread and wine are ‘converted’ into the body and blood of Christ. On the accepted view, when this happens, the substance of the bread and wine are not ‘transformed’, but converted – transubstantiated – into the body and blood of Christ, but the accidents survive. The bread and wine – these substances – are no longer present, but their accidents remain, inhering in no substance. Accidents thus capable of independent existence were called ‘real accidents’ and could be seen as mediaeval precursors of Williams's tropes.Footnote ⁴

As noted, modes are separable from the substances of which they are modes only in thought. You can consider a tomato's colour without considering the tomato. But if its colour is a mode, you could not separate the tomato's colour from the tomato. This is a form of what E. J. Lowe calls ‘rigid existential dependence’. Lowe distinguishes such dependence from ‘non-rigid dependence’ associated with universals of the sort defended by David Armstrong (see Lowe (Reference Lowe2006), § 3.1). According to Armstrong, a universal – redness, say – must be instantiated by some substance, but not by any particular substance (Armstrong (Reference Armstrong1997)).

Because a mode owes its identity to the substance it modifies, modes are not ‘transferable’: a mode cannot migrate from one substance to another. When the fire's heat warms a pot, the heat does not move from the fire to the pot; the momentum, or a portion of the momentum, of one billiard ball is not transmitted to the other when the first strikes the second. Efficient causation must be otherwise explicable.

I have said that, for Descartes, a person is a substance, a particular conscious, thinking being intimately related to a particular body, but, qua substance, capable of independent existence. Contrast this conception of persons with what I take to be Locke's. A person, for Locke, is not a substance. I read Lock as neutral on the question whether there are immaterial substances, souls. But even if there are souls, souls are not to be identified with persons. Persons are particular ways substances are: persons are modes. And, if persons are modes, it would seem to be possible for a single substance to be more than one person. After all, a tomato can have many modes – a particular shape, a particular colour, a particular mass, a particular momentum. Substances, quite generally, are typically many ways at once, multiply propertied. So you might think that, if persons are modes, a single substance could be many persons.

Yes and no. Consider Locke's example of Castor and Pollux:

Later in the Essay (ibid., ii, xxvii, 12–29) Locke dwells on the distinction between the identity of a substance and the identity of persons – or selves: Locke uses the terms interchangeably. My interest here is not in the details of Locke's conception of personal identity, but on his insistence that personal identity is not a species of substantial identity. Locke is willing to allow, at least for the sake of argument, that persons are housed in simple, immaterial substances, Cartesian souls. But, as the Castor and Pollux case illustrates, one and the same soul could accommodate distinct persons.

Locke's focus is on consciousness and the succession of conscious states that make up our conscious lives. Although persons, for Locke, are not substances, it is not quite right to say that persons are modes: persons are potentially intermittent successions of modes connected by the contents of memories. But, again, for purposes of the present discussion, the details of Locke's view are not what matters, only his rejection of the Cartesian conception of persons as substances.

You might suspect that I am softening you up for a straightforward Locke-inspired account of the Trinity: God is a single substance, and the three Persons are modes of this substance. The difficulty, or one difficulty, is that Locke would not countenance the concurrent presence of two or more selves or persons in a single substance. Why not? If consciousness is the source of personhood, and if consciousness is a mode (or a succession of modes), what is to prevent a single substance from encompassing several persons? The colour of a tomato is a mode, a particular way the tomato is. But the tomato's being this way does not preclude its being many other ways: the tomato, in addition to being coloured, has a shape, a size, a mass: one substance multiple modes.

The problem is that, although a substance can indeed be multiply modified, a substance can be many different ways; a substance's being a way of a particular kind precludes its simultaneously being another way of that kind. Suppose a tomato is spherical, the tomato is the spherical way. This does not prevent the tomato from being green: one substance, more than one way, more than one mode. But the tomato's being spherical does preclude its being cubical and the tomato's being green (all over) does prevent it from being red (all over) (see Campbell (Reference Campbell1990), 83–88, for discussion). Of course, a green tomato can become red and a spherical tomato could come to have another shape. But the tomato – as a whole – cannot have two shapes or two colours at once.

This is how Locke is thinking about persons. If a person is a mode (or a succession of modes), a substance, thus modified, could not, at the same time be a distinct person, could not at the same time be differently modified along the conscious dimension. Modes of consciousness, in this respect, resemble modes of shape or colour.

You might take issue with this idea, but I shall not. You might accept that a single substance could be consciously modified so as, at one time, to count as distinct persons.Footnote ⁵ That would open the way to an easy route to an account of the Trinity – to be sure, an account that others would find deeply flawed in one or another respect.Footnote ⁶ I propose, instead, to return to a theme I associated at the outset with Descartes. My hope is that looking a little more deeply at Descartes's official metaphysical picture will point towards a more interesting approach to the Trinity.

Attributes again

Recall the basic Cartesian ontological scheme of substance, attribute, and mode. Kinds of substance are distinguished by their attributes. Some substances are extended, some think. A substance is identified with its attribute: an extended substance, for instance, is its extension. But anything extended must be extended in some way. Ways of being extended, modes of extension, are what could be regarded as properties of material substances – shape, size, texture.

For Descartes every property of a material substance is a mode of extension, a way of being extended, a geometrical way. This appears, on the face of it, highly unlikely given the course of post-Cartesian physics, however. Descartes's physics is purely kinematic, purely geometrical, leaving no place for mass, no place for charge, neither of which are plausibly regarded as geometrical characteristics of material bodies. If these are modes, they are apparently modes of distinct attributes.Footnote ⁷ But if a substance is its attribute, how could a substance be multiply attributed? This would seem to make no sense.

One philosopher who thought it did make sense was Spinoza. For Spinoza, in many ways a better Cartesian than Descartes, there is but one substance, God or Nature: the universe as a whole. This one substance, however, is multiply – indeed, infinitely – attributed. The substance is extended and thinks. What you and I would regard as material bodies – particles, billiard balls, human beings, planets – are modes, modes of extension, not substances or composites made up of substances. As noted earlier, there is a way of reading Descartes according to which his conception of extended substance was similar: there are many immaterial substances, but only one extended substance. What interests me here is not Spinoza's monism, however, or the possibility that there is but one extended material substance, but Spinoza's conception of substance as being multiply attributed. For Descartes, a substance is its attribute. For Spinoza, a single substance can be extended and think (and much else besides); a single substance can be extended in various ways and conscious in various ways, all at the same time.

If modes are ways a substance is what it is, attributes are what a substance is. Just as colours and shapes or masses and charges do not exclude one another, so modes of distinct attributes do not exclude one another. Your being pale excludes your being dark, but does not exclude your being tall; your being tall and pale does not exclude your thinking of Vienna.

You can see where this is going. Start with the idea that persons are not substances, but modes. This allows for a single substance to be distinct persons, but not concurrently. Suppose, however, you followed Spinoza and allowed that a single substance could be multiply attributed, and suppose you thought of the Christian God in this way: one substance triply attributed. Now, if the Persons of the Trinity are modes, they could be modes of distinct attributes: one substance, three attributes, three modes, each a way of having a particular attribute, three Persons.Footnote ⁸ The different attributes can reflect differences as profound as the difference between thought and extension, so the differences among the three Persons are not simply modal, not simply the kinds of difference in play between differently shaped extended bodies. Yet, as I shall endeavour to show, these turn out to exhibit an underlying unity.

I am confident that some readers will already have thought of half a dozen reasons why this could not possibly provide an adequate account of the Trinity. But I knew that already. I am sceptical that there could be an account, or at least a clear account, that would satisfy all parties. What I propose to do in the remainder of this article is to address one line of objection, fully aware that this opens the door to a family of objections from the opposite direction. This would be worrisome were my aim to convince you that I have figured out the Trinity, but I have no such ambition. Rather, my goal is to show how an ontology of substances, attributes, and modes might comport with discussions of the Trinity and perhaps even represent a kind of advance over certain of its competitors.

Kinds of distinction

One worry you might have about the idea that the Persons of the Trinity are ways God has of exhibiting three distinct attributes is that this threatens to trifurcate God, to endow God with a kind of split personality. God would seemingly comprise three centres of consciousness – albeit consciousnesses of very different kinds corresponding to differences in the attributes – but these could know of the existence and activities of the others only by ‘external’ third-person observation. We have the three, but in having the three, we risk losing the unity essential to the Christian God.

This appears to be an instance of a previously mentioned dilemma that dogs accounts of the Trinity. On the one hand, you need diversity: three distinct Persons, one ‘begetting’ a second, and a third ‘preceding from’ the first two. On the other hand, you need unity: one God, one substance. Moves that satisfy the first frustrate the second, and vice versa. I believe I can obtain unity, but in doing so I realize that this will raise doubts concerning distinctness. Maybe it's true: you can't have your cake and eat it.

In his discussion of attributes and modes, Descartes appeals to a scholastic classification of kinds of distinction (Descartes (1644/Reference Descartes, Cottingham, Stoothoff and Murdoch1985), I, § 60; 1645; see also Suárez (1597/Reference Suárez and Vollert1947)). First, there are real distinctions:

• Real distinction: A and B are really distinct just in case A and B are distinct substances.

For Spinoza, if A and B are really distinct, each of A and B is ‘conceived through itself’, and A and B could exist apart, something possible only for substances (Melamed (forthcoming) ). Second, there are what you might call purely conceptual distinctions, distinctions of reasoning reason:

• Distinction of reasoning reason: A and B can each be conceived through itself, but A and B are not really distinct, and the distinction ‘has no foundation in reality’.

In discussing distinctions of reasoning reason, Suárez gives as an example ‘Peter is Peter’. Peter can be distinguished from himself in thought, but the distinction has no basis in reality. The distinction between Lewis Carroll and Charles Dodgson, or that between Hesperus and Phosphorus, would appear to be distinctions of reasoning reason. Finally, there is an intermediate species of distinction:

• Distinction of reasoned reason: A and B each can be conceived through itself, and, although A and B are not really distinct, the distinction has a foundation in reality.

Suárez explains distinctions of reasoned reason this way:

In summary,

For Descartes, the distinction between a substance and its principal attribute is a distinction of this kind, a distinction of reasoned reason. The substance and attribute could not exist apart – a material substance is its extension, an immaterial substance is its thinking – but the distinction reflects an important feature of reality, the distinction between a something and what that something is.

Spinoza, too, accepts that the substance–attribute distinction is one of reasoned reason. Now we have a complication, however. Unlike Descartes, Spinoza holds that a substance can have many – infinitely many – attributes.Footnote ⁹ Each of these is distinguished from the substance of which it is an attribute by reasoned reason. If a substance is extended and is thinking, its extension and its thinking are distinguished from it, the substance, by reasoned reason. But how are the various attributes related? How are they distinguished from one another?

Suppose A and B are attributes of a substance, s. The distinction between A and s and between B and s is one of reasoned reason: not a real distinction but still a distinction ‘founded’ in reality. What of the distinction between A and B? Given that A and B are attributes, not substances, the distinction between A and B could not be a real distinction. And given that s is A and s is B, it is hard to see how it could fail to turn out that A is B. (Remember, the ‘is’ here is the ‘is’ of strict identity, hence, reflexive symmetrical, and transitive.) So is the distinction between A and B one of reasoning reason, a purely conceptual distinction lacking a foundation in reality?

Before addressing this question, let me remind you that I have suggested that it might be possible to understand the Trinity as a case of a single substance triply attributed, where the three Persons of the Trinity are understood as modes, albeit modes of distinct attributes. The initial worry was that this threatens God's unity. Perhaps this worry was misplaced.

Thus suppose that the distinction among attributes is not merely one of reasoning reason with no foundation in reality, but one of reasoned reason. This would provide an underlying unity coupled with a kind of diversity that reflects an important feature of reality. Put somewhat unhelpfully, the attributes are distinct expressions of a single underlying nature.

I realize that this is all much too vague, but I think it might be possible to make something of it. Doing so will require temporarily moving away from the theological context.

Although not a player in contemporary analytic metaphysics, a substance–attribute–mode ontology holds many attractions. Consider the Cartesian idea that kinds of substance are distinguished by their attributes. Extended substances are distinguished from thinking substances. Substances’ properties are modes, fully determinate ways of being attributed, particular ways of substances’ being the substances they are. Properties of material substances are modes of extension, ways of being extended; properties of immaterial substances are modes of thought, ways of thinking or being conscious. This makes the inherence relation – the relation between the tomato's shape, for instance, or its colour, and the tomato – an internal relation. You could not have this very shape or this very colour without having this tomato. Properties are not glued to their bearers; they are ways of being those bearers. And every bearer, every substance must be some way or other.

An obvious difficulty for the Cartesian view, however, is that it is implausible that every property of a material substance is a mode of extension. An electron might be thought to have a determinate shape and size, and a determinate location. But electrons have, in addition, mass and charge. And mass and charge seem not to be modes of extension, seem not to be ways of being extended.

Suppose, however, you thought of particles as multiply attributed. A particle, such as an electron, is extended, but it is also massive, and charged. Its properties would be modes of these attributes. Particles of other kinds are distinguished from electrons by virtue of being different masswise or different chargewise. Some particles altogether lack these attributes and possess others.

This makes sense, but now you lose one of the features that make the original Cartesian view so elegant. For Descartes, a material object is its extension and its properties are just determinate ways it is extended. There is no asking why a given body is extended. In creating a material body, God creates an extended thing, a something extended in various ways. Now, however, it looks as though God must not only create the bodies, but also allocate attributes across those bodies: some are massive, some are not; some are charged, some are not. This is not merely a change in detail; this is a much bigger deal.

Suppose, however, that the attributes turned out to be unified; suppose the distinction between mass and charge, for instance, turned out to be one of reasoned reason. Something like this is what physics aims for in seeking a theory that unifies the forces. If there were such a theory, the forces would be unified at a deep level. The distinction among them, however, would be not merely one of reasoning reason, would not be merely conceptual; it would be one of reasoned reason, one founded on the way reality is and appears to us. Here is Spinoza:

If this is right, or sort of right – rightish – not only would it support an elegant substance–attribute–mode ontology, it would provide an independently motivated, non-theological basis for understanding how the Persons of the Trinity could be unified, yet distinct: one substance, three immutable attributes, each expressing the nature of the substance in a distinctive way. Each Person is a mode of a distinct attribute, but the attributes are unified at a deeper level: the distinction among them is one of reasoned reason, a distinction founded in reality. Each attribute is strictly identical with the one substance; hence, owing to the transitivity of identity, the attributes are strictly identical with one another, yet distinguishable by reason.

Although I find this approach to the Trinity hugely appealing, I leave it to others to judge just how likely it is that such a view could accommodate the Father's begetting the Son, and the Spirit's proceeding from the Father and the Son. I will retire from the field and leave the topic in the hands of others more qualified than I to do better.