7 Trinity
During the Middle Ages, theology is the preeminent academic discipline and, as a result, most great thinkers of this period are highly trained theologians. Although this much is common knowledge, it is sometimes overlooked that the systematic nature of medieval theology led its practitioners to develop full treatments of virtually every area within philosophy. Indeed, theological reflection not only provides the main context in which the medievals theorize about what we would now recognize as distinctively philosophical issues, but it is responsible for some of their most significant philosophical contributions. To give just a few examples: it is problems with the Christian doctrine of the Incarnation that prompt medievals to develop the notions of substance and person in striking and original ways; it is problems with the doctrine of the Eucharist that lead them to consider the possibility of accidents that do not inhere; and it is problems of interpreting particular scriptural texts, such as the Book of Job, that introduce refinements in their understanding of the nature and purpose of evil.
In this chapter, I show how Abelard’s treatment of a deep, logical problem associated with the Christian doctrine of the Trinity gives rise to important developments in his philosophy. As will emerge, in addressing this problem he not only presents a philosophically interesting account of the Trinity, but also develops a highly sophisticated theory of identity or numerical sameness, as well as a distinctive approach to issues now generally recognized under the rubric “the problem of material constitution.”
I. THE LOGICAL PROBLEM OF THE TRINITY
It is well known that the orthodox Christian doctrine of the Trinity poses a serious philosophical problem. According to this doctrine, God exists in three Persons – Father, Son, and Holy Spirit – each of whom is distinct from each of the others: the Father is not the Son, and the Holy Spirit is not the Father or the Son. At the same time, however, the doctrine requires that each of the Persons is God: the Father is God, the Son is God, and the Holy Spirit is God. The problem arises when we add to these claims the traditional Christian commitment to monotheism – that is, the view that the divine persons (in the words of the Athanasian creed) “are not three Gods, but there is one God.”
As even this brief description of the doctrine makes clear, the problem of the Trinity is the logical problem of explaining the relationship of the divine persons to one another. On the one hand, it seems that the relationship must be identity, since each is divine and there is only one divine being. On the other hand, it seems that the relationship must be distinction – indeed, as the names of the divine persons suggest, they are traditionally thought to possess different essential attributes: only the Father begets, only the Son is begotten, and only the Holy Spirit proceeds or “spirates” from that of which it is the spirit. But no things, not even divine persons, can be both identical to and distinct from one another.
The logical problem of the Trinity is a topic to which Abelard devoted a great deal of attention. As he tells us in his autobiography, this problem led to the writing of his first major work in theology, the Theologia “summi boni,” on the basis of which he was first condemned as a heretic (HC 83; Radice 1974, 79). Given Abelard’s temperament, it is not surprising that the embarrassment and public humiliation caused by this condemnation failed to produce in him any lessening of interest in the problem of the Trinity, or any inclination to abandon his original solution. On the contrary, it served rather as an impetus to develop the details of that original solution further and to defend it at greater length. As John Marenbon has pointed out:
When Abelard was forced, at the Council of Soissons, to commit his Theologia Summi Boni to the flames with his own hands, his reaction was not to give up the project he had begun, nor even to modify or soften his approach. Within four or five years he had produced a new Theologia, boldly entitled Theologia Christiana, which incorporated about nine-tenths of the Theologia Summi Boni into a treatise nearly three times its size.1
Abelard never completed his Theologia Christiana, and apparently never intended it to circulate widely. He does, however, incorporate parts of it into the final version of his Theologia, namely, the Theologia “scholarium.” As in the case of the Theologia Christiana, this work remains true to the spirit (if not to the letter) of his earliest views about the Trinity; and although he twice introduces changes into the published version of this work – as part of a futile attempt to respond to criticisms that eventually led to his being condemned as a heretic for a second time – he shows no interest in altering the basic structure of his solution to the logical problem of the Trinity.
Abelard adopts the same basic strategy for resolving the logical problem of the Trinity in all three versions of the Theologia. He starts by distinguishing various senses in which the terms “same” (idem) and “different” (diversum)2 are used and then argues that the sense in which the divine persons are different is compatible with the sense in which they are the same.3 The details of these distinctions vary from work to work, but the underlying conception of the Trinity for which they are mobilized is the same: the divine persons, Abelard always says, are the same in virtue of their substance or essence, but differ in virtue of what is proper to each. In his earliest work, the Theologia “summi boni,” Abelard describes the difference of the persons in terms of a difference in definition.4 In his later works, however, he states this difference more precisely in terms of a difference of property, though he continues to associate this notion closely with that of difference in definition (cf. TC 3.164 and TSch 2.97). Thus, in the Theologia Christiana, the work in which the notion of difference in property makes its first appearance, and which is representative of his mature view about the Trinity, Abelard says the following about the divine persons:
Their substance is entirely the same – where by “the same” I mean essentially or numerically the same, just as the substance of a blade and a sword, or of this man and this animal, is the same. Nevertheless, the persons – that is, the Father, the Son, and the Holy Spirit – are different from one another in a way analogous to those things that are different in definition or property. That is, they are different by virtue of the fact that, although God the Father is entirely the same essence as God the Son or God the Holy Spirit, there is one feature proper (proprium) to God the Father, insofar as he is Father, another to God the Son, and yet another to the Holy Spirit.
(TC 3.164)
Although Abelard invokes various notions of sameness and difference to explain the relationship among the divine persons, we shall see that two are at the heart of his account – namely, essential sameness and difference in property.
In what follows, I present and then offer a limited assessment of Abelard’s account of the Trinity, focusing on the extent to which it succeeds in providing a solution to the logical problem just mentioned. My discussion is divided into three main parts. I begin (in §II) by providing a preliminary account of the notions of essential sameness and difference in property; since the former notion is (at least initially) the more difficult to understand, I focus most of what I say here on it. I turn next (in §III) to the application of essential sameness and difference in property to the divine persons. Here I argue that there is a straightforward and natural application of these notions, one that is not only suggested by Abelard’s discussion of material constitution, but also provides us with an attractive solution to the logical problem of the Trinity. As it turns out, this is not Abelard’s own way of applying the notions. Like most other medieval philosophers, Abelard accepts the doctrine of divine simplicity, and this, as we shall see, requires him to make certain departures from the straightforward application of the notions. In the final section of the paper (§IV), I discuss Abelard’s own account of the Trinity. Here my conclusion is that, for all its subtlety and sophistication, it remains incomplete as a response to the logical problem.
II. SAMENESS AND DIFFERENCE
II.1 Sameness in essence and difference in property
The divine persons, says Abelard, are the same in virtue of their substance. Whenever he describes this type of sameness, he does so in terms of the notion of essential sameness, which he explains in the Theologia Christiana as follows:
We call something essentially the same as another when the essence of each is numerically the same – that is, when the one thing and the other are such that they are numerically the same essence, just as for example a sword is numerically the same essence as a blade (mucro),5 a substance is numerically the same essence as a body (or an animal, or a man, or even Socrates), and something white is numerically the same essence as something hard.
(TC 3.139)6
According to Abelard, an object a is essentially the same as an object b just in case the essence of a – that is, the essence which is a – is numerically the same as the essence which is b. Indeed, as he goes on to say, a and b are essentially the same just in case they are numerically the same essence. It is important not to misunderstand Abelard here. In contemporary philosophy, the term “essence” is associated with essential properties or abstract objects such as Platonic forms. When Abelard uses this term, however, or the corresponding Latin term, essentia, he is merely following a standard twelfth-century convention according to which essentia means a concrete, particular thing.7 Thus, when he says that a and b are essentially the same, he just means that a and b are the same thing (essentia).
If this were all Abelard had to say about essential sameness, it would be natural to suppose that what he has in mind is just our notion of identity – that is, the notion of identity associated with ordinary predicate logic. After all, how could a be the same thing as b and yet fail to be identical with b? It is at this point, however, that essential sameness becomes difficult to understand. For whatever else Abelard thinks about it, it is clear that he does not think essential sameness is identity in our sense.8 If a is identical with b, then a and b must share all the same properties or attributes. But according to Abelard, this is not true of things that are the same in essence:
Some things are essentially the same even though they are distinguished by their properties. This is because their properties remain so completely unmixed that a property of the one is never participated in by the other, even if the substance of each is completely the same in number. For example, in the case of a particular waxen image, the wax – that is, the matter itself – is numerically the same as what is made from it [namely, the waxen image]. In this case, however, the matter and what is made from it do not share their properties in common, since the matter of the waxen image is not made from matter (that is, the wax itself is not made from wax), just as what is made from the matter in this case is not the matter (that is, the waxen image is not the matter of the waxen image).
(TC 3.140)
According to Abelard, things may be essentially the same and yet distinguished by their properties. To support this claim, he introduces the example of a lump of wax that has taken on an image, say, from a particular signet ring. The wax, he says, is essentially the same as the waxen image, even though the wax and the image have different properties. The waxen image has the property of being made from wax, but the wax itself does not have this property (indeed, he thinks it cannot have it). We shall have to return to this example later on (see §II.2 below). For now, however, I merely want to call attention to something this example helps to make clear – namely, that essential sameness is not identity. Things essentially the same can differ in property, and things different in property cannot be identical. As in the case of Abelard’s example, we shall have to return to the notion of difference in property later on (§III). For now, however, we may suppose that an object a differs in property from an object b just in case a has a property that b lacks or vice versa.
So far so good. But a difficulty still remains. If essential sameness is not to be understood in terms of identity, then how is it to be understood? I want to suggest that the best way to characterize essential sameness is by saying that although it is not identity, it is a genus of which identity is a species (or, a determinable of which identity is a determinate). As we have seen, some of the things that are essentially the same are also identical (as in the case of a sword and a blade), but some of them are not identical (as in the case of a waxen image and the wax from which it is made). By introducing the relation of essential sameness, therefore, and claiming that it is compatible with difference of property, I contend that Abelard is attempting to distinguish a type of sameness without identity.
It is important to emphasize that essential sameness is not just a type of sameness, but a type of numerical sameness. For as we have seen, Abelard thinks that an object a and an object b are essentially the same just in case a and b are numerically the same in a certain respect, namely, in respect of their essence (i.e., the concrete thing which “they” are). The following passage from the Theologia Christiana helps to explain why Abelard thinks the notions of essential sameness and numerical sameness must be connected in this way:
All these things – that is, the things that are essentially the same – are also said to be numerically the same. The reason is that, since the essence of each is the same, the number of things cannot be multiplied in them, nor can an enumeration (computatio) of these things be performed on the basis of their distinction (discretione) – that is, an enumeration such that “one,” “two,” etc., may be said of them.
(TC 3.139; cf. also TSB 3.92 and TSch 2.168)
Whenever Abelard speaks about numerical sameness, or sameness in number (eadem numero), he always does so in terms of counting. Things that are the same in number are to be counted as one thing, and “they” are to be counted in this way, not because of any arbitrary decision on our part, but because in cases of numerical sameness there is only one thing to count. Thus, when Abelard says that a and b are essentially the same – that is, numerically the same thing (essentia) – this is because a and b are one thing, and hence must be counted accordingly.9
In light of its connection to numerical sameness, we can provide the following, much more definite, characterization of essential sameness. Essential sameness is a relation whose relata are to be counted as a single thing. In some cases, the relata of this relation will be identical, as in the case of Abelard’s sword and blade, while in other cases, such as the wax and image, the relata will be distinct in property, and hence non-identical. Even in cases of the latter sort, however, the relata will not be numerically distinct, since they are one thing. Thus, numerical sameness without identity is intended by Abelard to be a relation that is weaker than identity (because its relata do not share all the same properties) but stronger than numerical distinction (because its relata are a single thing). Indeed, we can just think of numerical sameness without identity as a two-place relation standing midway between identity and numerical distinctness of essence, as figure 1 indicates.
If we return to the logical problem of the Trinity with the distinctions indicated at figure 1, we can see that the type of relation identified at (IB) – namely, numerical sameness without identity – provides a basis for a solution to the problem. For as we seen, the logical problem of the Trinity is just that of explaining how there can be both a single divine being and three distinct persons each of whom is divine. The relation at (IB), however, appears to provide the resources for an explanation. For assuming it makes sense to suppose such a relation exists, then we can say that each of the divine persons is numerically the same as God but nonetheless distinct from one another. In other words, the relation at (IB) allows us to preserve a real distinction among the persons without abandoning the claim that there is one and only one God.
Of course, the success of this type of solution depends on the coherence of supposing that there is a relation of the sort identified at (IB). But could there be such relation? Most contemporary philosophers would say “no,” since they suppose that for any a and b, a and b are to be counted as the same thing only if a = b. But if this is correct, there can be no relation weaker than identity that is nonetheless a kind of numerical sameness.
The notion of essential sameness may be unfamiliar, but it is not by any means incoherent. Indeed, as Abelard’s use of the example involving the waxen image is intended to show, this notion is not only coherent, but has a strong intuitive appeal. In order to explain its appeal, as well as to prepare for Abelard’s own account of the Trinity, we need to examine the example of the waxen image, and others like it, in more detail.
II.2 Numerical sameness without identity and material constitution
Abelard appeals to the relation of essential sameness – or more specifically, that species of essential sameness I am calling numerical sameness without identity – in the course of explicating a number of philosophical and theological doctrines. In each case, he appeals to what is, at bottom, the same type of example, that of a material object’s taking on some shape or form and thereby coming to constitute a further object.10 We have already seen him appeal to a lump of wax which, after being imprinted with an image, comes to constitute a waxen image. In the course of explicating certain other doctrines, he also appeals to examples involving blocks of stone or lumps of bronze which, in virtue of their shape, constitute statues of various kinds.11
These types of examples are familiar from contemporary literature and are at the root of what is now commonly referred to as “the problem of material constitution.” In general, we may say that the problem of material constitution arises whenever we appear to have a single object falling under different kinds – that is, kinds associated with incompatible sets of defining properties. Thus, in the case of a statue and its constituent lump of bronze, we appear to have a single object (namely, some matter) falling under different kinds (namely, statue and lump of bronze) that clearly have incompatible sets of defining properties (as is clear from their different persistence conditions: a lump of bronze can, whereas a statue cannot, survive being melted down and recast as another statue). In such cases, the problem is to decide whether we really have one object or two – or, as the question is now commonly put, whether the relation of constitution is just identity. The lesson to be drawn from Abelard’s discussion of such examples, I now want to argue, is that even if constitution is not identity, this does not imply the existence of more than one object.12
As Abelard’s own examples help to make clear, the problem of material constitution is generated, at least in part, by the fact that we have conflicting intuitions about the individuation of (and hence the proper way to count) certain kinds of material objects. When we are presented with a bronze statue, say of Athena, common sense tells us to count only one object – “there is one and only one object on Athena’s pedestal.” And this is because common sense individuates such objects according to their matter. Thus, in the case of Athena, whose constituent matter fills precisely the same region as it does, common sense tells us to count one and only one object in this region – and this despite that fact that statues and lumps have different persistence conditions and so must be different kinds of material object.
If we turn our attention, however, to the difference between statues and lumps, we find ourselves strongly inclined to count (at least) two objects in the region occupied by Athena. That is to say, in addition to having common sense intuitions that dispose us to individuate material objects according to their matter, we also have rational intuitions disposing us to individuate them according to their identity conditions. Since the region occupied by Athena contains a statue and a lump of bronze, and no statue is identical with its constituent lump, reason tells us that there must be (at least) two objects in that region. The problem, as we can now see, is that in the case of Athena we are led, on the basis of common sense and rational intuition, to accept claims of the following sort:
Claims (1) and (2) are clearly incompatible. As is evident from their incompatibility, moreover, our intuitions about how to individuate material objects are inconsistent as well. Since these intuitions are responsible for generating the problem of material constitution in the first place, we can think of the problem, at least initially, as that of deciding which of our conflicting intuitions to accept.
As we have seen, Abelard thinks the statue and lump of bronze constitute a single object. Thus, he sides with the intuitions favoring (1). In order to explain how a single material object can nonetheless belong to two genuinely different kinds, however, he introduces the relation of numerical sameness without identity. In this way, he is able to count the statue and its constituent lump of bronze as a single material object while at the same time allowing for the obvious fact that being a statue and being a lump of bronze are different kinds to which objects can belong.
Unlike Abelard, contemporary philosophers typically side with the intuitions favoring (2). Moreover, there is a perfectly good reason for this: the intuitions favoring (2) provide us with a straightforward and principled way of counting material objects, whereas the intuitions favoring (1) do not. According to the intuitions favoring (2), we should count one and only one material object wherever a and b are identical, and more than one such object wherever a and b are distinct or non-identical. But how are we to count if we adopt the intuitions favoring (1)? These intuitions allow us to count a single object even in a region filled by a statue and a lump of bronze distinct from it. But this seems problematic. For if we cannot count two material objects in a region filled by a statue and a lump of bronze distinct from it, then how are we supposed to count?
If Abelard’s solution left him with no way of responding to this problem, there would indeed be grounds for rejecting it. But in fact this is not the case. There is a principled way of counting material objects that is consistent both with common sense and with the rejection of (2). Michael Rea, one of the few contemporary philosophers to have discussed this sort of view, formulates the principle in this way:
We count one object (and only one object) in every region that is filled by matter unified in some object-constituting way. We count one statue in every region that is filled by matter arranged statuewise; we count one lump in every region that is filled by matter arranged lumpwise; and we count one object in every region that is filled by matter arranged in either or both of these ways (or any other object-constituting way). Thus, when we recognize a statue and a lump in a particular region and deny that the statue is identical with the lump, we are committed to the claim that there is matter in the region arranged both statuewise and lumpwise, and that being a statue is something different from being a lump; but all of this is consistent with there being just one object in the region.13
This passage suggests a general principle for counting that nicely accommodates Abelard’s views about material objects. If we substitute talk of kinds where Rea talks of objects being arranged F-wise, we can state the principle as follows: count one object wherever there is matter belonging to kind F; count one object wherever there is matter belonging to kind G; and count one (and only one) object wherever there is matter belonging to either or both of these (and perhaps some other) kinds.14 While this principle is explicitly formulated for counting material objects, it can easily be extended to cover (at least a certain class of) immaterial objects. For to the extent that immaterial objects have forms or properties, they too can be said to have a kind of “matter” – namely, whatever it is that plays the role of subject for these forms or properties. But, then, to the extent that even immaterial objects have “matter,” they too can be counted in a way that is consistent with this principle.
As far as I can tell, there is no reason to think that this principle for counting material objects is incoherent, nor indeed any compelling reason to prefer the intuitions favoring (2) rather than (1). If I am right about this, however, Abelard’s appeal to the relation of numerical sameness without identity would appear to be perfectly defensible. He must, of course, pay an intuitive price for appealing to such a relation to solve the problem of material constitution – namely, giving up the idea that material objects are individuated according to their identity conditions. But note: there is an intuitive price to pay no matter how we solve the problem, since the intuitions favoring (1) and (2) are both very strong, and hence whichever option we take entails the rejection of deep-seated intuitions. It is also worth noting that those who, unlike Abelard, reject (1) in favor of (2) have a further price to pay. For it apparently follows from the acceptance of (2) that more than one material object can occupy the same place at the same time – and hence that in cases such as Abelard’s statue and lump of bronze, we have non-identical material objects that are literally co-located.15 This, however, is extremely unintuitive, and something which almost no medieval would accept.16 As Boethius says, “two bodies will not occupy one place” (De Trin. 1).
Considerations of the sort just mentioned may well provide reason for thinking that Abelard’s solution to the problem of material constitution is not only coherent but preferable to other, more familiar ways of solving the problem. Even so, my argument to this point is intended not as a defense of the plausibility of Abelard’s solution to this problem, but only as a defense of its coherence. For provided that the notion of numerical sameness without identity is coherent – and hereafter I shall take its coherence for granted – we have all the resources needed to resolve the logical problem of the Trinity.
III. SAMENESS AND DIFFERENCE IN THE TRINITY
III.1 An Abelardian (but not Abelard’s) account of the Trinity
As we have seen, each of the examples that Abelard discusses in the context of material constitution involves one kind of material object (a lump of bronze, stone, or wax) taking on some shape or form and thereby coming to constitute another kind of object (a statue or an image). It is between these two kinds of object, moreover, that Abelard thinks the relation of numerical sameness without identity holds. Now, since these two kinds of object are related in the way that matter, on an Aristotelian view, is related to the form-matter composite of which it is a constituent, Abelard’s view is that the relata of the relation of numerical sameness without identity are the matter of hylomorphic compounds on the one hand and the hylomorphic compounds themselves on the other.
On the basis of Abelard’s account of material constitution, we can develop a useful model for understanding of the nature of the divine persons and their relationship to one another. According to this model, each of the divine persons is a hylomorphic structure or unity. Thus, just as in our earlier example of Athena we have a single object (namely, matter) falling under distinct kinds (namely, being a statue and being lump of bronze), so too in the case of the Trinity we have single object (namely, the divine substance) falling under distinct forms or properties (namely, being a father, being a son, and being a spirit). Moreover, just as in the earlier case we have distinct hylomorphic structures (a statue and a lump of bronze) constituting a single object (namely, Athena), so too in the case of the Trinity we have distinct hylomorphic structures (a Father, Son, and Holy Spirit) constituting a single divine being (namely, God).
On this material-constitution model of the Trinity, therefore, each of the divine persons is conceived of along the lines of a hylomorphic structure having the very same thing (namely, the divine substance) as one of its constituents. But since each of the divine persons will be essentially the same as this constituent – on the grounds that hylomorphic compounds are essentially the same as their constituent matter – it will follow (due to the transitivity of essential sameness) that each of the divine persons will also be essentially the same as each of the others. On the other hand, since each of the divine persons is also a compound consisting of the divine substance together with a distinct form or property, each of the persons will also be really distinct from each of the others. The virtue of this model, therefore, is that it allows for both enough unity to preserve the numerical sameness of the divine persons and enough complexity to preserve their real distinction in form or property.17
Of course, there are some obvious dissimilarities between the Trinity and ordinary material objects. For example, what plays the role of the matter in the case of material objects is literally material, and hence the hylomorphic structures or unities constituted from their matter will be genuine form-matter composites. In the case of the Trinity, however, what plays the role of matter is an immaterial object and hence the divine persons can be said to be “hylomorphic” compounds only in an extended or analogical sense. Again, in the case of material objects such as a waxen image, the hylomorphic structures constitute only accidental unities – that is to say, they are what Abelard would call artificial, as opposed to natural, kinds of object, since their forms (for example, their shapes) are accidental – that is, only contingently possessed – and hence can be lost without the destruction of their matter. The same is not true, however, in the case of the Trinity. Following tradition, Abelard conceives of properties such as being a father and being a son as essential properties of the divine substance, and hence such that the divine substance could not exist without them. Despite these and other such dissimilarities, however, conceiving of the Trinity on the model of material objects allows us to say that, although the persons are numerically the same, they are nonetheless distinct in form or property (provided of course that “form” or “property” is taken broadly enough to cover the attributes of either material or immaterial objects).
At this point it might be objected that a mere distinction in property among the persons, which is all the material-constitution model seems to allow us, is not enough to preserve the orthodox doctrine of the Trinity. For according to this doctrine, there is a definite number of persons, namely, three. But to preserve the existence of three persons, we must say that the divine persons are not only distinct, but numerically distinct. And yet it is hard to see how there could be three of anything to count on the model of the Trinity just described. For although this model preserves the non-identity of the divine persons – the Father is not identical to the Son, and the Holy Spirit is not identical to the Father or the Son – nonetheless, it requires us to individuate things according to their matter (as opposed to their identity conditions) – that is, according to whatever serves as the subject of their distinct forms or properties. But in that case, it would seem that if we are to count the divine persons at all, we must count them as one (and only one) thing.
The objection, however, overlooks the fact that we can count things other than material objects (or subjects of properties). Admittedly, if we count the Father, Son, and Holy Spirit only in the way we count material objects, then we must count them as one. But material object (or subject of properties) is not the only standard or unit that can serve as a basis for counting. As we have seen, even in the paradigm cases of material constitution, such as the case of Athena, we can count (at least) two distinct kinds – being a statue and being a lump of bronze – and we can even count two distinct hylomorphic compounds – the statue and the lump of bronze. In neither of these cases, however, are we counting material objects. Hence the principle for counting articulated earlier does not apply to them, and there is nothing to prevent us from counting them according to their identity conditions.18
Once it is realized, however, that we can count things other than material objects (or subjects of properties), and that we can count these other things according to their identity conditions, it should also be clear that nothing prevents us from saying that things that are numerically the same in one respect (say, material object) are nonetheless numerically distinct in another respect (say, hylomorphic compound). But this is all that is needed to show that the material-constitution model of the Trinity can preserve the numerical distinction of the persons, and hence escape the objection under consideration. For on this model each of the persons is analogous to a hylomorphic compound. Hence, according to it there are three numerically distinct persons, though only one substance or God.
The material-constitution account of the Trinity just developed ought to hold considerable interest for contemporary philosophers of religion. For one thing, it provides a genuine alternative to the standard contemporary approaches to the logical problem of the Trinity – which almost always take one of two forms. The first attempts to interpret monotheism, or the Christian claim that there exists only God, in such a way as to make it consistent with the existence of three divine beings. This is the approach defended by Richard Swinburne,19 and it is also usually accepted by those theologians who adopt a so-called social view of the Trinity.20 The second approach, which as far as I can tell originates in the work of Peter Geach, adopts the assumption that identity is always sortal relative, and with it the view that things can be identical relative to one sortal (say, substance) but distinct relative to another (say, person).21
Both of the standard contemporary approaches to the Trinity face serious difficulties. The first approach appears to be coherent, but also inconsistent with the orthodox view of the Trinity. Indeed, it appears to be committed to a form of tritheism – the heresy according to which (to invert the Athanasian formula) “there is not one God, but there are three Gods.”22 As for the second approach, the main difficulty is whether the notion of identity it presupposes is acceptable. Admittedly, a system of formal logic employing the notion of “relative identity” can be constructed in such a way that no contradiction can be deduced from it, as Peter van Inwagen has shown.23 But as even van Inwagen himself admits, it is unclear whether the implications of this system, in particular its ontological implications, are ultimately coherent, much less acceptable.24
The difficulties facing these approaches bring us to a second reason why the material-constitution account of the Trinity is of significant interest. In addition to providing a genuine alternative to the standard contemporary approaches, it appears to be preferable to them. For it is both consistent with monotheism and coherent. Indeed, it may very well be that Abelard’s notion of “numerical sameness without one identity” provides the only coherent and orthodox way of resolving the logical problem of the Trinity.25
III.2 Divine simplicity
Despite the appeal of the material-constitution account of the Trinity, and the fact that it is naturally suggested by Abelard’s own discussion of material constitution, it is not an account of the Trinity that Abelard himself accepts. This account presupposes a certain amount of complexity in God – in particular, distinct forms that together with the divine substance constitute distinct objects, namely, each of the divine persons – whereas Abelard, like most other medieval philosophers, accepts the doctrine of divine simplicity.
According to the doctrine of divine simplicity, God is an absolutely simple being, with no distinct parts, properties, forms, or metaphysical complexity of any kind. Although Abelard assumes this doctrine in all three versions of his Theologiae, he discusses it at length only in the Theologia “scholarium.” Indeed, in this work he prefaces his whole discussion of the logical problem of the Trinity with a long section entitled “How there is unity in God” (quanta sit unitas in deo). Here is how Abelard initially formulates the doctrine of divine simplicity:
We confess the unity, or simplicity, or identity of the divine substance in such a way that just as it remains completely devoid of parts, so also it remains completely devoid of accidents; nor can it be changed in any way at all, nor can there be anything in it that is not it itself. And so it is the same completely simple and individual substance that is the Father and the Son and also the Holy Spirit; and the same thing is also the whole Trinity itself, that is, these three persons simultaneously.
(TSch 2.68)
Note that this initial formulation of the doctrine appears to be consistent with the presence of genuine complexity in God. Indeed, from this formulation it might appear that Abelard is concerned with excluding only certain kinds of complexity in God – namely, those associated with parts, accidents, and change – and on the basis of their absence in God to infer merely that the divine persons, and indeed the whole Trinity, must be the same substance or thing. If this were all that Abelard thought divine simplicity required, his understanding of the doctrine would be perfectly compatible with the account of the Trinity developed above. For as we have seen, the divine persons can be numerically the same substance or thing while at the same time possessing distinct forms or properties. Nor would admitting complexity of this sort compromise the view that God is simple in the sense of having no parts (since he has no material parts), no accidents (since all of his forms or properties are essential), and being incapable of change (since the possibility of change requires the possession of accidents).
But Abelard takes divine simplicity to require much more than this. Indeed, as he interprets the doctrine, it excludes not only the complexity associated with material parts, accidents, and change, but also the complexity associated with the possession of forms or properties (cf. TSB 2.105; TC 3.166; and TSch. 2.65–66 and 2.71–72). Thus, speaking of the divine properties, he says at one point: “I affirm that these properties are not other than God himself or the persons themselves” (TC 3.167). We have already seen that Abelard thinks the divine persons are essentially the same as the divine substance. Here, however, he goes further in two respects: first, by suggesting that the divine persons are also essentially the same as their properties (so that the Father is essentially the same has his fatherhood, the Son is essentially the same as is sonship, and likewise for the Holy Spirit and its procession); and second, by suggesting that the properties themselves are essentially the same as the divine substance.
Although Abelard sometimes articulates the doctrine of divine simplicity positively, saying that the divine properties are the same thing as God, he thinks the doctrine is stated most perspicuously in negative terms: “there are no forms or properties in God.” Recognizing that authorities speak as if there were forms or properties in God, as well as his own tendency to slip into this way of speaking, Abelard cautions us against interpreting such language too literally:
Now when we hear “properties” being spoken of, it must not be thought that we have in mind any forms in God. Rather we speak of “properties” as though we are speaking of “what is proper [to something]” – just as Aristotle says that every substance has it in common not to be in a subject, nor to admit of more or less, nor to have anything contrary to it. Now Aristotle does not have any forms in mind when he assigns these common features. On the contrary, he assigns these common features for the sake of removing rather than introducing something. Thus, just as we say . . . that it is proper to a formless thing, such as God himself, not to have forms, or to a simple thing that it lack parts, and in this way seem to introduce no forms, but rather to accomplish the removal of all forms and parts completely (or if anyone also understands any forms by this way of speaking, it is certain that they are not things different in any way from the those substances in which they inhere), so also we say that one feature is proper to the Father, another to the Son, and yet another to the Holy Spirit.
(TC 3.166)
In this passage, Abelard makes it clear that there are no forms or properties in God, and hence the term “properties” (proprietates), taken in its usual sense, cannot be applied to God. This by itself, however, is sufficient to show that the broadly Abelardian account developed earlier cannot be Abelard’s. For if there are no forms or properties in God, then the divine persons cannot be literally distinguished in property (since this sort of distinction literally applies only to compounds of matter and form, or subject and property).
In the foregoing passage we not only find evidence for how Abelard’s account of the Trinity should not be understood, but also some indication of how it should be understood. The key to Abelard’s final account lies in the distinction he draws between a thing’s differing from another in property and a thing’s differing from another in what is proper. Even though the divine persons do not differ from one another in property, according to Abelard, they do differ in an analogous way – namely, in what is proper to each. Judging from the comparison to Aristotle, Abelard intends these two modes of difference to be explained in terms of different types of predication. For example, when I truly predicate a property of a thing – say, a certain shape of a lump of wax – this predication requires the introduction of some positive feature or “form.” By contrast, Abelard suggests, when I truly predicate of something what is proper to it, the predication does not have this implication. This is especially clear, he suggests, in cases of the sort mentioned by Aristotle – that is, in cases where what is proper to a thing involves a privation or negation. For example, when I predicate not being in a subject of a substance, not only does my predication not imply the existence of a positive form or property (presumably, there are no such properties as not being in a subject), but it actually implies the non-existence or “removal” of a positive form or property (namely, being in a subject or inherence, which apparently is a positive form or property). Thus, things that differ in property differ with respect to positive forms or attributes, whereas things that differ in what is proper differ merely with respect to the predicates that apply to them.
Evidently, therefore, the distinction of the divine persons is to be understood not in terms of their possessing different forms or properties, but in terms of the different sorts of predicates that apply to them. Although differences in what is proper are marked by what predicates apply to a thing, and not by what forms or properties it has, it is important to recognize that this sort of difference is not be understood as a mere conceptual or verbal distinction. For in each case there will be a real difference grounding the application, or better the applicability, of the relevant predicates. This is especially clear in the case of the Trinity, as Abelard explains in the Theologia “summi boni”:
It is asked . . . whether the Trinity of persons in God should be understood verbally or in reality. For our part, we say that it should be understood in reality itself in such a way that from eternity that unique, entirely simple and individual thing, which is God, has been three persons . . . that is, Father, Son, and Holy Spirit.
(TSB 3.1; cf. also TC 4.1)
Again, in the Theologia Christiana he says:
It was not because a distinction of names was made that there is a Trinity, but rather because this Trinity has existed from eternity a distinction of names was made at some point in time.
(TC 4.5)26
It is clear, therefore, that if we are to understand Abelard’s own account of the Trinity, we must come to grips with its chief underlying assumption, namely, that there can be real distinction even without any distinction of forms or properties. Before examining this assumption in detail, however, we need to recognize a complication that it introduces into our discussion so far.
Up to now, we have been speaking of numerical sameness without identity as a relation that obtains only between things that differ in property. And this is because, until now, we have been operating on the assumption that numerical sameness, together with sameness of properties, is sufficient for identity. In terms of what Abelard says about difference in what is proper, however, we can now see that this is mistaken. For even though the divine persons are numerically the same and do not differ in property (since there are no properties in God by which they could differ), nonetheless Abelard wants to say that they are really distinct, inasmuch as they differ in what is proper to each. Evidently, therefore, Abelard thinks the relation of numerical sameness without identity can obtain even when its relata are the same in property (provided of course that they also differ in what is proper). The point of all this can perhaps best be made if we return to figure 1 and revise it in the way indicated at figure 2.
As figure 2 illustrates, our earlier attempt to associate numerical sameness without identity with the relation at (IB) was too quick. According to Abelard, this is a form of numerical sameness without identity, but it is not the only form, since the relation at (IA2) also qualifies as a form of numerical sameness without identity. For the same reason, our earlier attempt to associate the relation at (IA) with numerical sameness with identity – or just identity simpliciter – was too quick. According to Abelard, this relation is a genus with two species, only one of which qualifies as identity.
The coherence of Abelard’s account of the Trinity, as well as these further distinctions, depends upon the coherence of saying that a real distinction can obtain between things that are numerically the same and identical in property. So far we have little to go on in understanding what such a distinction could amount to. In order to put ourselves in a position to evaluate Abelard’s account of the Trinity, therefore, we need first to acquire a better understanding of this distinction and the justification for introducing it in the context of the Trinity. I shall undertake this project by examining in more detail Abelard’s notion of difference in what is proper. I then return, in the final section of the paper, to assessing the overall coherence of his account.
III.3 Abelard’s account of the Trinity
As we have seen, the notion of difference in what is proper is closely related to that of difference in property – indeed, it is just an analogical extension of it. Any clarification of difference in what is proper, therefore, must come by way of clarifying its analogue, difference in property. It turns out, however, that to understand what Abelard says about difference in property, we must consider his treatment of a closely related but more general notion, namely, difference in definition. For as we shall see, Abelard characterizes difference in property in terms of this latter sort of difference.
The following passage from the Theologia Christiana contains what is perhaps Abelard’s clearest description of “difference in definition”:
Things are different in definition when they cannot be terminated at the same definition associated with the meaning [of their terms] – that is, when they are not mutually requiring of one another, even though each is the same thing as the other, as in the case of a substance and a body, or a white thing and a hard thing. For something is not a body insofar as it is a substance, or a hard thing insofar as it is a white thing, since the one can exist without the other; nor does it require the other in virtue of itself.
(TC 3.154; cf. also TSB 2.96–98, TSch 2.95–99, and LNPS 559.5–29)
According to Abelard, the characteristic feature of things that differ in definition is that they do not require one another. What Abelard has in mind by this characteristic can be made clearer by considering one of his examples. To say that a white thing and a hard thing do not require one another is just to say that a white thing is not required to be a hard thing insofar as it is white, and a hard thing is not required to be a white thing insofar as it is hard. From Abelard’s use of “requires” in this and other contexts (most notably in his discussions of entailment27), it is clear that he intends to be making a point about the meanings of expressions. To say that a white thing is not required to be a hard thing is just to say that being white is no part of the meaning of the expression “hard thing.” Things differing in definition, therefore, differ only insofar as they fall under descriptions – and a sufficient condition for their differing in this way is that their descriptions differ in meaning.28 Thus, a white thing and a hard thing differ in definition because the descriptions “the white thing” and “the hard thing” differ in meaning. And the same account applies to the example of a substance and a body, and other such cases.29 In general, therefore, we may characterize difference in definition as follows:
The F is different in definition from the G just in case the descriptions “the F” and “the G” are different in meaning (which, for Abelard, is equivalent to saying that the descriptions are associated with different concepts).
It is worth noting that as Abelard understands “difference in definition,” it is intended to apply only to the case of a single concrete individual. Hence, things that differ in definition are, for that very reason, the same in essence or number.30 The same is true of the other forms of difference we shall be considering.
Now initially, it might be thought that the notion of “difference in property” is straightforwardly related to that of “difference in definition.” As we have seen, things differ in definition just in case they fall under different descriptions. Moreover, as Abelard recognizes, different descriptions often have different forms or properties associated with them. In light of this, it might be thought difference in definition plus different forms or properties (corresponding to the relevant descriptions) is all that is required for difference in property. In that case, we could say, in reference to a particular block of marble that is both white and hard, that the white thing differs in property from the hard thing. For the descriptions “the white thing” and “the hard thing” not only differ in meaning (and hence are different descriptions), but also have different forms or properties associated with them, namely, whiteness and hardness.
In fact, however, this is not what Abelard has in mind by “difference in property.” Abelard explicitly discusses the case of something white and hard, but only to show that, despite their difference in definition, the white thing and the hard thing are the same in property. And the reason for this, he says, is that their different properties are so “thoroughly mixed” (permixtae) that each of their subjects can be characterized by the property associated with the other:
One thing is said to be the same in property as another when the one participates in the property of the other, just as what is white [participates] in what is hard and what is hard [participates] in what is white. For something white participates in hardness, which is a property of what is hard – that is to say, something white is hard. And conversely something hard [participates in a property] of what is white.
(TC 3.140)
As this passage makes clear, when Abelard says that something white is the same in property as something hard, this does not mean that whiteness and hardness are the same property. Rather, it just means that the properties of whiteness and hardness “participate in one another” in the same subject – that is to say, whiteness can be attributed to the hard thing and hardness can be attributed to the white thing (as Abelard indicates by the fact that we can say “the white thing is hard” and the “the hard thing is white”). Thus, when Abelard says that the white thing and the hard thing are the same in property, what he means is that whiteness and hardness have the very same subject of possession.
Abelard’s discussion of the white and hard thing provides a clue to as to the proper understanding of difference in property. This form of difference requires not only a difference in definition plus different properties for different descriptions; it also requires that the properties in question be so “completely unmixed” (penitus impermixtae) that they have different subjects of possession.31 This, I take it, is the point that Abelard is emphasizing in the discussion of the waxen image that we have already examined.32 In this passage, it may be recalled, Abelard says that the wax (i.e., the matter of a form-matter composite) and the waxen image made from it (i.e., the form-matter composite itself) are different in property despite the fact that they are numerically the same thing. Moreover, he explains this difference by appealing to the fact that there is a property of the wax that cannot be attributed to the waxen image – namely, being the wax from which something is made – and conversely, that there is a property of the waxen image that cannot be attributed to the wax – namely, being made from wax. And this, I take it, is intended by Abelard to show that the subject of the first property is distinct from the subject of the second property, even if their subjects are the same in essence.33
In light of all this, we can see that, despite its misleading connotations, what Abelard calls difference in property involves not only different properties, but different properties that are related in such a way that they cannot be attributed to the same subject. If we keep this in mind, as well as Abelard’s view that whenever things differ in property they will also differ in definition, we may offer the following general characterization of difference in property:
The F is different in property from the G just in case (i) the F and the G are different in definition, (ii*) F-ness and G-ness are distinct properties, and (iii*) F-ness cannot be attributed to the G and G-ness cannot be attributed to the F at the same time and in the same respect.
With this characterization in hand, we are now finally in a position to return to the notion of difference in what is proper.
As we have seen, Abelard denies that the distinction of the divine persons can be understood literally in terms of the notion of difference in property, since there are no forms or properties in God. Strictly speaking, therefore, he says that the distinction of the divine persons must be understood on analogy with the notion of difference in property, and he introduces “difference in what is proper” to cover the relevant analogical extension. Now as far as I can tell, the only respect in which difference in what is proper is supposed to be unlike difference in property is in not requiring the existence of any forms of properties. Evidently, therefore, we can offer a general characterization of difference in what is proper by modifying our earlier definition of difference in property so as to remove the unwanted ontological commitment:
What is proper to the F is different from what is proper to the G just in case (i) the F and the G are different in definition, (ii) “F” and “G” are different predicates, and (iii) “F” cannot be applied to the G and “G” cannot be applied to the F at the same time and in the same respect.
The only difference between this definition and that of difference in property occurs in the second and third clauses (to which I have added asterisks, for the sake of emphasizing their difference). Thus, instead of speaking of different properties, F-ness and G-ness, this definition speaks of a different predicates, “F” and “G.” And instead of speaking of the attribution of properties, it speaks of the attribution of predicates. Thus, whereas before we had unmixed properties that distinguish subjects of possession, here we have unmixed predicates that distinguish subjects of predication. In order to get a better idea of how this sort of difference is to be understood, let us consider how it applies to the case for which it was specifically introduced, namely, the case of the Trinity.
The God of Christianity, says Abelard, is an absolutely simple being, lacking any sort of metaphysical complexity whatsoever. Nonetheless, this being has existed from all eternity in three persons, Father, Son, and Holy Spirit – from which it follows that there is something in extramental reality, namely, the simple divine substance, that from all eternity grounds the applicability of the predicates “father,” “son,” and “spirit.” Insofar as the simple divine essence grounds the applicability of the first predicate, it is God the Father, and insofar as it grounds the applicability of the second, it is God the Son, and likewise for God the Holy Spirit. If we allow ourselves to focus for the moment on the case of the Father and the Son, we can see how they differ in what is proper by seeing how they satisfy the three clauses of our definition.
To begin, it seems clear that the Father and Son differ in definition, and hence satisfy the first clause. For descriptions “the Father” and “the Son” clearly differ in meaning, and hence qualify as different descriptions. This last point, however, guarantees that the Father and the Son also satisfy the second clause of the definition. For presumably “the Father” and “the Son” are different descriptions just because “father” and “son” are different predicates. Finally, the relationship between the predicates “father” and “son” also seems to guarantee that the third clause of the definition will be satisfied. For “father” and “son” are relatively opposed – that is to say, they cannot be simultaneously applied to the same subject in relation to the same thing. This is not, of course, to deny that someone can be both a father and a son. Rather it is to deny that someone can be both a father and a son of the same thing.34 According to Abelard, however, the simple divine substance is both a father and a son, but not a father and a son of something extrinsic to the divine substance. But, then, insofar as the simple divine substance is God the Father – that is, insofar as it is the subject of the predicate “father” – the predicate “son” cannot be applied to it, and likewise, insofar as the simple divine substance is God the Son – that is, insofar as it is subject of the predicate “son” – the predicate “father” cannot be applied to it. But if this is correct, then insofar as the simple divine substance satisfies the predicate “father,” it (i.e., the Father) is a distinct subject of predication from the simple divine substance insofar as it satisfies the predicate “son” (i.e., the Son). Since in general a distinction qualifies as real, however, just in case it is not dependent on any activity of the mind, it would seem that the distinction between the Father and the Son is real. For as we have seen, Abelard assumes that the divine substance satisfies the predicates “father” and “son” by its very nature, quite apart from how we think or speak of it.
Assuming, therefore, that a similar story can be told about the Holy Spirit and the relationship of its distinctive predicate, “spirit,” to “father” and “son,” we would appear to have a real distinction among all the divine persons, despite their being numerically the same simple divine substance. Indeed, since the type of distinction in question makes no appeal to forms or properties, we would appear to have a genuine case of a real distinction whose relata are not only numerically the same, but also the same in property. And of course, if this is correct, Abelard has a genuine solution to the logical problem of the Trinity.
By now it may be clear that Abelard’s account of the Trinity parallels the broadly Aristotelian or material-constitution account of the Trinity developed earlier. Before turning to the evaluation of Abelard’s account, therefore, it may be useful briefly to compare it to the earlier account, which may be summarized as follows:
- (MC1)
Each of the divine persons is a “hylomorphic” compound consisting of the divine substance plus some further form or property (namely, fatherhood, sonship, or procession).
- (MC2)
Each of the divine persons is numerically the same as the divine substance (since hylomorphic compounds are numerically the same as their constituent matter).
- (MC3)
Each of the divine persons is a numerically distinct “hylomorphic” compound from each of the others (since the forms or properties of each are distinct, or as we might say now, unmixed).
- (MC4)
Hence, there are three numerically distinct divine persons each of whom is numerically the same substance or God.
As in the case of the material-constitution account, Abelard’s own account may be summarized in four claims:
- (AB1)
Each of the divine persons is the divine substance insofar as the divine substance satisfies each person’s distinctive name or predicate (namely, “father,” “son,” or “spirit”).
- (AB2)
Each of the divine persons is numerically the same as the divine substance (obvious from [AB1]).
- (AB3)
Each of the divine persons is a numerically distinct subject of predication from each of the others (since the predicates of each are unmixed).
- (AB4)
Hence, there are three numerically distinct divine persons each of whom is numerically the same substance or God.
As we can see, the chief difference between these two accounts is that the first distinguishes the persons on the basis of unmixed properties, whereas the second distinguishes them on the basis of unmixed predicates. In fact, once this difference is taken into consideration, the other differences between the two accounts fall out fairly straightforwardly.
Having presented Abelard’s account of the Trinity, and seen its relationship to the material-constitution account developed earlier, let us now turn to its evaluation.
IV. A LIMITED ASSESSMENT OF ABELARD’S ACCOUNT OF THE TRINITY
The main question for Abelard’s account, as I see it, is whether it succeeds in providing us with three, really distinct divine persons. The account clearly presupposes the existence of a single (absolutely simple) divine being, and hence succeeds in upholding monotheism. But when it comes to the distinction of the persons, it is not so obviously successful. The simple divine substance, he tells us, is by its very nature a Father, Son, and Holy Spirit. That is to say, in virtue of being what it is, the simple divine substance grounds the applicability of the unmixed predicates “father,” “son,” and “spirit.” But why should we think this provides us with anything more than a mere conceptual or verbal distinction among the persons?
As we have seen, Abelard has an answer to this question. Because predicates such as “father” and “son” are “unmixed” – or as we might put it, because they are converse asymmetrical relational expres-sions – their subjects of predication must be distinct. Thus, assuming that the simple divine substance really does ground their applicability, we must distinguish the Father from the Son. For nothing can be its own father, just as nothing can be its own son. And yet since it is clear from scripture and tradition that each of the persons is divine, God cannot be regarded as Father or Son in relation to something extrinsic to the divine substance. Hence, if the simple divine substance satisfies the predicates “father” and “son,” it must do so in such a way that, insofar as it satisfies the one, it cannot also satisfy the other, and vice versa. But this is just a way of saying that insofar as the divine substance is a Father (i.e., insofar as it is a subject of the predicate “father”) it is not the Son (i.e., the simple divine substance insofar as it is a subject of the predicate “son”). Of course this is not yet to say why the distinction in question is real. But here, too, Abelard has an explanation. According to him, the reality of the distinction owes to the fact that the applicability of the predicates “father” and “son” is grounded by the nature of the divine substance itself, not in the way we conceptualize or speak of it. But, then, if these two predicates are by their nature unmixed, and hence distinguish their subjects of predication, and yet the divine substance satisfies both of them by its very nature, it follows that the distinction must be real as opposed to being merely conceptual or verbal.
What all of this serves to emphasize is that the coherence of Abelard’s account, and hence his solution to the logical problem of the Trinity, ultimately depends on the coherence of his assumption that the simple divine substance can ground the applicability of predicates such as “father” and “son.” For once we grant this assumption, it would appear that Abelard is justified in concluding that there is a distinction among the persons that is both real and numerical. Now as far as I can tell, Abelard does not himself give us any compelling reason to accept this assumption, or even to think it is coherent. He does discuss the specific relations among the divine persons at length, but it is not clear that this discussion actually provides us with any reason for thinking that it is possible for an absolutely simple thing to serve as the subject of predicates of this sort.35
Ultimately, therefore, I think it must be said that Abelard’s account of the Trinity is incomplete. Although it does not seem obviously incoherent, without further development and defense it cannot be regarded as successful in providing a genuine solution to the problem of the Trinity. This is not to say, of course, that Abelard’s account is destined for failure, but only that, for all he has shown, it may yet fail.
Despite its incompleteness, I think there are at least two respects in which it must be granted that Abelard’s account is successful. First of all, and perhaps most importantly, it is successful in carving out the dialectical space open to anyone constrained by both the Christian doctrine of the Trinity and the doctrine of divine simplicity. In fact, his discussion not only carves out the relevant dialectical space, but also indicates what may very well be the only possible strategy available for preserving a real distinction among the persons without compromising the absolute simplicity of God. In this way, his discussion is also historically important, as it paves the way for later medieval developments. In fact, we can see the great philosophers and theologians of high and later Middle Ages, such as Thomas Aquinas, picking up precisely where Abelard’s discussion leaves off, addressing themselves directly to such questions as whether it is possible for a single thing to ground the applicability of such “unmixed” predicates as “father” and “son,” and introducing elaborate analogies to show that it is.36
Secondly, Abelard’s account is successful in steering a middle course between the twin heresies that threaten to afflict every account of the Trinity, tritheism and modalism. Abelard tells us in his autobiography that tritheism is among the charges brought against him at the Council of Soissons, where he was first condemned as a heretic – indeed that he narrowly escaped being stoned on the first day of his arrival at the council on the grounds that he had “preached and written (so the people had been told) that there are three Gods” (HC 83, Radice 1974, 79; cf. also HC 88, Radice 1974, 83). The details of Abelard’s condemnations are complicated, and involve much more than just his solution to the logical problem of the Trinity.37 Nonetheless, it seems clear from what we have seen that the charge of tritheism carries no weight. Indeed, if Abelard’s views commit him to any form of heresy, it is much more likely to be modalism than tritheism, that is, the view that there are not three really distinct persons in God, but only one person. Even here, however, Abelard’s account has the resources to resist the charge, inasmuch as it provides us with a principled reason for saying the divine persons are really distinct.38
In the end, therefore, it seems to me that Abelard must be credited with having developed a philosophically sophisticated and theologically interesting account of the Trinity, one that not only calls attention to the implications of standard medieval views about the Trinity, but also highlights the sort of work that must be done if such views are to be rendered ultimately defensible. Abelard’s discussion helps us to appreciate, moreover, why it is so often the case that specifically theological considerations lead medievals to make their most important and original philosophical contributions. For apart from the difficulties associated with such theological doctrines as the Trinity, one might never have the opportunity to develop the sorts of refinements that Abelard introduces in his discussion of identity and material objects.39
2. I follow the usual convention in Abelardian scholarship of translating diversum as “different” rather than “diverse.” This notion of difference, however, should not be confused with the technical Aristotelian notion of difference, which literally involves a differentia – that is, the property or feature that together with a genus constitutes a species.
3. In TSB 2.82–102, Abelard distinguishes six modes of sameness and difference (in essence, number, definition, likeness, change, and function). Much of this account is repeated in TC 3.138–164 with the addition of one further mode of sameness and difference (namely, in property). The account of sameness and difference in TSch 2.95–100 is deliberately simplified, and hence treats only four of the modes of identity (in essence, number, likeness, and “property or definition” – which is really an amalgam of each). Since the account in TC is the most complete, and clearly presupposed in TSch, I will often be relying on it in what follows for Abelard’s mature views about the proper resolution of logical problem of the Trinity. For Abelard’s discussion of sameness and difference outside these theological contexts, see LNPS 558.1–560.28.
4. TSB 2.103: “The persons – that is, the Father, the Son, and the Holy Spirit – are different from one another in a way analogous to those things that are different in definition.”
5. It is standard to translate mucro as “blade,” as I do here, but it is important to emphasize that Abelard uses the term as a synonym of “sword,” whereas in ordinary speech, a sword has a blade – that is, the blade is just one part of the sword, the hilt being the other part.
6. This description of essential sameness is derived nearly verbatim from TSB 2.83. But cf. also the discussion at TSch 2.95 and LNPS 558.15–17.
7. Cf. Jolivet 1975, 538–543; 1982, 293, n. 48. See also Kretzmann 1982, 497.
8. Hereafter I shall drop the qualification “in our sense” and simply use the term “identity” to refer to the relation of identity as we ordinarily understand it.
9. Abelard’s views about numerical sameness change over time. He always maintains that essential sameness entails numerical sameness, at least in respect of essence. In Theologia “summi boni,” however, he claims that essential distinctness is compatible with sameness in number, as he thinks is clear from the case of parts and wholes: “it is necessary for all these things – namely, all those which are the same essentially – to be the same in number, but the converse is not true. For perhaps this hand is the same in number as this man of which it is a part, and no part is different in number from its whole. Nevertheless, a part is not essentially the same as a whole” (TSB 2.83). In later works, however, Abelard comes to deny that essential distinctness is compatible with numerical sameness, and to argue instead that parts are neither numerically the same or different from their wholes. Cf. especially TC 3.148–153.
10. For an excellent discussion of these examples, as well as their methodological importance for Abelard’s thought, see Wilks 1998. As Wilks himself notes, the theoretical importance of these examples was first suggested by Tweedale 1976, 147–157 and briefly commented on by Normore 1987, 209–210 and 1992, 89–90. For some background on the use of these examples among Abelard’s predecessors, see Constant Mews’s editorial introduction to TSch, 207–209.
11. See, e.g., Abelard’s account of universals in LNPS 522 and the account of good and evil in Coll. 128–129; cf. also the discussion of both in Wilks 1998.
12. The problem of material constitution has been widely discussed by contemporary philosophers, but until recently the theory proposed by Abelard has not been recognized among the candidates for a possible solution. In an important article, however, Michael Rea (1998) explicitly develops and defends the type of solution that I attribute to Abelard, and my own discussion is indebted to his. For the development and defense of other views that are in many ways similar to Abelard’s, see also Paul 2002; Robinson 1985; Yablo 1987.
13. Rea 1998, 321–322.
14. It might seem somewhat odd to speak of matter as belonging to a kind – as if it were itself a kind of object. This way of speaking, however, is fairly well entrenched in Aristotelian metaphysics, and hence apparently just shows how differently contemporary and Aristotelian philosophers use the term “matter.”
15. Strictly speaking, this follows only on the assumption that (a) there are such things as statues and lumps of bronze, and (b) that identity is necessary (i.e., that if a = b, then necessarily a = b). One could, of course, deny either of these assumptions. But on the face of it, denying either of them seems just as implausible as allowing for co-located objects.
16. The lengths to which contemporary philosophers have gone to avoid co-locationism testifies to just how implausible it can seem. Part of what makes the view implausible is that it is difficult to see how two material objects, which are wholly co-located, and hence share exactly the same micro-physical structure, could differ in their persistence conditions. For a discussion of this, as well as other objections to co-locationsim, including the objection that it involves a needless multiplication of entities, see Merricks 2000, esp. 38–40 and 82–83.
17. Actually, if we say that each of the persons is a hylomorphic structure we will be committed to admitting four distinct kinds of object in the Trinity (the divine substance, the Father, the Son, and the Holy Spirit). It is not clear to me that this is a problem for Christian orthodoxy. But if one wants to preserve the existence of only three kinds of object in the Trinity, one can always identify one of the divine persons (say, the Father) with the divine substance and then construe each of the other two persons as “hylomorphic” structures. In fact, Abelard’s discussion of the generation of the Son encourages just this sort of view. The Father, he says, is power, whereas the Son is a certain kind of power – that is, power plus a certain differentia: “Just as . . . to be a man (i.e., a mortal rational animal) is to be a certain kind of animal, so also divine wisdom [i.e., the Son] is said to be of the substance of divine power [i.e., the Father], since to be wisdom (i.e., the power of discerning) is to be a certain kind of power” (TSch 2.116). Cf. also TC 4.87.
18. In the case of properties it is, perhaps, perfectly clear that they are not material objects, but the same should be clear even in the case of hylomorphic compounds. After all, we have seen that one material object can be comprised by two (or more) hylomorphic compounds – as in the case of Athena, which is comprised by a statue and a lump of bronze.
19. Swinburne 1988; cf. also Yandell 1994.
20. E.g. C. Plantinga 1988.
21. See Geach and Amscombe 1963, 118–120. For further development and defense of the “relative identity” approach to the Trinity, cf. Martinich 1978; van Inwagen 1988.
22. I have defended this claim at more length in Brower forthcoming.
23. van Inwagen 1988, esp. 248–260.
24. Cf. van Inwagen 1998.
25. For further development and defense of the material-constitution account of the Trinity, see Brower and Rea forthcoming.
27. See, e.g., Dial. 284. For detailed discussion of this aspect of Abelard’s views, see Martin 1987a, 1992a; and chapter 5 of this volume. Cf. also Stump 1989, 87–109 and Marenbon 1997a, 44–45.
28. It is clear, therefore, that Abelard is using the term ‘definition’ in a deliberately broad sense, which extends beyond the strict Aristotelian sense requiring a genus and specific difference.
29. This explains why Abelard suggests at one point that only “univocals” can be the same in definition. Cf. TSch 2.95.
30. This fact helps to explain why, in his earliest discussions of the Trinity, Abelard thought that the distinction of the divine persons could aptly be characterized in terms of this mode of difference. By the time of the Theologia Christiana, however, he came to think that difference in definition was not fine-grained enough to capture the distinction of the divine persons, and hence introduced the notion of difference in property (and its analogical extension, difference in what is proper).
31. Abelard comes close to putting the requirement in just this way at TC 3.186, where he is discussing the distinction of the divine persons: “It is clear that the distinction of the persons consists not only in the distinction of their definitions and properties, but also in the exclusion of their predication from one another (in remotione praedicationis ipsarum ab invicem), since one of the persons is no way another.”
32. See TC 3.140, discussed in §II.1 above.
33. It is significant, therefore, that at one point in this passage Abelard speaks of the things differing in property as things “distinguished by their properties” (proprietatibus suis distinguuntur). See TC 3.140.
34. “Father” and “son” are what we would nowadays call converse, asymmetrical expressions – which is just to say that if a is father of b, then b cannot be father of a, but must instead be son of a, and conversely, if b is son of a, then a cannot be b’s son, but must instead be b’s father.
35. In support of this assumption, Abelard could, of course, appeal to scripture and tradition, which certainly refer to God as both “father” and “son.” But while this would provide him with reason to suppose that a single thing (namely, God) can ground the applicability of predicates “father” and “son,” it would do nothing to show that an absolutely simple thing can ground their applicability – at least without some further argument for the claim that scripture and tradition also support the doctrine of divine simplicity as he understands it.
36. See, e.g., Aquinas’s discussion in ST I.27–30.
37. At the Council of Sens, where Abelard was condemned for a second time, nineteen heretical propositions or capitula were imputed to him, only five of which deal directly with Trinitarian issues. For a discussion of these propositions, see Luscombe 1969.
38. Even if Abelard’s account could not resist the charge of modalism, however, it is hard to see how this would render it any worse off than that of most other medievals who also accept divine simplicity.
39. I read earlier versions of this chapter to the 2001 Cornell Summer Colloquium in Medieval Philosophy and to the Philosophy Department at Purdue University. I am grateful to the audiences on those occasions for stimulating comments and discussion. I am also grateful to Michael Bergmann, Martin Curd, Kevin Guilfoy, Patrick Kain, Peter King, Eleonora Lorenzetti, John Marenbon, Michaeal Rea, Eleonore Stump, and especially Susan Brower-Toland for helpful comments on earlier drafts of this chapter.