Metaphysical Options

The following analysis aims to provide an exhaustive typology of theories on the relation between particulars and universals. There is nothing much original about the typology, and the aim in providing it is merely to oflEr a helpful template for understanding theological analyses ofthe Trinity, rather than to shed

4 Pace, e.g., John Zizioulas, Being as Communion: Studies in Personhood and the Church (London: Darton, Longman & Todd, 1985), pp. 40—1: 'Among the Greek Fathers the unity of God, the one God, and the ontological ''principle'' or ''cause'' of the being and life of God does not consist in the one substance of God but in the hypostasis, that is, the person of the Father. The one God is not the one substance but the Father, who is the ''cause'' both of the generation of the Son and of the procession of the Spirit.' There clearly are derivation accounts of divine unity in Gregory of Nyssa (see, e.g., Gregory, Oratio Catechetica 3, edited by E. Muhlenberg, GregoriiNysseni Opera [= GNO], 3/4 [Leiden, New York, Cologne, 1996], 13.23—6). But these accounts are inconsistent with Gregory's general theory of the divine essence. Although it is often held that the Eastern tradition remains faithful to Athanasius in this matter, it seems to me—and I shall provide some evidence for this claim in what follows—that the respect paid in the Eastern tradition to Athanasius's view is little more than lip-service, and that it is Gregory's view that comes to dominate.

5 And it would not be hard to demonstrate also fundamental agreement on the claim that the Father—and not the divine essence—is the ultimate source of the other two persons too (though East and West are in genuine disagreement on the question of the possible communication of the Father's 'spirative' power to the Son): what else could be the point of the claim that the Son and Spirit proceed from the Father? See the comments on Augustine in Lewis Ayres's review of Colin Gunton, The Promise of Trinitarian Theology (Edinburgh: T. & T. Clark, 1991), in The Journal of Theological Studies 43 (1992), pp. 780-2, at p. 781.

any light on the substantive philosophical question. The exhaustive nature of the typology, I hope, makes it clear that the sorts of distinction that I am making are conceptual matters, and to that extent logically unavoidable. Equally, while the typology is, as far as I can see, exhaustive, there are many different ways in which the theories proposed could be developed. The philosophical issue is, thus, more complex than my analysis may suggest. Still, I hope to provide a set of tools sufficient for my theological purposes here. I will state now that the conclusion of the discussion will be that a universal is a (numerically) singular item that can be a property of more than one substance. Someone considerably more interested in the application of this conclusion to the theological question than in the establishment of the conclusion in the first place could skip this first section altogether and go straight on now to section II.

Let me start with a distinction between a property and a substrate. Very roughly, a property is a describable characteristic of a thing. A substrate is a bearer of such characteristics, in itself distinct—in some way or other—from any and every property. This distinction yields the first disjunction in the basic typology. For we could hold that a thing—a substance—includes both a substrate and one or more properties; or we could hold that a substance includes only properties—that it is a bundle of properties. (Nothing could be just a substrate, because such a thing would lack any describable characteristics, and would thus be nothing at all.) A second distinction will increase the number of options. For we could hold that properties are particulars, or we could hold that properties are universals. If properties are particulars, then the properties of numerically distinct substances—even indiscernible properties—are numerically distinct from each other. If properties are universals, then the indiscernible properties of numerically distinct substances are (numerically) identical with each other. For example, if the redness of this rose is numerically distinct from just the same shade of redness in that rose, then the two rednesses are two particular properties. If, on the other hand, the redness of this rose is (numerically) identical with the redness of that rose, then redness is a universal, shared by the two roses.6 This distinction—between particular and universal properties—allows us to increase the range of our typology. Suppose we accept that a substance includes

6 I speak of 'numerical' identity here. Some theories of universals have denied that numerical identity is the relevant sort of identity, at least in the case of creaturely properties. Duns Scotus, for example, famously claims that the identity that obtains between two instances of a property is 'less than numerical'. But this introduces a complication that makes no difference to my argument, so I ignore it here (except for my brief discussion of Scotus below). For the 'numerical' identity of universals, see the classic modern discussion in D. M. Armstrong, Nominalism and Realism (Cambridge: Cambridge University Press, 1978), p. 112, with reference to Scotus's claims about less-than-numerical unity: 'For myself, I cannot understand what this second, lesser, sort of identity is. Partial identity, as when two things overlap but do no more than overlap, or when two things have some but not all the same properties so that their nature ''overlaps'', can be understood readily enough. But identity is just identity... I take it that the Realist ought to allow that two ''numerically diverse'' particulars which have the same property are not wholly diverse. They are partially identical in nature and so are partially identical.'

both substrate and properties. We could accept that the properties in question are particular properties, or we could accept that the properties in question are universal properties. For that matter, we could suppose that some of the properties are particular, and some universal. Equally, suppose we accept that a substance is simply a bundle of properties. We could hold that the properties in question are particulars, or universals, or a combination of the two. This yields six basic models in the typology. I am not interested here in which of these models is true as a matter of fact: merely in seeing how the models impact on the doctrine of the Trinity.

It is important to note that accepting one of these bundle theories does not in itself entail abandoning talk of substances. Philosophers who accept bundle theories appeal to a notion first introduced by Bertrand Russell—himself a thinker who accepted that a particular is a bundle of universal properties: the notion of compresence. Compresence is a basic unanalysed relation that is symmetrical and intransitive: that is to say, if a is compresent with b, then b is compresent with a (symmetry); but, if a is compresent with b, b's compresence with c does not entail as compresence with c (intransitivity).7 The intransitivity criterion allows two sets of compresent properties to overlap. The possibility of overlapping is vital for Russell's theory, since if a property is a constituent of more than one substance (as must be possible if a property is a universal), then that property will be a constituent of more than one set of compresent properties. Substances, on Russell's sort of view, tend to overlap (for reasons just suggested), and there is no further whole thing constituted by the union of overlapping substances.

By definition, then, a universal is a property that can be a constituent of more than one substance. This is sufficient to distinguish universal properties from particular properties: unlike universal properties, particular properties cannot be constituents of more than one substance.8 It follows straightforwardly from this

7 For a useful and accessible discussion of Russell's view, see Armstrong, Nominalism and Realism, pp. 89-91.

8 The situation needs somewhat careful handling, however, since even philosophers who deny the existence of universal properties may need to allow for overlapping: some of the parts of a mereologically complex particular substance (a substance, that is to say, that includes parts) are themselves overlapping sets of particular properties. Without going into needless complexity here, we simply need to note that the properties included in these overlapping sets are not properties of more than one substance—even though they may be properties of both a substance and one or more of its parts. For this, then, all we need is an intuitive account of the sorts of things that may count as substances. I have tried in this short account to proceed on the assumption that the set of substances on any bundle theory of substance includes objects that are themselves mereologically complex, composed of parts that are themselves bundles of compresent properties, whether particular or universal. Substances are (let us say) complete bundles of properties, that may (though need not) include various overlapping sets of compresent properties. A complete bundle is a bundle to which (whether for physical or logical reasons) no further property can be added. On the view that substances themselves can include overlapping sets of compresent properties, it follows that not all of the properties of a substance are compresent. (Thus, I am using 'complete' to include, in principle, properties which need not all be compresent. What account we give of the union of such account that the only bundle sort of ontology that can allow for overlapping substances is one that accepts universals. This claim is of extreme importance for my analysis of the Trinitarian debates, for if it is firmly grasped, it can help us to see why the supposed divergence of Eastern and Western views on this topic is not what it appears to be.9

One terminological matter. I am talking about substances here; the standard theological terms for such things in the Trinitarian context are 'hypostases' and 'persons'. The divine essence is the sort of thing that I am referring to as a property. As Western theologians have long recognized, there is a terminological divergence between East and West that only serves further to muddy the waters of Trinitarian discussion. What the Western theologians tend to call 'substance' is labelled 'ousia' ('essence') by the East; the Eastern term 'hypostasis' (literally substance) is labelled 'person' by the West.10 I treat 'substance' and 'person' as synonyms for the sake of this discussion, and (following Augustine's preferred usage) employ 'essence' for 'ousia'.11

I shall assume that the divine essence is just one property—and not, for example, a bundle of properties.12 It is for reasons of simplicity that I shall accept the view that the divine essence is just one property. Historically, those theologians who have been interested in the question of divine simplicity have tended generally, though not universally, to affirm that the divine essence does not include more than one property (namely, itself), and making this concession means that we can ignore the vexed question of the simplicity of the divine essence.13 It does not mean that we can ignore the question of the simplicity of a divine person, since such a person is generally held somehow to include more than just the divine essence—an issue to which I will return below. Still, nothing substantive of a strictly Trinitarian nature turns on the assertion or denial of the sets is well beyond the scope of my article here—indeed, it would require a full account of the logic of mereology [viz., of part-whole relations]: a matter of extreme philosophical complexity. Fortunately, it is irrelevant for my very limited purposes here.)

9 We could allow that the parts of substances are themselves substances. In this case, we should simply have to claim that the only ontology that can allow for complete substances to overlap is one that includes universals. Nothing substantive turns on this clarification.

■0 For this, see Augustine, De Trinitate [=Trin.] 5.9.10 (edited by W. J. Mountain, 2 vols. CCSL, 50 [Turnhout: Brepols, 1968], pp. 216-17).

ii For Augustine's preference here, see below, note 46.

12 It could not, of course, be a complete bundle of properties, for then it would be a substance or person. But it could be a bundle ofcompresent properties that is included in one or more substances or persons—things in other words that on this view are complete bundles of properties.

13 In the context of a general discussion of divine simplicity, Augustine makes the point that the essence cannot be anything other than one simple property: 'God however is indeed called in multiple ways great, good, wise, blessed, true, and anything else that seems not to be unworthy of him; but his greatness is identical with his wisdom . . . and his goodness is identical with his wisdom and greatness, and his truth is identical with them all; and with him being blessed is not one thing, and being great or wise or true or good, or just simply being (esse), another': Trin. 6.7.8 (CCSL, L, 237). Unless otherwise noted, translations are my own, though I have consulted the standard English versions. See too Gregory of Nyssa, Contra Eunomium libri 2.501 (edited by W. Jaeger, 2 vols., GNO, I and II [Leiden: E. J. Brill, 1960], I, p. 372).

simplicity of the divine essence, and the argument is not affected by my assumption of simplicity here.

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