We may classify contemporary Latin accounts into several groups. There are those theories, going back to Duns Scotus, which take the relation of the Godhead to the persons of the Trinity to be something like the relation between universals and their instances.Footnote 5 There are accounts, following Abelard (Brower 2004, a similar view is defended more recently by Rea (2003)), according to which the relation that holds between the Godhead and the persons is a relation of numerical sameness but not one of genuine identity. Then there are the relative identity accounts, which hold that the Godhead is the same divinity as the Father, the Son, and the Holy Spirit, respectively (each of these is also the same divinity as each of the others); however, none of the persons is the same person as any of the others, or as the Godhead. According to a relative identity account of the Trinity, the relations ‘...is the same divinity as...’ and ‘...is the same person as...’ are not relations of classical identity (equivalence relations which guarantee the indiscernibility of their relata); nevertheless, they are relations of numerical identity (from ‘x is the same divinity as y,’ we can infer ‘there is one divinity’). Anscombe and Geach (1961) Martinich (1978, 1979), van Iwagen (1988, 2003), Cain (1989), and Conn (2012) have worked on this approach. The first we will consider, however, is Leftow’s own account, which involves an analogy with time travel.
If time travel is possible, then it is apparently possible for one and the same person to be multiply instantiated simultaneously (in public time) in different spatial locations. For example, it is possible for a person, Leftow names her ‘Jane,’ to journey through time and join her earlier self. Presumably, if this is possible, it is possible for three instantiations of Jane to be present in the same room at one public time. Leftow suggests that this possibility serves as a model for the Trinity (2004). Each of the divine persons is like one of the instantiations of Jane; just as the three instantiations are all one and the same person, even though they do not have all the same properties (at least, they seem not to), so too, all three persons are one and the same divinity, and that single divinity is to be identified with a single divine substance persisting through time. It is easy to see why this account is generally considered a version of Latin Trinitarianism. The most apparent worry here is modalism rather than tritheism.
Leftow’s account depends, then, on the coherence of time travel. There are, of course, well known objections to the metaphysical possibility of time travel, which I will not rehearse here. Assuming these can be answered, however, a theological worry remains. Leftow must explain what ‘Jane’ refers to here, the single substance or one of the instantiations? If the former, then it seems we have reached straightforward modalism. If the latter, and we take talk of ‘three Janes’ seriously, then how is this to be distinguished from accounts of Social Trinitarianism, whereby the persons are parts of the whole substance?Footnote 6
Leftow emphasizes that he conceives the relation between the substance and each of the instantiations as being one of identity. He rejects that the instantiations are parts of Jane, not even temporal parts (Leftow is an endurantist). This is sufficient to distinguish his position from Social Trinitarianism, but it raises interesting questions about the kind of identity relation Leftow has in mind.
It seems to me that if the kind of time travel that Leftow needs to motivate his case is possible, then one of the following must be false.
(7) ‘There are three divinities’ if and only if ‘There is some x, some y, and some z, where each is non-identical with the others and each is adivinity.’
(8) All relations of numerical identity are characterized by unrestricted Leibniz’s Law, that is, that if x and y are identical, then x and y have all their properties in common.
It is easy to see why this is, if every Jane is identical to one common substance, then (assuming the Transitivity of Identity, which I do not imagine anyone wishes to reject) each is identical with each of the others. At the same time, the Janes do not have the same properties, for if they did then by parity of reasoning, so would the persons of the Trinity, and this really would be modalism. So either the Janes can be one in cardinality although they are non-identical, or they can be identical in spite of having different properties.
It seems, then, that Leftow has two options; reject (7) or reject (8). However, I think that, regardless of which of these Leftow adopts, his account will not satisfy (Divinity), the condition on successful Latin accounts of the Trinity which seemed implicit in Leftow’s own attack on Social Trinitarianism.
If Leftow rejects (7), then he rejects a very plausible thesis concerning the relationship between identity and cardinality. Even then, though, this will not provide an account of the Trinity on which (Divinity) is satisfied. For on this account, the Godhead is divine in virtue of being identical with the Godhead, whereas the persons are divine in virtue of being counted as one, without being strictly identical. On this version of the account, then, there remain different ways of being divine.
Alternatively, one might reject (8). For example, one might restrict Leibniz’s Law in the case of diachronic identity relations so that, rather than ranging over all properties, it ranges over only intrinsic properties. Perhaps Leftow can show that all the distinguishing properties of the individual persons are extrinsic and therefore no obstacle to identifying the persons as one (whether this turns out to be modalism is still a real worry, but not the one that interests me here). However, this attempt does no better with respect to satisfying (Divinity), because, again, a importantly different kind of relation obtains between the persons and the Godhead from that which obtains between the Godhead and the Godhead. In the former case, to avoid contradiction, it must be the case that the relation that holds between any one of the persons and the Godhead is non-Leibnizian, because they clearly do not have exactly the same properties. If it is an identity relation, it must be a diachronic relation where sameness of property is restricted to intrinsic properties, or something similar. The relation between the Godhead and the Godhead, by contrast is a relation of synchronic identity which does satisfy Leibniz’s Law. It is by virtue of satisfying the latter, more fundamental relation, that the Godhead is divine, whereas it is by satisfying a weaker relation that the persons are divine.
Similar considerations, unsurprisingly, show that numerical sameness and instantiation accounts of the Latin Trinity also fail to satisfy (Divinity). The former are no different than the rejection of (7) above. These accounts posit a relation weaker than identity, and claim that it holds between each of the persons of the Trinity and the Godhead. These accounts do not, however, deny that genuine numerical identity exists. The Godhead, then, is still numerically identical with itself. Once again, it seems this account is committed to the Godhead being divine in virtue of satisfying a more fundamental relation to itself than the relation that grounds the claim that each of the persons is divine. Accounts like that of Duns Scotus, on which the relation that holds between the Godhead and the persons can be understood by analogy to the relation between a universal and its instantiations (or on the Brower and Rea (2005) view, according to which the relation is like the relation between a primary substance and a second substance), of course, also fail to satisfy (Divinity) for the same reasons. Theses accounts do not reject that the Godhead is genuinely numerically identical with the Godhead, and the relation that they claim holds between the persons and the Godhead is weaker than this identity relation. The Godhead’s divinity is, then, grounded in a more fundamental relation than the person’s divinity.
I take it to be a plausible thesis that the Godhead is divine simply in virtue of being identical with the, by hypothesis, one and only Godhead. If this is so, however, it is clear that no account of the Trinity can satisfy (Divinity) while assuming classical logic. The price of orthodoxy, if orthodoxy really does involve the satisfaction of (Divinity), is adopting a non-classical logic. There are several prima facie possibilities.
One possibility that has not been discussed at any length in the existing literature is to adopt aparaconsistent logic, accepting that the orthodox account of the Trinity is inconsistent, yet nevertheless true. However, paraconsistent logic, apart from its radical departure from classical logic, also accords ill with theological orthodoxy. The prospective benefit of adopting aparaconsistent logic, with respect to the doctrine of the Trinity, is that it allows the logical possibility of the various theological doctrines being simultaneously true, although they contradict one another. However, this sort of solution is very difficult to square with orthodoxy, statements of which are often framed in terms which seem to presuppose the law of non-contradiction. Take, for example the Athenasian Creed once again. It is not sufficient for orthodoxy that we hold that the inconsistent conjunction ‘there is exactly one God and it is not the case that there is exactly one God, because there are three’ be true. Consider the 18th line of the Creed,
[f]or like as we are compelled by the Christian verity; to acknowledge every Person by himself to be God and Lord; So are we forbidden by the catholic religion; to say, There are three Gods, or three Lords.
Affirming the doctrines, then, is necessary but not sufficient for orthodoxy. Orthodoxy also involves not affirming the negations of the doctrines. This is just what would be involved in a solution depending on paraconsistency.
Apart from paraconsistency, the obvious alternative for blocking the deduction on page 2 is by rejecting the problematic rule of inference that I have called ‘SRI.’ This can be done by adopting a non-classical view of how relations like ‘ =
’ work. This is represented in the literature by the relative identity response to the logical problem of the Trinity, to which we turn next.
The Relative Identity Solution
The relative identity response was first proposed by Anscombe and Geach (1961) and Geach (1967). Geach attributes atheory of relative identity to Thomas Aquinas, and we can get abetter grasp the significance of relative identity for Latin Trinitarianism, if we consider Geach’s account of Aquinas.
A few remarks on the logic of ‘there is but one God’ and ‘the one and only God.’ On Russell’s theory of descriptions ‘the one and only God is X’ would be construed as meaning:
‘For some y, y is God, and for any z, if z is God, z is the same as y, and y is X’; And this, shorn of the final clause ‘and y is X,’ would also give the analysis of ‘there is but one God.’ Aquinas would certainly have objected, on general grounds, to the clause ‘z is the same as y’; the sameness, as we saw, must for him be specified by some general term signifying aform of nature. Now the general term that we need to supply here is clearly ‘God’; so ‘there is but one God’ will come out as:
‘For some y, y is God, and, for any z, if z is God, z is the same God as y.’ It is important to notice that this would leave open the possibility of there being several Divine Persons; there would still be but one God, if we could truly say that any Divine Person was the same God as any other Divine Person. Anscombe and Geach (1961: 118)
Therefore, on this view, all the x s that are divine are also the same divinity as the Godhead, and together add up with the Godhead to a total of one divinity. The relation ‘... is the same divinity as...’ is taken, by relative identity theorists, to be a genuine relation of numerical identity. This means that numerical identity relations can cross-cut, such that some x and y can be the same divinity and yet be different persons. On this view, this is simply how numerical identity relations work, and does not involve any incoherence. Some entity(ies) can be one when divided up according to one sortal-relative identity relation, while they can be three when divided up according to a different sortal-relative identity relation. If the relations ‘... is the same divinity as...’ and ‘... is the same person as...’ were relations of classical identity (that is, relations characterized by Leibniz’s Law, Symmetry, Transitivity, and, given the presence of sortals in these relations, Weak Reflexivity) this would be contradictory.Footnote 7 So relative identity theorists reject that these sortal-relative relations of numerical identity satisfy Leibniz’s Law.
It is important to note that this account comes in several importantly different forms. The distinction that matters for our present purposes is that between what I shall call ‘strong’ and ‘weak’ theories of relative identity. Weak theories of relative identity hold that there are absolute identity relations (characterized by Leibniz’s Law) and relative identity relations (for which Leibniz’s Law fails). Strong theories of relative identity hold that the only numerical identity relations that there are are non-Leibnizian relative identity relations.
Historically, Geach has been alone in committing himself to strong relative identity (1967). Other relative identity theorists have typically taken the rejection of absolute identity to be an unnecessary encumbrance to the theory which undermines its independent plausibility.Footnote 8 Peter van Inwagen, in his influential 1988 paper ‘And yet there are three Gods,’ which reintroduced relative identity as an approach to the logical problem of the Trinity, declares himself neutral on the existence of absolute, non-relativized, identity (1988: 259). However, it is with respect to the satisfaction of (Divinity) that we can see why a relative identity theorist interested in providing a response to the logical problem of the Trinity might reject the existence of absolute identity altogether.
The weak relative identity theorist is in the same position as the defender of a ‘sameness-without-identity’ account of the Trinity, indeed they have a difficult time explaining how their account is any different. Once again, if it is allowed that there are genuine relations of absolute unrelativized identity, then it is overwhelmingly plausible (barring any particular reason for thinking otherwise) that the Godhead has this relation to itself. The Godhead, then, has this fundamental relation to itself, while the persons have the weaker, and one might certainly think derived, relation of sortal-relative identity ‘...is the same divinity as...’ to the Godhead. This account fails to satisfy (Divinity) and certainly seems to be involving two different ways of being divine, one more fundamental than the other and attaching only to the Godhead.
The Strong Theory of Relative Identity, by contrast, will not, in fact cannot, say that the Godhead is absolutely identical with itself, for it holds that there is no such relation as ‘... is absolutely identical with...’. Rather, the strongest relation that the Godhead bears to itself is the relation ‘... is the same divinity as...’. It is in virtue of this relation, then, that the Godhead is divine. This is of course the same relation that each of the persons of the Trinity has to the Godhead as well. In addition, the three divine persons bears the relation ‘... is a different person from ...’ to each of the other persons. This is why there are three persons, but one divinity. Note that on this account the threeness of the persons has no priority over the oneness of the divinity, the relative identity account of the Trinity involves two different relations of genuine identity (as opposed to equivalence) which cross-cut each other. On this account, the Trinity is not three different objects that have some common property that allows them to be counted as one in some derivative way. Rather it is a reality that does not in itself have a cardinality, but can be counted as one or three according to which of several equally legitimate identity relations is employed in the counting.
(Divinity) can only be satisfied by an account of the Trinity according to which the strongest relation that the Godhead holds to the Godhead is the same relation that each of the persons holds to the Godhead. This relation cannot be absolute identity if the resulting account of the Trinity is to be consistent, so it seems that the strongest relation that the Godhead can hold to the Godhead must be a relative identity relation or something very much like it. This speaks in favor of a strong relative identity account of the Trinity as the appropriate one for the particular theological view that I have been interested in in this paper.