RI-Trinitarianism

The Christian doctrine of the Trinity is held by critics to be logically incoherent in so far as it is committed to both monotheism and the distinctness of divine persons. As monotheists Christians – at least those who endorse the Athanasian Creed – hold that the Persons of the Trinity are one God;Footnote ¹ as trinitarians they affirm that Father, Son, and Holy Spirit are three Persons. Peter van Inwagen and others (Cain (Reference Cain1989); Martinich (Reference Martinich1978); van Inwagen (Reference van Inwagen2009)) have argued that the doctrine can be shown to be logically coherent if it is recognized that identity, at least when it comes to the doctrine of the Trinity, is sortal relative, so that while Father, Son, and Holy Spirit are not the same trinitarian person they are the same being.

This solution to the Trinity puzzle has not found favour in recent years. Relative identity is in bad odour and the theory of relative identity initially proposed by Geach, in particular, is problematic. ‘Due to the extravagance of his theory’, Pawel Garbacz writes, ‘relative identity (RI for short) has not been warmly welcomed by his contemporaries. In particular Geach's rejection of absolute identity (AI) turned out to be fatal for any future theory of RI.’Footnote ² Theories of relative identity, however, need not exclude absolute identity. A number of writers, including Nicholas Griffin (Reference Griffin1977) and Harry Deutsch (Reference Deutsch1998; Reference Deutsch2007) – and, some suggest, John Locke – have developed relative identity theories that recognize absolute identity as well as sortal-relative identity relations. More recently, Garbacz (Reference Garbacz2002) has explored a ‘minimal’ theory of relative identity that is not committed to a number of controversial theses, including the doctrine that absolute identity statements are either syntactically or semantically incomplete. Still, relative identity theories, however minimal, are controversial. And philosophers concerned to make sense of the Trinity doctrine are reluctant to hitch their theology to theses that are, at best, disputed.

Michael Rea and others (Rea (Reference Rea, McCall and Rea2009); Hasker (Reference Hasker2013); Tuggy (Reference Tuggy2014)), however, have argued that even if we do not reject relative identity tout court, relative identity theories do not yield theologically acceptable or logically coherent articulations of the Trinity doctrine. Rea argues that advocates of the relative identity approach are faced with a dilemma: relative identity theories that reject absolute identity are committed to an anti-realist metaphysic, which is theologically unacceptable; those who admit absolute identity as well as sortal relative identity relations do not succeed in saving the doctrine of the Trinity from logical incoherence. I shall argue that we can safely grasp the second horn of Rea's dilemma.

Rea's objection to RI theories that admit absolute identity rests on his intuition that ‘x is (absolutely) distinct from y’ is synonymous [sic] with ‘x is not the same being as y’. The principle P, on which his argument rests, follows from his synonymy intuition:

P says that for all x, y, if x is not absolutely identical to y then x is not the same being as y. The consequences for RI-Trinitarianism are dire. According to this account, the Father is the same being as the Son but not the same trinitarian person and so the Father ≠ the Son. Given P it follows, therefore, that they are not the same being. So even if the Relative Identity theorist's contention that, for some sortals, F, G, it is possible that x be the same F as y but not the same G as y, is correct, it is not possible that x be the same being as y but not the same F as y. It is not, in particular, possible for the Father to be the same being as the Son but not the same trinitarian person as the Son. But P is questionable and, as I shall show, there is no reason why an RI theorist should endorse it. And so, it will be shown, RI-Trinitarianism is logically coherent.

Before further consideration, however, we need to determine how P should be read for the purposes of this discussion.

Being and identity

According to relative identity theories that recognize absolute identity, x ≠ y is ambiguous: it can be given a ‘strong’ or ‘weak’ reading:

According to the orthodox, absolutist account of identity this is a distinction without a difference: x and y are either identical or not identical – if it is not the case that they are absolutely identical then they are absolutely non-identical. According to RI theories that recognize absolute identity however this does not exhaust the possibilities. On such accounts, absolute identity is understood as identity under all sortals, so that x = y if and only if for all sortals, F, x is the same F as y. The negation of x = y is therefore ambiguous. On the ‘weak’ reading x ≠ y says that it is not the case that for all sortals, F, x is the same F as y; on the ‘strong’ reading x ≠ y says that there is no sortal F such that x is the same F as y.Footnote ³

Given the strong reading of ‘x ≠ y’ P says that if there is no sortal, F, such that x is the same F as y then x is not the same being as y and, consequently, that if x is the same being as y then there is some sortal, F, such that x is the same F as y. Relative identity theorists accept P if ‘≠’ is given this reading since, understood in this way, P is trivial: it simply rehearses the truism that if there is no sortal-relative identity relation that holds on x and y then a fortiori the same being relation does not hold on x and y. Moreover, if P is understood in this way, Rea's argument does not get off the ground. On this reading, assuming the Father is the same being as the Son, it follows only that there is some sortal, F, such the Father is the same F as the Son – not that the Father is the same trinitarian person as the Son.

Assuming the weak reading of ‘x ≠ y’ P says that if there is some sortal, F, such that x is not the same F as y then x is not the same being as y, and so that if x is the same being as y, then for all sortals, F, x is the same F as y. Understood in this way, P implies that if the Father is the same being as the Son then the Father and Son are the same under all sortals, hence that the Father is the same trinitarian person as the Son. If P is understood in this way, then the RI-trinitarian's claim that the Father and Son are the same being but not the same trinitarian person is, as Rea argues, logically incoherent. For the purposes of this discussion, therefore, we should accept the weak reading of ‘x ≠ y’ and understand P accordingly, to say that unless x is absolutely identical to y, x is not the same being as y.

A number of writers have taken P, presumably on this reading, to be plausible and have regarded Rea's argument as decisive. So Dale Tuggy (Reference Tuggy2014), in the industry-standard Stanford Encyclopaedia of Philosophy, writes: ‘It seems that any things which are non-identical are not the same being . . . Thus, van Inwagen has not demonstrated the consistency of (this version of) trinitarianism’ – without further comment. William Hasker, in Metaphysics and the Tri-Personal God, the first full-length study of the doctrine of the Trinity from the standpoint of analytic philosophical theology, rehearses Rea's objection to the relative identity account of the Trinity doctrine, apparently endorsing his critique:

So Rea's objection to RI-Trinitarianism has been propagated through the literature. But Rea is wrong.

Relative identity

RI-trinitarians, as Hasker notes, endorse the following two claims:

Predicates of the form ‘is the same F as’, where F is a sortal term, are relative identity (RI) predicates and statements in which they figure, like (1) and (2), are relative identity (RI) statements. Relative identity statements are statements of the form ‘x is the same F as y’.

According to the standard analysis, RI statements ‘break down’ into property ascriptions and identity claims (Perry (Reference Perry1970), (Reference Perry1978)):

On this account, for all x, y, and any sortals F, G, it is not possible that x be the same F as y but not the same G as y: RI statements, on the standard analysis, entail absolute identity so, given the Indiscernibility of (Absolute) Identicals, since x is the same G as x, y must be the same G as x too. Thus, given the standard analysis of RI statements, (1) and (2) are inconsistent. (1) implies that the Father = the Son and so that the Father and Son are, with respect to every property, indiscernible. Since the Son is the same trinitarian person as the Son, it follows that the Father is the same trinitarian person as the Son.

Relative identity theories reject the standard analysis of RI statements. On such accounts, to be an F is to be the same F as something or other:

And relative identity statements are understood accordingly:

Since sortal-relative identity relations are transitive, it follows that x is the same F as y.

This account captures the spirit of the standard analysis of relative identity statements without involving absolute identity. As on the standard analysis, x is the same F as y only if x is an F and y is an F. This account, however, does not require further that x = y but only that there be something or other to which x and y each bear the same F relation.

All relative identity theories, in addition, are committed to

R specifies, first, that (i) the predicates in question be substantival.Footnote ⁴ Where a predicate, F, is adjectival, statements of the form ‘x is the same F as y’ do not, on anyone's account, imply x = y. My piano is the same colour as my wastebasket but not the same shape. They have the same colour property and different shape properties, but neither is itself either a colour or a shape. In such cases, identity – at least the identity of particulars – does not enter into the picture. R, however, says that it is possible for individuals to be the same F but different Gs even where F and G are sortals, that is, count nouns conveying criteria of identity.

Second, R says that, (ii) where F and G are sortals, it is possible for individuals to be the same F but not the same G in non-trivial cases. Everyone agrees that things can be the same F but not the same G if they (or it) are not Gs at all. Mark Twain is the same person as Samuel Clemens but not the same number as Samuel Clemens since Mark Twain, aka Samuel Clemens, is not a number. That is to say, Mark Twain is neither the same number as Samuel Clemens nor a different number from Samuel Clemens. The standard analysis allows that x and y be the same F but not the same G in such trivial cases. R, however, says that even where x and y are Gs, x and y may be the same F but not the same G – that is, they may be the same F but different Gs.

Some relative identity theories, notably the theory originally proposed by Geach, reject absolute identity altogether. According to Geach:

These accounts, henceforth D-theories, affirm D as well as well as R:

Other relative identity theories, henceforth R-theories, admit statements of the form ‘x = y’ but deny that RI statements break down into property ascriptions and absolute identity claims.

R by itself does not, however, guarantee the consistency of (1) and (2). It says only that there are some pairs of RI predicates, same F and same G, such that it is possible for x and y to be the same F but not the same G – not that that is true of all pairs of predicates. And it remains to be seen whether divine individuals can be the same being but not the same trinitarian person.

Where it is not possible that x and y be the same F but not the same G we say that same F dominates same G. Peter van Inwagen, who has argued that relative identity theories can be exploited to develop a logically coherent doctrine of the Trinity, understands RI dominance as follows:

Dominance: An RI-predicate I dominates a predicate F (F may be of any polyadicity and be either ordinary or RI) if all sentences of the form ‘Iαβ → (F . . . α ←→ F . . . β)’ are true. We say that an RI predicate that dominates every predicate is dominant. (van Inwagen (Reference van Inwagen2009), 230)

On this account, RI predicates may dominate other RI predicates. Same F dominates same G if being the same F entails being the same G. We call RI predicates dominant if they dominate all predicates, including sortal-relative identity predicates, so if same H is dominant, then being the same H entails being the same F for all sortals F. Finally, domination may be mutual: for some F, and some G, same F dominates same G and vice versa. Indeed, to reject R is precisely to hold that all RI predicates are dominant – that is, that for all x, y and all sortals F, G, x is the same F as y if and only if x is the same G as y, where x is an F and y is an F and x is a G and y is a G. To embrace R is to hold that one-way or asymmetric dominance is possible, that is, that there can be predicates that are not dominant. According to the RI defence of the Trinity doctrine, same being is not dominant: in particular, the claim is that same trinitarian person dominates same being but not vice versa.

Uncontrived non-theological cases of asymmetric dominance are hard to come by: Geach, notoriously, introduced the purpose-built sortal surman to produce an example. There do, nevertheless, seem to be some uncontrived examples. To see how a case of asymmetrical dominance looks, consider the stock case in which we might say that different airline passengers are the same person, e.g. that the occupant of Seat 6a on last week's flight to Baltimore is the same person as the occupant of Seat 17c on today's flight to San Diego but a different passenger.

Airlines, as the relative identity theorist understands it, count by passenger: when it comes to determining how much business they've done over a period of time what they care about is how many seats per flight were filled. It does not matter to them whether Seat 6a and Seat 17c were occupied by the same person or by different people: in either case, the airline did two units of business – that is, it served two passengers, who happened to be the same person. Person therefore, does not dominate passenger: 6a and 17c are the same person but different passengers. Passenger, however, dominates person. Passengers are people. And airlines assign no more than one person to a seat on any given flight – babes in arms and companion animals count as baggage. So on any occasion the same legal seat occupant, i.e. the same passenger, is the same person.

Dominance is theory-relative. In Airline Theory, passenger asymmetrically dominates person because the identity conditions for passenger are more stringent than the identity conditions for person. To be the same passenger you not only need to satisfy the identity criteria for person (whatever they are): you also have to satisfy an additional condition concerning seat assignment, which confers legal seat-occupancy. Passengers 6a and 17c fail that additional condition: they do not legally occupy the same seat on the same flight and so are the same person but different passengers.

Consider, however, Airline Theory Minus, which lacks the resources to distinguish passengers by legal seat occupancy. Its ideology does not include any of the familiar customer service predicates, such as ‘reservation’, ‘confirmation number’, ‘ticket’, ‘flight number’, or ‘seat-assignment’, but it is, in every other respect, like Airline Theory. In Airline Theory Minus the only predicates available for distinguishing passengers are those that distinguish persons, so in Airline Theory Minus person–passenger dominance is mutual: you have the same person if and only if you have the same passenger.

Adding customer service predicates to the theory, to make Airline Theory proper, does not bring entities of a new kind into existence. Passengers are just people. And people don't dominate – predicates do. Dominance is a grammatical feature of predicates, like ‘passenger’, that marks entailment relations. If 6a is the same passenger as the one who picks up the first bag on BWI Airport Carousel #3, it follows that 6a is the same person as that individual. Dominance depends upon a theory's stock of predicates and, most importantly, on its sortals, which convey identity criteria, that is, shortlists of conditions that are necessary and sufficient for the identity of objects of that sort. An RI predicate same F dominates an RI predicate same G within a theory if the theory has predicates that figure in the identity criteria for F to distinguish individuals as different Fs that do not distinguish them as different Gs.

The relative identity account of airline practices is metaphysically innocent. It is not an account of what there is and it does not introduce passengers into our ontology in addition to persons. It says only that we can adopt different procedures for counting what there is: we can count by person or count by passenger.

The relative identity account of the Trinity doctrine is, likewise, metaphysically innocent. It does not favour Latin Trinitarianism or Social Trinitarianism, or provide any reason to prefer orthodox doctrines to heterodox accounts or vice versa. It merely provides a way of understanding (1) and (2) that avoids contradiction. RI-Trinitarianism is not yet another speculative, metaphysical account of the nature of God: it is, rather, a strategy for avoiding speculative metaphysics. Even if there is real, substantive, metaphysical disagreement between Latin Trinitarians and Social Trinitarians, or between orthodox trinitarian Christians and Arians, Sabellians or advocates of other heterodox theologies, RI-Trinitarianism is neutral: dominance is a semantic notion, without ontological import.Footnote ⁵

If dominance is understood in this way, the prospects for a coherent, orthodox Trinity theory, which articulates the doctrine developed by the Fathers of the Church, look promising. During the first centuries ce, according to the RI-trinitarians' rational reconstructionist account, the Fathers enriched the theology they inherited from Second Temple Judaism – God Theory Minus – with a stock of specifically Christian predicates. To the inherited generically divine predicates, among them those designating omnipotence, omniscience, omnibenevolence, and other perfections, they added hypostasis, homoousios, and a variety of other terms needed to articulate specifically Christian doctrines. Engaging in rational reconstruction, an RI-trinitarian can understand the development of the Trinity doctrine as a programme for licensing some inferences while blocking others – in particular, for ascribing a range of properties to the Son but not to the Father, while maintaining monotheism.

A sortal-relative identity relation is an indiscernibility relation for a restricted range of predicates and the character of a given sortal, F, determines which predicates pass from F to same F and which do not. Theologians wanted generically divine predicates to pass from trinitarian person to trinitarian person, so that when it came to godhead, glory, omnipotence and the like they could affirm ‘Such as the Father is; such is the Son; and such is the Holy Ghost’ (Athanasian Creed). But they did not want specifically hypostatic predicates to pass promiscuously around the Trinity. They were keen, in particular, to avoid Patripassionism, the heterodox doctrine that the Father suffered on the Cross. So, according to the RI-trinitarian's reconstruction, they developed trinitarian God-Theory to block the inference from ‘the Son suffered on the Cross’ to ‘the Father suffered on the Cross’. Within their predicate-enriched theory it was possible to distinguish trinitarian persons and to block heretical inferences. Same being was an indiscernibility relation for generically divine predicates but not for specifically hypostatic predicates. Father, Son, and Holy Spirit were the same being, indiscernible with respect to generically divine attributes, but not with regard to paternity, filiation, procession, incarnation, or passion.Footnote ⁶

Adding specifically hypostatic predicates to prevent promiscuous predicate-passing did not, of course, bring additional divine beings into existence any more than the introduction customer-service predicates added passengers to the San Diego–Baltimore round trip. Passengers are just people and trinitarian persons are just God. Father, Son, and Holy Spirit are homoousios – the same being – but not the same trinitarian persons on this account, which is to say, same being, at least within Trinity Theory, does not dominate same trinitarian person. If this is correct, then we cannot infer from (1), according to which Father and Son are the same being, that they are the same trinitarian person. (1) and (2) are therefore consistent and, to that extent at least, the doctrine of the Trinity can be coherently stated. So says the RI-trinitarian.

Rea's reductio

Rea's objection to the RI-trinitarian argument turns on the claim that being, because it is maximally general, is dominant and, hence, dominates trinitarian person.Footnote ⁷ P is just the contrapositive of the claim that the RI predicate being dominates absolute identity – and so same trinitarian person.Footnote ⁸

Rea claims that since P is ‘highly intuitive’, positive reason must be given for rejecting it. He has not, however, made the case that P is intuitively correct or that any intuitions we might have regarding P should be taken seriously. ‘Being’ is a term of art: the Folk have no intuitions about P. And, arguably, most philosophical identity connoisseurs’ intuitions have been corrupted by prior commitments to analyses of relative identity statements that advocates of relative identity repudiate. If, however, P is correct then, unless absolute identity statements are rejected as ‘incomplete and therefore ill-formed’, (1) and (2) entail a contradiction. Rea's proof is as follows (Rea (Reference Rea, McCall and Rea2009), 263):

(RT8) follows from (1) and (2). (1) says that there are x, y, viz. the Father and the Son, such that x is the same being as y and (2) that there is an individual, viz. the Father, which is the same trinitarian person as himself but not the same trinitarian person as the Son. If absolute identity is admitted, (RT8) implies (RT9), which says that there is an x, y, such that x is the same being as y but x ≠ y. A relative identity theorist who rejects absolute identity will, of course, reject (RT9) as incoherent because she deems statements of absolute identity, like ‘x = y’, and so presumably their negations, to be incomplete and ill formed. If, however, absolute identity and therefore absolute non-identity are admitted, then (RT9) is unavoidable: according to (RT8), x is the same trinitarian person as x but not the same trinitarian person as y, so x ≠ y. A relative identity theorist who rejects D is therefore committed to (RT9). Given P, however, we have (10) which is a contradiction. Nothing in the premises is incompatible with R so if this argument is sound then the RI defence of the Trinity doctrine fails – as Rea claims.

(RT10), however, follows from (RT9) only if principle P is admitted. And the only reason Rea gives for accepting this principle is his intuition that ‘x is (absolutely) distinct from y’ is synonymous [sic] with ‘x is not the same being as y’ – which may be anomalous.

Why should we endorse P? For the purposes of his argument Rea cannot appeal to any principle that is inconsistent with R to make the case for P. His aim is not to show that RI theories, which are committed to R, are incoherent, unmotivated, or otherwise objectionable but rather that even if such accounts are in good order they cannot save the doctrine of the Trinity from logical incoherence.Footnote ¹⁰ He cannot, therefore, appeal to the following principle in support of P:

A says that if x is not identical to y then it is not relatively identical to y under any sortal. It follows that if x ≠ y then x is not the same being as y. A therefore implies P. However, A implies that R is false. It says that if x and y are not absolutely identical then there is no sortal, F, such that x is the same F as y. It follows that if there is some F such that x is the same F as y then x = y; therefore, that it is not possible that x and y be the same F but different Gs. So, for Rea's purposes, A is out.

Rea, however, appears committed to a principle that is compatible with R, viz.

A′ says that if everything is an F, that is, if F is maximally general, then x ≠ y → ~ xFy. Assuming that being is maximally general, P follows. A′ (or maybe a biconditional principle like it) seems to be what Rea has in mind when he writes ‘“being” is plausibly the most general sortal . . . Thus, “x is (absolutely) distinct from y” seems to be synonymous with “x is not the same being as y”’ (Rea (Reference Rea, McCall and Rea2009), 258). It follows from A′ that if a sortal is maximally general the RI predicate in which it figures is dominant, hence P – since being is maximally general.

If this is correct then even without assuming P (1) and (2) imply a contradiction. Being is, as Rea notes, maximally general: whatever is, is a being. A′, moreover, is compatible with R. It allows for the possibility that x be the same F as y but not the same G so long as F is not maximally general. There is, however, is no obvious reason why an R-theorist should endorse A′.

At this point we may as well drop P. It has little to recommend it and if we accept the A′, which seems to capture Rea's intuition, it is superfluous. In the following section it will be shown that this intuition should be resisted.

Generality and Dominance

Being is, indisputably, maximally general. So if A′ is correct, then (1) and (2) imply a contradiction. But, as will be shown, A′ is false.

To make the case I first show that, given the RI-theorist's account of RI statements, sortal generality, and sortal dominance, generality does not imply dominance: assuming that G is more general that F, that x and y are Fs, and x is the same G as y, it does not follow that x is the same F as y. Second, I argue that maximally generality makes no difference. Assuming that x and y are Fs, and that x is the same G as y, it does not follow that x is the same F as y even if G is more general than all (non-maximally general) sortals.

Recall that to be an F is to be the same F as something or other. Sortal generality can therefore be understood as follows:

That is to say, G is more general then F just in case anything that is an F is a G. A sortal, G, is maximally general if there is no sortal, F, that is more general than G.

G dominates F if being the same G implies being the same F. Given our account of RI statements, we can understand sortal dominance accordingly:

The antecedent says that x is the same G as y and the consequent says that x is the same F as y, hence that same G dominates same F.

A′ says that where G is maximally general being the same G implies being the same F (for all sortals F that are not themselves maximally general). Before turning our attention to A′, however, let us consider the suggestion that generality, whether maximal or not, implies dominance, that is:

Prima facie, it looks as if G&D implies A′ but not vice versa. However, arguably, if R&D is false there is no good reason to endorse A′. And, as will be shown, G&D is false.

Given our understanding of sortal generality and sortal dominance G&D says that from (3) we may infer (4):

(3) says that G is a maximally general sortal: every sortal, F, is either as general or less general than G – so every F is a G. (4) says that same G dominates same F, that is, that if for any x, y if x is the same G as y then x is the same F as y. (3), however, does not imply (4).

Let F and G be sortals. First, assume only that G is more general than F so that if an object x bears the same F relation to some y, it bears the same G relation to y. Suppose a is an F and b is an F, that is:

Since G is more general than F it follows that a and b are Gs, so

(6) says that there is a something to which a bears the same G relation and that there is something to which b bears the same G relation. Maybe there is something to which both a and b bear the same G relation – but maybe there isn't. Let us say that there is such an object, c, to which both a and b bear the same G relation. That is,

Since RI relations are equivalence relations, it follows from (7) that

1. (8) a is the same G as b.

It does not, however, follow that a is the same F as b. (5) says that there is something to which a bears the same F relation and something to which b bears the same F relation. Again, maybe there is something to which both a and b bear the same F relation – but maybe there isn't. (5) does not imply

(5) says that a is an F and b is an F, that is, that a is the same F as something or other and that b is the same F as something or other – not that there is some x such that a is the same F as x and b is the same F as x. Let us say that a is the same F as d and b is the same F as e where d ≠ e, and that there is no object to which both a and b bear the same F relation. That is to say:

Since there is nothing to which both a and b bear the same F relation a does not bear the same F relation to b. That is:

a is an F and b is an F and a is the same G as b but a is not the same F as b. So we have a non-trivial case where the sortal G is more general than the sortal F but same G does not dominate same F – so we have a counterexample to G&D.

So far this shows that generality does not induce dominance: from the assumption that G is more general than F, it does not follow that same G dominates same F. Adding that G is maximally general, i.e. that it is more general than all other non-maximally general sortals as well, does not make any difference: the counterexample stills stands in the special case where G is maximally general.

Starting with any counterexample to G&D we can create a counterexample to A′. The current counterexample to G&D is the conjunction of (3), (7), (9), and (10). (3) says that G is more general than F. (7) says that a is the same G as b. (9) and (10) together say that a is an F and b is an F but a is not the same F as b. To produce a counterexample to A′ we only need to add that in addition to being more general than F, G is also more general than all other non-maximally general sortals, and so is maximally general.

Suppose that besides F the only other non-maximally general sortal around is H and that no Fs are Hs. In the small world of the supposition, G is maximally general if, in addition to (3) we have

So in the impoverished language of this small world, the following story is a counterexample to A′:

Since F and H are the only non-maximally general sortals around, (3) and (12) together say that G is maximally general. Since no Fs are Hs, the addition of (12) has no bearing on the truth of (7), (9), or (10). If this is correct then G's being more general than F doesn't entail that G dominates F even where G is maximally general. A′ is therefore false.

Relative identity redux

Relative identity solutions to the Trinity puzzle are currently out of favour because relative identity is at least mildly disreputable and, more to the point, because a number of writers have assumed that P is plausible and that Rea's objection is decisive. But neither Rea, nor other writers who cite his argument with approval, have offered any compelling reason to believe that P is true. Moreover, A′, which arguably, is what provides intuitive backing for P, is false.

I have argued that the doctrine of the Trinity, at least in so far as it entails that the Father and Son are the same being but different trinitarian persons, is coherent given a minimalist R-theory of relative identity. Being is, indeed, maximally general; however, as we have seen, maximal generality does not imply dominance and same being does not dominate same trinitarian person. An orthodox Christian can, therefore, without logical impropriety, hold that the Father is the same being as the Son but not the same trinitarian person.Footnote ¹¹