Three Persons in One Being On Attempts to Show that the Doctrine of the Trinity is Self Contradictory

Peter van Inwagen

Enemies of the Church have frequently contended that two of its central doctrines are not only false but violate various elementary logical principles. These two doctrines are, of course, the doctrine of the Incarnation of the Word and the doctrine of the Holy Trinity. I shall investigate the contention that the doctrine of the Trinity is logically self-contradictory.

I shall proceed as follows. I shall try to imagine a way of stating the doctrine of the Trinity that has the following feature: when the doctrine is stated in this way, it can be shown not to be self-contradictory. I shall leave the following question to theologians (for I am a philosopher, not a theologian): Is what I describe as "a way of stating the doctrine of the Trinity'' properly so described—or should it be called a way of misstating the doctrine of the Trinity? I claim only this: a strong case can be made for the thesis that the formulation of the doctrine of the Trinity I shall propose does succeed in being a statement of what has historically been called 'the doctrine of the Trinity'; and an even stronger case can be made for the thesis that this formulation is consistent with historical orthodoxy. Even if these theses are false, they are, in my view, plausible enough to be worthy of a considered refutation.

My project, therefore, belongs to Christian apologetic. It is a Christian philosopher's attempt to meet a certain kind of philosophical attack on Christian belief. Whether my attempt at apologetic in fact distorts Christian belief is a point on which I humbly (and sensibly) defer to trained theologians. In matters of speculative theology—and particularly when the question at issue is whether certain theological speculations are in accord with historical orthodoxy—theologians must sit in judgment over mere philosophers. (Just as, in my view,

* From Melville Y. Stewart (ed.), The Holy Trinity, pp. 83-97. © 2003 Kluwer Academic Publishers with kind permission from Springer Science and Business Media.

bishops and councils must sit in judgment over theologians.) I claim only one kind of authority that is denied to theologians: I am the ultimate arbiter of what my own words mean. If a theologian tells me that my proposed way of stating the doctrine of the Trinity is wrong (that is, that what I have proposed as a way of stating "the doctrine of the Trinity'' has implications inconsistent with what the Church has always understood by "the doctrine of the Trinity''), I allow myself only one defense: "If I had said what you think I've said, you'd be right; but I didn't say what you think I said.''

Now a qualification. When I said I should propose a way of stating the doctrine of the Trinity, I spoke loosely. What I am going to propose a statement or formulation of is a part of the doctrine of the Trinity, the part that is alleged to violate certain principles of logic. In one sense, there can be no more important questions of Trinitarian theology than those raised by the filioque. These questions are important because they have consequences for the immensely important task of restoring Christian unity. But these questions would not interest those enemies of the Church who attack the doctrine of the Trinity on logical grounds. They attack aspects of the doctrine that are common to the Eastern and the Western understandings of the Trinity (if indeed there is still any difference between Eastern and Western understandings of the Trinity). Their attacks are not directed at theses concerning the relations the persons of the Trinity bear to one another, but are directed, so to speak, at the persons themselves. But it is time to turn from the abstract to the concrete and to see how the attacks I am going to consider have been formulated. I am going to concentrate on attacks made by present-day unbelievers, but these attacks do not differ in their essential content from those made by Socinians in the seventeenth century, and I should be surprised if similar objections to Trinitarianism had not been raised by Jewish and Muslim philosophers and theologians—although I cannot speak to this question of my own knowledge. The essential points made in these arguments, moreover, were known to the great Trinitarian theologians of the first millennium, and to the philosophers and theologians of the Latin Middle ages. I will consider two arguments. Here is the first.

The term 'God' applies without qualification to the Father, to the Son, and to the Holy Spirit. The Father is not the Son; the Son is not the Holy Spirit; the Holy Spirit is not the Father. Hence, there are at least three Gods. We may compare this argument with the following argument:

The term 'king' applies without qualification to Gaspar, to Melchior, and to Balthasar. Gaspar is not Melchior; Melchior is not Balthasar; Balthasar is not Gaspar. Hence, there are at least three kings, and we may note that the former argument and the latter appear to be logically identical, and that the second is certainly logically valid. But monotheism is essential to Christian belief, and indeed, to the doctrine of the Trinity; therefore, the doctrine of the Trinity is logically self-contradictory. For this argument to be valid, the word 'God' must be understood as what linguists call a count-noun, that is a noun that, like 'king,' has a plural form (and in languages that have an indefinite article, can follow the indefinite article). But this seems to be so: We say, ''There is one God, the Father Almighty, maker of heaven and earth'' and ''Our God is a God of love'' and ''The doctrine of the Trinity does not imply that there are three Gods''; and each of these sentences is grammatically correct.

Here is the second argument:

The Father is God. The Son is God. Hence, the Father is the Son. We may compare this argument with the following argument:

The capital of Russia is Moscow. The largest city in Russia is Moscow.

Hence, the capital of Russia is the largest city in Russia, and we may note that the former argument and the latter appear to be logically identical, and that the second is certainly logically valid. But it is essential to the doctrine of the Trinity that the Father is not the Son; therefore, the doctrine of the Trinity is logically self-contradictory. For this argument to be valid, the word 'God' must be understood as a proper name—like 'Moscow' or 'Zeus' or 'Socrates.' But this seems to be so: We say, ''O God make speed to save us'' and ''The peace of God, which passeth all understanding, keep your hearts and minds in the knowledge and love of God''; and each of these sentences is grammatically correct.

We have noted that these two arguments presuppose two different grammatical functions for the word 'God.' But this does not imply that at most one of the two arguments is logically valid, for the word 'God' does function both as a count-noun and as a proper name. In every language I know of, a proper name can function, or one might say, be forced to function as a count-noun. (Here is an example used by the German philosopher Frege: Trieste is no Vienna.) But the use of 'God' as a count-noun in the first argument is not a case of a proper name being forced to function as a count-noun. No force is required when we choose to employ 'God' as a count-noun. It is part of the meaning of'God' that it has a dual grammatical function, that it is syntactically ambiguous as it were: it can function both as a count-noun and as a proper name. And if we suppose that 'God' functions as a count-noun at each of its occurrences in the first argument, the premises of that argument seem to be true. If, moreover, we suppose that 'God' functions as a proper name at each of its occurrences in the second argument, the premises of that argument seem to be true. (The fact that God has a proper name in the more usual sense—as we learn from Exodus 3:14—does not affect the point that the word 'God' often functions as a proper name. I may mention in this connection that Professor Peter Geach has argued that 'God' is never a proper name, owing to the fact that, in translations from one language to another, the word is itself translated—the word that means 'God' in the original language is replaced with a word of the other language that means 'God'—and is not merely phonetically adapted. A contrastive example will make Geach's point clear. The English word 'God' is a true translation of the Russian word 'Bog,' to which it bears no phonetic resemblance and to which it is etymologically unrelated. By way of contrast: the English proper name 'Moscow' is not in anything like the same sense a translation of 'Moskva'; it is merely an adaptation of the name Russians have given to their largest city, a phonetic adaptation that was made because it is easier for someone whose tongue is accustomed to the vowel-and-consonant patterns of English to say 'Moscow' than to say 'Moskva.' Whether or not this argument of Geach's is cogent, its target is not the thesis that I have endorsed. I have not said that 'God' is a proper name as 'Yahweh' is a proper name, but only that in some contexts it functions logically like a proper name. More exactly: I have not said this; I have said only that the second of the above arguments depends on the word's so functioning, and that examination of the way the word is used seems to endorse the thesis that it can so function.)

Now what shall we say of these two arguments? I have heard of (but cannot cite) theologians who are, in eflEct, willing to concede that our two arguments are logically valid and that their premises are true. They concede, therefore, that the doctrine of the Holy Trinity is internally inconsistent; and they go on to say that it is nevertheless to be believed. Having made these concessions, they proceed to deprecate 'merely human logic.' Their point (so I have been told) is not that the doctrine is not inconsistent but seems to be inconsistent owing to the deficiencies of merely human logic; it is rather that it is only because of the deficiencies of merely human logic that inconsistency (at least in theology) seems objectionable. This position has (to be gentle) little to recommend it. If one maintains that something is to be believed, one thereby commits oneself to the thesis that that thing is true, for to believe something and to believe that it is true are one and the same thing. And nothing that is true can be internally inconsistent. If a theological doctrine or political ideology or scientific theory comprises three statements, and if that doctrine or ideology or theory is true, then its three constituent statements must be individually true. We might put the matter this way: every ''part'' of anything that is true must also be true, and anything that is true is consistent with anything else that is true—and an inconsistent doctrine or ideology or theory is one such that some of its parts are inconsistent with others of its parts. Those who are willing to believe what is logically inconsistent have failed to take account of the logically elementary fact that a truth cannot be inconsistent with a truth.

I have said that I could find no theologian who has actually said that inconsistencies were to be believed. Professor Geach claims to be able to identify (although he does not provide explicit citations of) certain medieval Latin thinkers who held a closely related thesis: that there are bodies of truth—just those that comprise the doctrines of the Trinity and the Incarnation—that somehow constitute exceptions to logically valid principles or reasoning. These medievals, Geach says, appended the following warning to their statements of certain rules of logical inference: Haec regula habet instantiam in mysterio Sanctae Trinitatis. (Here is a gloss: WARNING: Do not use this rule when the subject-matter of your reasoning is the mystery of the Holy Trinity; applied to that subject-matter, the rule can license the inference of false conclusions from true premises.)

To say this, or anything like this, is to misunderstand the concept of logic. Nothing is, or could be, above, beyond, or outside the province of logic. The idea does not make sense. And, certainly, it is blasphemous to say that any part of Christian theology is above, beyond, or outside the province of logic. Jesus Christ, in addition to being the Way and the Life, is the Truth. In him there is no darkness at all. In him there is no falsehood. The faith we have from him, and from the Holy Spirit whom he has sent to us, is therefore entirely true, true in every part. And nothing that is entirely true can be above, beyond, or outside the province of logic, for (as I have said) a truth cannot be inconsistent with a truth. If, per impossibile, there were some doctrine, some ideology, some theory, that was above, beyond, or outside the province of logic, it would not be entirely true; for what is entirely true is logically internally consistent, and what is logically internally consistent conforms to the rules of logic and cannot therefore be said to be above, beyond, or outside the province of logic.

To say this, however, is not to say that Christian doctrine (or, for that matter, a scientific theory like quantum mechanics; the suggestion has been made that quantum mechanics has just this feature) cannot be in violation of principles of reasoning that are generally believed to be logically correct. It is to say that Christians are committed to the thesis that if an essential Christian doctrine violates some principle of reasoning, then that principle is not logically correct, however many reputable professional logicians believe it to be logically correct. Logic—and this statement pertains to the essence of logic—makes a universal claim. It claims to apply to the whole of the Real—and nothing has a securer place in the Real than God, who alone can say, "I should be real if nothing else was.'' (The Austrian philosopher Alexius Meinong believed there to be—in a sense of 'to be' he was never able adequately to explain—things that lay outside the Real, and he believed that some of these violated the principles of logic. He thereby denied the universal claim of logic, whose scope he confined to the Real. He in fact denied that, ''I pertain to the whole of the Real'' is a claim to universality. His philosophy, however, seems to me to be nonsense, and—I say—unless one is prepared to follow Meinong into nonsense, one must accept the claim of logic to be of absolutely universal applicability.)

I said I should propose a way of stating the doctrine of the Trinity that was demonstrably consistent. I am not the first to have proposed to do this. Certainly various heretics have. Very roughly speaking, their heresies fall under two headings: modalism and tritheism. Modalism is the heresy that the Father, the Son, and the Holy Spirit are three modes in which the one God is known by us or presents himself to us—three faces that God shows us, so to speak, as God's Ape does in the Inferno. Tritheism is, of course, the heresy that there are three Gods: that God the Father is one God, God the Son another God, and God the Holy Spirit a third God. I shall take it for granted that everyone present will agree that modalism is a heresy. It might be thought equally clear that tritheism was a heresy. ("Hear, O Israel, Yahweh our God is one Yahweh.'') But there is a modern attempt at a demonstrably consistent statement of the doctrine of the Trinity—at least I should be willing to say that its consistency was demonstrable—according to which there are three Gods, and its author's defense of its historical orthodoxy is well thought out and not simply to be dismissed. (I have in mind Professor Swinburne's important essay on the Trinity, "Could There Be More Than One God?'') But whether Professor Swinburne's account of the Trinity is, or is consistent with, historical orthodoxy is a subtle question, and one that is not, in the end, to be answered by a philosopher. What I can do, as a philosopher, is to exhibit the consequences of his theory—subject, of course, to correction by Professor Swinburne, whose authority to contend that I have got him wrong and whose authority to contend that I have made a mistake in reasoning are both unassailable. I shrink from the risks implicit in criticizing the work of a philosopher who is not only alive but is present as I speak, and will say nothing in detail about his views. I have mentioned these views only to make the point that the question whether tritheism is a heresy is a subtle question—and to make the related point that the question "What, exactly, is tritheism?'' is likewise a subtle question. I am happy to make these points because, if any charge of heresy were to be lodged against my own speculations concerning the Trinity, it would certainly be that I have fallen into some form of tritheism. No one—I certainly hope this is so—could reasonably accuse me of having embraced modalism in any form.

My attempt to state the doctrine of the Trinity (and I do intend presently to get round to doing it) rests on the contention that certain rules of logical inference that are commonly supposed to be valid are not in fact valid, that these rules must be replaced by other rules, rules that are valid, and that the doctrine of the Trinity does not violate any valid rule of logical inference.

That part of logic whose rules the doctrine of the Trinity is in violation of (or is in violation of if the two arguments I set out earlier are valid) is the logic of identity. According to standard textbook logic, the logic we have from Frege and Russell, there is a relation called identity. This relation is defined by two properties. First, everything whatever bears this relation to itself. Secondly, this relation forces indiscernability. That is to say, if a thing x bears identity to a thing y then whatever is true of x is true ofy and whatever is true ofy is true of x. From these two defining properties of identity (it is easily shown) two other important properties of identity immediately follow: identity is symmetrical (that is, if a thing x bears the relation of identity to a thing y then y bears the relation of identity to x), and identity is transitive (that is, if x bears identity to y and y bears identity to z, then x bears identity to z). These properties of identity entail the validity of four principles of reasoning or logical rules. In stating these rules, I will use the words 'is identical with' instead of'bears the relation of identity to.'

The rule of Reflexivity tells us that if we are engaged in a piece of reasoning, and if a name like 'Ivan the Terrible' occurs in this reasoning, and if this name (unlike, say, 'Zeus') actually designates something, we may introduce the sentence formed by surrounding the phrase 'is identical with' with two occurrences of that name into our reasoning. For example, if the name 'Ivan' occurs in our reasoning, and if 'Ivan' designates something, we may introduce into our reasoning the sentence 'Ivan is identical with Ivan.' This rule, moreover, applies not only to names but also to any phrase that purports to designate a single thing; 'the first czar' for example: Reflexivity licenses us to include in any piece of reasoning the sentence 'the first czar is identical with the first czar.'

In stating the rule "Reflexivity," I had to strain to state it generally (and a logician will tell you that I did not really succeed, since I said nothing about what logicians call ''variables,'' a point I will concede). In the sequel, I will not even attempt to give general statement of the rules whose validity follows from the properties of identity; I shall instead proceed by example and illustration.

The rule called Leibniz's Law or The Indiscernibility of Identicals (note that I did not say ''The Identity of Indiscernibles''!) allows us to introduce the following sentence into our reasoning:

If Moscow is identical with the city in which the Kremlin stands, then Moscow is populous if and only if the city in which the Kremlin stands is populous.

In this example the first or 'if' part of the statement is true, and the predicate 'is populous' in fact applies to the one thing that is both Moscow and the city in which the Kremlin stands. But I must point out that logic is in a certain sense blind to truth, and that Leibniz's Law would allow us to introduce the following sentence into our reasoning:

If Helsinki is identical with the capital of Japan, then Helsinki is a moon of Jupiter if and only if the capital of Japan is a moon of Jupiter.

No doubt no sane person would want to introduce this sentence into any piece of reasoning; but a madman who did so would be reasoning logically—something madmen are often very good at. (And, anyway, when you think about it, isn't it true that if Helsinki is identical with the capital of Japan, then Helsinki is a moon of Jupiter if and only if the capital of Japan is a moon of Jupiter?)

The rule called Symmetry (its validity can be proved, given the validity of Reflexivity and Leibniz's Law) licenses inferences like these:

Cicero is identical with Tully; hence, Tully is identical with Cicero Peter the Great is identical with Catherine the Great; hence, Catherine the Great is identical with Peter the Great.

The rule called Transitivity (its validity can be proved, given the validity of Reflexivity and Leibniz's Law) licenses inferences like these:

Byzantium is identical with Constantinople; Constantinople is identical with Istanbul; hence, Byzantium is identical with Istanbul Turgenev is identical with Dostoevski; Dostoevski is identical with the author of Anna Karenina; hence, Turgenev is identical with the author of Anna Karenina.

Infinitely many other rules of inference involving the phrase 'is identical with' can be proved valid given the defining properties of identity. Some of them are even interesting and important; Euclid's Law, or the Substitution of Identicals, for example, which allows us to infer 'Tolstoy was excommunicated' from the two premises 'The author of Anna Karenina was excommunicated' and 'Tolstoy is identical with the author of Anna Karenina,' but one must make an end somewhere, and perhaps at least the most general features of the logic of identity are now reasonably clear. And this logic of identity is all but universally regarded as an established part of logic. ''How, ask the proponents of the validity of these rules, could they fail? Consider Transitivity. Suppose that the sentence 'Byzantium is identical with Constantinople' is true; if this sentence is true, that must be because there is a single thing, a certain city, that bears the two names 'Byzantium' and 'Constantinople.' And if 'Constantinople is identical with Istanbul' is true, that can only be because there is a single thing, a certain city that bears the two names 'Constantinople' and 'Istanbul.' It obviously follows that this ''certain city'' bears the two names 'Byzantium' and 'Istanbul' (we have said so), and that, therefore, 'Byzantium is identical with Istanbul' is true.

Now consider the first of the two anti-Trinitarian arguments I set out a moment ago. This argument depends on the idea of number; the idea expressed by the question ''How many?'' Number is explained in terms of identity. The proposition that there is exactly one phoenix can be expressed this way:

Something x is a phoenix and any phoenix is identical with x.

(For this sentence would be false if there were no phoenixes, and it would be false if there were two or more phoenixes: it is true in just exactly the remaining case, the case in which the number of phoenixes is one.) The proposition that Mars has exactly two moons can be expressed this way: Something x is a Martian moon and something y is a Martian moon and x is not identical with y and any Martian moon is identical with either x or y. If we delete the last clause from this sentence (thus): Something x is a Martian moon and something y is a Martian moon and x is not identical with y, the result is a way of expressing the proposition that there are at least two Martian moons. (The truncated sentence is false if Mars has no moons or has only one; it is true otherwise.) Now consider the sentence

Something x is a God and something y is a God and something z is a God and x is not identical withy and x is not identical with z andy is not identical with z. This sentence says that there are at least three Gods. Now suppose someone says these things:

The Father is a God The Son is a God The Holy Spirit is a God The Father is not identical with the Son The Father is not identical with the Holy Spirit The Son is not identical with the Holy Spirit. If these six things are true, then it would seem that we have our 'x,' our ' y and our 'z,' and it would seem, therefore to follow that there are at least three Gods. And are these six things true? Well, I concede that it might be hard to get a Christian to give his unqualified assent to any of them. Christians who speak a language that uses the indefinite article are likely, to say the least, to feel uncomfortable saying 'The Father is a God.' But consider: they will want to say the following two things: 'The Father is God' and ' God is a God'; does that not commit them to the truth of The Father is a God,' however reluctant they may be actually to utter these words? As to the final three sentences, perhaps these two will make the Christian uncomfortable. But they will certainly want to say these two things: The following is true of the Son: that he is begotten of the Father. The following is not true of the Father: that he is begotten of the Father. And it follows from these two sentences by Leibniz's Law that the Father is not identical with the Son: for if the Father were identical with the Son, then everything that was true of the Father would also be true of the Son. It would seem, therefore, to follow by the logic of identity from things all Christians assent to that there are at least three Gods. And, since it is an essential element in the doctrine of the Trinity that there is one God, and one only, a logical contradiction can be deduced by the logic of identity from the doctrine of the Trinity. What I have just done, of course, is to present our first argument in a form which makes its reliance on the standard logic of identity explicit. This was a rather complex undertaking. To present our second anti-Trinitarian argument in this form, however, is simplicity itself:

The Father is identical with God

The Son is identical with God

Hence, by Symmetry, God is identical with the Son

Hence, by Transitivity, the Father is identical with the Son.

And this conclusion certainly contradicts the doctrine of the Trinity. For one thing, as we have seen, it would imply—given that the Father begets the Son and given the standard logic of identity—that the Son begets the Father. For another, it would imply that there was a single thing for which 'the Father' and 'the Son' were alternative names—as there is a single thing for which Constantinople' and

'Istanbul' are alternative names—and this is modalism. Might the Christian respond by simply denying the premises, by simply denying that the Father is identical with God and that the Son is identical with God? (The Christian might appeal to Leibniz's Law to establish this: God comprises all three persons of the Holy Trinity; the Father does not comprise all three persons of the Holy Trinity; hence, the Father is not identical with God.) But this response leads to ''counting'' problems, like those on which our first argument turns. The Father is, as we have seen, a God. And God is certainly a God. Therefore, if the Father is not identical with God, there is something x that is a God and there is something y that is a God and x is not identical with y. That is to say: there are at least two Gods.

It has long seemed to me that the problems our two anti-Trinitarian arguments raise are insoluble, if the standard logic of identity is correct.

That is, it has seemed to me that the doctrine of the Trinity is self-contradictory if the standard logic of identity is correct. I wish, therefore, to explore the possibility of rejecting the standard logic of identity. But it is not possible to reject the standard logic of identity root and branch. There is obviously much that is right about it. I wish therefore, to investigate the possibility of a logic that preserves what is obviously right about the standard logic of identity, but which diflErs from the standard logic in a way that does not allow the deduction of a contradiction from the doctrine of the Trinity.

The logic of identity I shall propose turns on the idea that there is not one relation of identity but many. Thus, I do not so much propose a logic of identity according to which the rules governing identity I have laid out above are invalid as a logic according to which they are vacuous: I deny that there is one all-encompassing relation of identity for them to govern. When I say that there is no one all-encompassing relation ofidentity, I mean that there is no relation that is both universally reflexive and forces indiscemibility. When I speak of ''many relations of identity,'' I have in mind relations like these: ''being the same horse as,'' ''being the same artifact as,'' and ''being the same apple as.'' I call these relations of relative identity, since the use of any of them in an assertion of sameness relativizes that sameness to a kind; it is for that reason that each of the phrases I have mentioned contains a count-noun like 'horse' or 'artifact' or 'apple.' Thus, one might call the relations expressed by the phrases 'horse-identity,' 'artifact-identity,' and 'apple-identity.' In pieces of reasoning whose validity turns on relations of relative identity, count-nouns will occur only in phrases like the ones I have used as examples—'horse' will occur only in the phrase 'is the same horse as,' and so on. Having said this, I qualify it: I will allow predicates not of this form to occur if their form is that illustrated by 'is a horse.' I allow this because predicates of the this sort can be regarded as mere abbreviations for phrases of the sort I allow ''officially.'' For example, 'Bucephalus is a horse' can be understood as a mere abbreviation for 'Bucephalus is the same horse as Bucephalus.' Since 'Bucephalus is the same horse as Bucephalus' expresses (so I contend) the thought expressed by the ordinary sentence 'Bucephalus is a horse,' it is clear that the logic of relations of relative identity must have no rule corresponding to the rule Reflexivity. If we had such a rule, or, rather, if we had a separate rule of reflexivity for every relation of relative identity, this would have disastrous consequences. For example, the 'horse'-rule would allow us to introduce the sentence 'Tolstoy is the same horse as Tolstoy' into our reasoning. And we do not want that, for that sentence says that Tolstoy is a horse.

I also decline to allow anything corresponding to Leibniz's Law—that is to supply each relation of relative identity with its own little version of Leibniz's Law. The logic of relative identity thus does not give us its permission to introduce into our reasoning the sentence

If Bucephalus is the same horse as Alexander's favorite horse, then Bucephalus was fond of apples if and only if Alexander's favorite horse was fond of apples.

If the logic of relative identity does not give us its permission to introduce this sentence into our reasoning, neither does it forbid us to do so. I myself think that this sentence expresses a truth, even a necessary truth, and I am therefore perfectly willing to introduce it into my reasoning (and would be equally willing to introduce any sentence built round 'is the same horse as' in the same way), but I would justify this willingness by an appeal to what I believe to be features of horse-identity, features that (in my view) may not be shared by all other relations of relative identity.

I in fact allow only two logical rules to govern reasoning about relations of relative identity. First, Symmetry, which is illustrated by this inference:

Bucephalus is the same horse as Alexander's favorite horse; hence, Alexander's favorite horse is the same horse as Bucephalus.

Secondly, Transitivity:

Byzantium is the same city as Constantinople; Constantinople is the same city as Istanbul; hence, Byzantium is the same city as Istanbul. (In the standard logic of identity, Symmetry and Transitivity are derived rules; in the logic of relative identity, they must stand on their own.) Now let us apply these ideas to the doctrine of the Trinity. Suppose we have the two relations of relative identity:

is the same being (substance, ousia) as is the same person as.

I shall not attempt to explain what either of these phrases means in any philosophically satisfactory way, but I shall make two remarks. First, I use 'being' for whatever it is that ''there is one of'' in the Trinity, and I use 'person' for what it is that ''there are three of'' in the Trinity. Secondly, there has been some debate about the relation between 'person,' the technical term of Trinitarian theology, and 'person,' the word of ordinary speech. Without attempting to resolve this debate, I will say that I regard 'x is the same person as y as meaning more or less the same as 'x is someone andy is someone—but not someone else.' But nothing I shall say here depends on whether I am right about this. Now it might be thought that all this apparatus of relative identity does not enable us to escape the force of the skeptic's arguments. Consider the second argument. May the skeptic, even if he has only relations of relative identity at his disposal, not present the following argument?

The Father is the same person as God The Son is the same person as God Hence, God is the same person as the Son Hence, The Father is the same person as the Son.

And is it not true that the Father and the Son are both the same person as God? One way to answer this argument might be to say that strictly 'person' applies only to the three persons'' of the Trinity, but does not apply to the Godhead. I will not say anything of this sort. It seems to me that in Holy Scripture God frequently refers to himself as ' I'—depending on how you understand the Hebrew of Exodus 3:14, it may even be that his name is ' I Am' or ' I Am who Am'—and it would, I believe, be heretical to maintain that the God who speaks in the Hebrew Bible is simply God the Father, one of the persons of the Trinity. No, the theologians tell us, and I think that nothing else makes sense in the light of the doctrine of the Trinity, the God who spoke to Moses and Elijah and Ezekiel was the Triune God. And if this is so, God, the Triune God, must be a person. I would say, rather, that the defect in this argument comes from the way it uses the terms 'the Father,' 'the Son,' and ' God.' It uses these phrases as what logicians call singular terms' by which they mean terms that bear a relation called 'denoting' or ' reference' or 'designation' or 'naming' to a single object. But the very notion of a singular term is infected with the idea of the single all-encompassing relation of identity that we have rejected. If, for example, ' Catherine the Great' is a singular term, it follows that if Catherine the Great' denotes x and also denotes y, then x is identical with y. A logic that, like the logic of relative identity, rejects the very notion of a single, all-encompassing identity relation, must, therefore reject the notion of a singular term. But singular terms pervade, or seem to pervade, all our discourse, religious and non-religious. If we '' reject'' singular terms we must find something to put in their place, something to do at least some of their work. I will show by example how to do this. Let us first consider the word ' God.' One thing we must be able to say that we ordinarily say using this singular term (at least it appears to be a singular term) is this: God spoke by the prophets. Suppose we introduce the predicate is divine' to express the divine nature or Godhead. Instead of saying ' God spoke by the prophets' we may say this:

Something is divine and anything divine is the same being as it, and it spoke by the prophets.

(Here I use 'something,' 'anything,' and 'it' as logicians do: when one is speaking very generally, one many use these words to speak of, well, anything, including human beings, angels, and God himself.) Now what of singular terms that purport to denote the individual persons of the Trinity, terms like 'the Father,' 'the Son,' 'the second person of the Trinity,' and 'he who proceeds from the Father'? The Father, the Son, and the Holy Spirit are individuated; each is made who he is by, the relations that hold among them. The Father, for example, begets the Son, the Holy Spirit proceeds from the Father through the Son (or perhaps proceeds from the Father alone), and the Father proceeds from no one and is unbegotten. Suppose we so understand the predicates 'begets' and 'is begotten' that no one but the Father begets and no one but the Son is begotten. We could then understand theological sentences that contain 'the Father' and 'the Son' after the following models: The Father made all things

Something begets and whatever begets is the same person as it and it made all things

All things were made through the Son

Something is begotten and whatever is begotten is the same person as it and all things were made through it. Now, what of our embarrassing argument? Is the Father the same person as God? Is the Son the same person as God? If these things are conceded, does it follow that the Son is the same person as the Father. The statement 'The Father is the same person as God' would be written like this:

Something x begets and whatever begets is the same person as x and something y is divine and whatever is divine is the same being as y and x is the same person as y. And similarly for 'The Son is the same person as God':

Something x is begotten and whatever is begotten is the same person as x and something y is divine and whatever is divine is the same being as y and x is the same person as y.

But 'The Son is the same person as the Father' would be written thus:

Something x begets and whatever begets is the same person as x and something y is begotten and whatever is begotten is the same person as y and x is the same person as y.

And this last statement does not follow from the first two, despite the fact that the rule Transitivity applies to the relation ''is the same person as.'' I will in fact show you how to prove that the last statement does not follow from the first two— using devices from what logicians call the theory of models. Consider the following little story:

There are exactly two dogs in Ivan's shop. They are of the same breed and are for sale at different prices. One barks at the other, and the other never barks at all.

This little story is sufficient for the truth of the following two statements (if we consider "Ivan's shop'' to comprise the whole universe):

Something x barks and whatever barks is the same price as x and something y is a dog and whatever is a dog is the same breed as y and x is the same price as y.

Something x is barked at and whatever is barked at is the same price as x and something y is a dog and whatever is a dog is the same breed as y and x is the same price as y. Now consider the following statement:

Something x barks and whatever barks is the same price as x and something y is barked at and whatever is barked at is the same price as y and x is the same price as y.

This statement is not true in our story, for one thing in the story barks, another is barked at, and they are for sale at different prices. Now consider this question: does the third statement follow from the first two by the standard logic of the textbooks? Unless our story about Ivan's shop is self-contradictory, the answer to this question must be No, for the standard logic of the textbooks is known to have this property: if a story is not self-contradictory, then no statement that is false in the story can be deduced by the rules of the standard logic of the textbooks from any set of statements that are true in the story. But our little story of Ivan's shop and its canine inhabitants is obviously not self-contradictory, and, therefore, the third statement does not follow from the first two.

Now let us return to our three theological statements, our statements that represent 'The Father is the same person as God' and 'The Son is the same person as God' and 'The Father is the same person as the Son.' Does the third, which is certainly inconsistent with the doctrine of the Trinity, follow from the first two (which I, at least do not find objectionable)—I mean does it follow given the logic of relative identity that I have presented? The answer to this question is, No it does not follow, and this may be shown as follows. If it did follow, then it would be possible explicitly to write down the steps of the reasoning, each valid according to the logic of relative identity, by which the third statement was deduced from the first two. That reasoning could, by a purely mechanical set of transpositions of terms, be turned into a piece of reasoning, valid according to the standard logic of the textbooks, by which 'Something x is barked at and whatever is barked at is the same price as x and something y is a dog and whatever is a dog is the same breed as y and x is the same price as y follows from the story of Ivan's shop. And we have seen that this statement does not follow from that story by the standard logic of the textbooks. If all this is too complicated to take in at one sitting, here is a statement of what I claim to have shown that is not too wide of the mark.

Suppose this set of statements was self-contradictory: 'The Father is the same person as God. The Son is the same person as God. The Father is not the same person as the Son.' It would follow that the simple story of Ivan's shop— There are exactly two dogs in Ivan's shop; they are of the same breed and are for sale at different prices; one barks at the other, and the other never barks at all—was self-contradictory; but this simple little story is obviously not self-contradictory.

In a talk of this length I cannot say enough to establish my general thesis, or even to discuss our first anti-Trinitarian argument. My general thesis is this: All the constituent propositions of the doctrine of the Trinity can be expressed in the language of relative identity, and they can be shown to be mutually consistent, given that the correct logic of identity is the logic of relative identity. That is to say, they can be shown to be mutually consistent if a certain simple story about everyday life—a story hardly more complicated than the story of Ivan's shop—is not self-contradictory. And it will be evident to anyone that this simple little story about everyday life is not self-contradictory.

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