The Most Brutal and Inexcusable Error in Counting - Trinity and Consistency

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The most brutal and inexcusable error in counting?: trinity and consistency. by Keith E. Yandell A logically consistent model of the trinity interprets the trinitarian deity as an ultimate composite individual composed only of necessarily internally connected, essential parts. This analysis meets three major arguments against the doctrine of the trinity, arguments based on the absence of differentiating properties among the members of the Godhead, production of the contradiction through identity statements, and doctrines of individuation and entailment. Furthermore, the suggested model is monotheistic, not polytheistic, monistic or pantheistic. © COPYRIGHT 1994 Cambridge University Press INTRODUCTION

authors think, the doctrine of the trinity is a contradiction. CONSTRAINTS

The Anglican Thirty Nine Articles join catholic Christendom Anything that poses as a doctrine of the trinity, as this in affirming that: notion is understood in Christian theology, must satisfy certain constraints. If one of those constraints is that it be There is but one living and true God ... and in unity of this logically consistent, and no attempt to state the doctrine Godhead there be three Persons of one substance, power, satisfies that constraint, then perhaps the best way to put and eternity; the Father, the Son, and the Holy Ghost.(1) the critic’s claim is to say that in fact there is no doctrine of the trinity, since the best candidates for being such are This doctrine has elicited some strong reactions. For inconsistent. Since I take that constraint to hold, I will not example, A Brief History of the Unitarians, called also mind if one reads this essay as an inquiry as to whether Socinians contains these remarks: there is such a thing as the doctrine of the trinity. There is also an exegetical constraint: the doctrine of the trinity You add yet more absurdly, that there are three Persons must be in accord with the content of the Old and New who are severally and each of them true God, and yet Testaments - with what the orthodox Jew will call the there is but one God: this is an Error in counting or Jewish Bible and the Christian Bible. There is a theological numbring; which, when stood in, is of all others the most constraint: it must link up in appropriate ways with the brutal and inexcusable; and not to discern it is not to be a doctrines of Creation and Providence, and Incarnation, man. (2) Atonement and Resurrection. There is a metaphysical constraint (or another theological one, as you wish): it Another author is less splenetic but more specific: must be incompatible with monism [the doctrine that there is but one ultimate reality and that this reality is It must be universally true, that three things to which the nonpersonal] and with polytheism (the doctrine that there same definition applies can never make only one thing to is more than one God). Perhaps there are other which the same definition applies ... If, therefore, the three constraints on a properly Christian doctrine of the trinity. persons agree in this circumstance, that they are each of My purpose is to state one version of a doctrine of the them perfect God, though they may differ in other trinity that is logically consistent, and is not monistic or respects, and have peculiar relations to each other and to polytheistic. I think that it can be further developed so as to us, they must still be three Gods; and to say that they are meet other appropriate criteria, but I will not argue that only one God is as much a contradiction, as to say that matter here; doing so, besides making the paper longer three men, though they differ from one another as much as than an editor’s patience could endure, would be an effort three men can do, are not three men, but only one man.(3) in stating a full trinitarian doctrine rather than (as is my purpose here) arguing that there is a noncontradictory Another author expresses a theological concern: logical outline that such a doctrine can fill in. Thus even if my argument is fully successful, one can complain that no Let it be admitted, that you had proved the supreme actual trinitarian doctrine can have this shape - but then divinity of Christ and the Holy Spirit, the natural conclusion one will have to maintain this without having any formal have been three distinct Gods, which is a doctrine reason for doing so (and so it will be mysterious indeed expressly condemned by Scripture and reason.(4) what the reason that underlies this complaint may be).(5) In what follows, I grant that all contradictions are necessary falsehoods. My question is whether, as our

THREE OBJECTIONS TO THE DOCTRINE OF THE TRINITY

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The most brutal and inexcusable error in counting?: trinity and consistency. I will consider three arguments for the conclusion that trinitarian theology is contradictory. Then I will develop an outline of trinitarian doctrine that is not subject to these objections. The first argument goes like this. Trinitarian doctrine posits three members of the Godhead. By nature, God is not located in space. Either God is eternal and so has no temporal properties or else God is everlasting and so exists at all times. Hence one cannot distinguish between one trinitarian member and another by reference to spatial properties (God has none) or by reference to temporal properties (God has none, or else every member of the Godhead is everlasting and so has the same temporal properties). Further, each member of the trinity has the property being divine, and so has such properties as being omnipotent and being omniscient. But here too every property that one alleged member has, every other also has. These are all of the properties that God necessarily has.(6) But all of the properties that God has, God has necessarily. God can have no accidental or non-necessary properties. Hence there are no properties that one member of the trinity might have and another lack. But if there are members of the trinity, then some member must have some property that some other member lacks. Hence there cannot be members of the Godhead. I will call this the no differentiating properties argument. The second argument begins with a passage from St Augustine. This affirms that there are the Father, the Son and the Holy Spirit, and each is God, and at the same time all are one God, and each of them is a full substance, and at the same time all are one substance. The Father is neither the Son nor the Holy Spirit; the Son is neither the Father nor the Holy Spirit; the Holy Spirit is neither the father nor the Son. But the Father is the Father uniquely; the Son is the Son uniquely; and the Holy Spirit is the Holy Spirit uniquely.(7) A. P. Martinich notes that this commits Augustine to these claims:(8) 1. There is only one God. 2. The Father is God. 3. The Son is God. 4. The Father is not the Son. 5. The Holy Spirit is God. 6. The Holy Spirit is not the Father. 7. The Holy Spirit is not the Son. Now identity is reflexive (everything is identical to it self) and transitive (if X is identical to Y and Y is identical to Z, then X is identical to Z). Given 1 and 2, God = the Father. Given 1 and 3, God = the Son. Given 1 and 5, God = the Holy Spirit. Given these identities, the Father = the Son = the Holy Spirit and three have reduced to one. But then 4,

6 and 7 are false. Thus if 1, 2, 3 and 5 are true, 4, 6 and 7 are false. Since 1 through 7 express the doctrine of the trinity, that doctrine is contradictory. Since contradictions are false even in Heaven, the doctrine of the trinity is false. I shall refer to this as the producing the contradiction argument, since it allegedly produces the contradiction which the critic says the doctrine of the trinity entails. Martinich, in his very interesting article, endeavours to solve the problem by relativizing identity, which involves claiming that propositions of the form X = X and X = Y are ill-formed or nonsensical and regarding all assertions of identity to be assertions of identity relative to some property. Thus X = Y must be expanded to X is identical to Y relative to property P, and it may be true that X is identical to Y relative to properly P and X is not identical to Y relative to properly Q. The pile of glass on the floor thus may be identical to a crystal glass relative to containing the same matter but not relative to being worth one hundred dollars or being a vessel to drink from. Whether there is any good reason to replace plain identity by relativized identity is a controversial matter on which the vote, for whatever it is worth, seems to have gone against relativizing identity. I do not enter that dispute here. But I also do not rely on relativized identity for anything that I shall say.(9) The third argument claims that from a plainly true doctrine of individuation and a plainly correct account of entailment one can show that God cannot be trinitarian. The relevant doctrines of individuation and entailment are these: (I) X and Y are distinct individuals if and only if it is logically possible that X exist and Y not exist or that Y exist and X not exist. (E) Proposition P entails proposition Q if and only if it is logically impossible that P be true and Q be false. If God exists, then God has logically necessary existence. Thus if God exists is true, what is true is Necessarily, God exists. So if God is trinitarian, these also must be truths: Necessarily, the Father exists, Necessarily, the Son exists, and Necessarily, the Holy Spirit exists. Given (E), which expresses the standard account of entailment, every necessary truth entails every other. This can be easily seen. Let P and Q be necessary truths. Given (E), P entails Q if and only if it is logically impossible that P be true and Q be false; if Q is a necessary truth, then it is logically impossible that Q be false, and so it is logically impossible that P be true and Q false. So P entails Q. By reversing the occurrences of |P’ and |Q’ in this line of reasoning, one can prove that Q entails P. Given all this, if God exists is a necessary truth, it follows

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The most brutal and inexcusable error in counting?: trinity and consistency. that each of triad The Father exists, The Son exists and The Holy Spirit exists entails, and is entailed by, each of the others. But then it is logically impossible that one of the trinitarian members exist and some other not exist. But then they are not distinct after all. I shall call this the individuality and entailment argument. My purpose in the remainder of this paper is to reply to these apparently decisive arguments. A METAPHYSICAL MODEL FOR TRINITARIANISM Consider some simple, if abstract, definitions: 1 .X is an ultimate individual if and only if X exists, and it is logically impossible that there be anything other than X on which X depends for existence. 2. X is an individual if and only if it exists, and it is logically possible that X exist by itself or that X exist dependent only on an ultimate individual. 3. X is a part of Y if and only if X exists and it is logically impossible that X exist without Y also existing, and X is not all of Y. 4. X is an essential part of Y if and only if Y exists and X is a part of Y and it is logically impossible that Y exist without X existing. 5. X is an incomposite individual if and only if X exists, and nothing is a part of X. 6. X is a composite individual if and only if X exists, and something is a part of X. 7. Composite being X is necessarily internally connected if and only if, for any parts Y and Z of X, necessarily Y exists if and only if Z exists. Each part of a necessarily internally connected being is such that its existence is a necessary condition of the existence of each other part of that being. Given these definitions, we can see how to define the notion that I have been building toward, namely that of an ultimate composite individual composed only of essential parts which are necessarily internally connected. Here is the definition: 8. X is an ultimate composite necessarily internally connected individual composed only of essential parts if and only if X exists, X is an individual, X is ultimate and composite, X has no part that is not essential, each part of X is necessarily internally connected to every other part of X, and neither X nor any part of X depends for its existence on anything other than X or the parts of X. A trinitarian deity is an ultimate composite necessarily internally connected individual composed only of essential parts. How, then, does this suggestion help us in dealing with our three arguments? THE NO-DIFFERENTIATING-PROPERTY ARGUMENT

Let the preference profile of a person be a systematic description of all the action-outcomes that person would prefer, including those cases in which one would be indifferent. Different human beings obviously can, and typically do, have different preference profiles, and even allowing for indifference it seems that there are alternatives so complex that any of us might be hard pressed to understand the outcomes enough to have a preference, even if that preference were arbitrary. An omniscient being presumably can have a fully determinate preference profile in the sense that she has a preference between any set of exhaustive and exclusive action-outcomes in any possible situation. Suppose (I think this is true, but I will not argue the matter here) that there is no best possible world. What this amounts to is this: let a maximal proposition be a logically consistent proposition P such that, for any proposition Q, either P entails Q or P entails not-Q. Each maximal proposition describes a possible world. The claim that there is a best possible world amounts to this: let M be the true moral theory. A maximal proposition (the terminology, of course, is Alvin Plantinga’s) describes the best possible world if and only if there is some such proposition P about which the following is true: on the criterion that M provides, creating the world that will correspond to P is morally better than creating any world that corresponds to any maximal proposition other than P. The claim, then, that there is no best possible world is the denial that there is any maximal proposition P of the sort just described. If there is no best possible world, then presumably there are various other possibilities. Perhaps it is possible that two worlds (two maximal propositions - possible worlds are only descriptions of ways things might be, save of course for the maximal proposition that corresponds to the actual world) tie in the desirability of their instantiation, given M’s criterion. (To instantiate a maximal proposition, of course, is to create a world.) Then it will be morally neutral which of those worlds is created. The same will hold if three or more worlds tie. But it is not clear that there is any reason to think that there is a tie between top-notch worlds. Suppose what is true is this: possible worlds fall into three sorts. One sort is better not to create than to create. A second sort is such that it is neither better to create it than not nor better not to create it than to do so. The third sort is the kind it is better to create than not. Call these sorts, respectively, negative worlds, neutral worlds and positive worlds. If maximal propositions Pi and P2 describe positive worlds, and it would be better to create the world described by P1 than to create the world described by P2,

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The most brutal and inexcusable error in counting?: trinity and consistency. then P1 is more positive than P2. Then consider these claims: (G1) God’s existing being itself a marvellous state of affairs, God’s creating a world does not make what exists better than there being nothing but God. (G2) If God creates, this is a free and gracious act. (G3) If God creates, God will create a positive world. (G4) For any maximal proposition P that describes a positive world, there is a maximal proposition Q such that Q is more positive than P. (G5) If God creates a positive world described by P, there is some proposition Q that describes a better world that God could have created. Call the conjunct formed from (G1-G5) the creation situation; I will assume that this proposition is true.

morally significant. Think of MA as related to PA in this way: MA differs from PA only as little as it is possible that a positive world differ from PA in a way that makes it a more positive world than PA (it differs only in one morally relevant respect, or only in one such respect plus whatever differences that entails - these things are tricky). There need not be any one way in which two possible worlds differ minimally in a morally relevant manner. But suppose that PA and MA do minimally differ, and that MA is marginally better than PA. It does not follow from Jahweh’s being omnicompetent that if Jahweh creates either PA or MA, Jahweh will create MA. Suppose another possible world GRANDMA is a lot more positive than either PA or MA. I t does not follow from Jahweh’s being omnicompetent that Jahweh will create GRANDMA rather than PA or MA. Under the indicated circumstances, I have suggested, we have the following truths: 1. MA, PA, and GRANDMA are positive possible worlds. 2. GRANDMA is the most positive of the three.

If this is the creation situation, it is true that for any world God created, God could create a better one. If this is true, it is necessarily true, and then so long as our world is positive the |objection’ that God could have created a better world than this one is rendered moot. (Strictly, perhaps there are evils of some sort whose presence in a world would not make it better not created than created but which it would be wrong of God to allow, e.g. being tortured by God; if so, the description of the creation situation needs to be, and can be, correspondingly complicated.) Consider an omnipotent, omniscient, morally perfect being Jahweh and a full list of the positive worlds. If the creation situation is as described, there is no one world such that if Jahweh does create, Jahweh will create that world. If Jahweh does create, Jahweh must choose to create one or another world. There is no single non-arbitrary choice among positive worlds that an omnicompetent being will make by virtue of being omnicompetent. Let the world that Jahweh will create if jahweh creates at all be Jahweh’s preferred world. There is no need that I am aware of to suppose that the propositions that describe positive possible worlds are related by any principle of minimal difference/corresponding value. Consider two possible worlds, PA and MA. Tess exists in both PA and MA. She has one more tooth in PA than she has in MA, and in neither case is she better or worse off regarding her dental situation. That difference will bring about no difference in the value of our two worlds. But some differences will be

3. MA is better than PA. 4. Jahweh is omnicompetent. 5. Given the creation situation, from 1-4 none of the following follow: (i) Jahweh will create GRANDMA if Jahweh creates, (ii) Jahweh will create MA rather than PA if Jahweh creates one or the other. (iii) Jahweh should create GRANDMA rather than either MA or PA if Jahweh creates one of the three; (iv) Jahweh should create MA rather than PA if Jahweh creates one or the other. Still, presumably, there is some truth of the matter about whether, if Jahweh were to create MA or PA, which it would be, and some truth of the matter about whether, if Jahweh creates at all, it will be GRANDMA that is created. (Strictly, possible worlds, as maximal propositions, presumably are abstracta and so are not created at all. I have talked about creating maximal propositions as shorthand for creating the world that such propositions describe, and I will continue to use this shorthand.) Let the whole truth about what choices Jahweh would make regarding creating this possible world rather than that be Jahweh’s total preference pattern. Jahweh’s being omnicompetent determines no single total preference pattern. Of course, where A and B are different total preference patterns, having total preference pattern A and having total preference pattern B are distinct properties, and no rational being could have both at once.

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The most brutal and inexcusable error in counting?: trinity and consistency. It is not clear to me that being omniscient entails being rational; I see no reason to suppose that X knows every proposition that it is logically possible that X know entails X cannot, or will not, act irrationally without surrendering omniscience. The stronger claim X is omnipotent, omniscient, and morally perfect presumably does entail X cannot, or will not, act irrationally without surrendering omnipotence, omniscience, or moral perfection. But it does not en tall There is some one total Preference pattern that X possesses. If this is so, then one omnicompetent being can differ from another by virtue of having a different total preference pattern than another. Hence it is not logically impossible that there be more than one omnicompetent being. (Being here is neutral between individual and part.) Hence the fact that the doctrine of the trinity entails that there can be more than one omnicompetent being, if that is a fact, does not make that doctrine self-contradictory. I see no reason to think that the profile preferences of two omnicompetent beings cannot differ. If so, two trinitarian members might differ regarding their distinct preference profiles. Hence there may be distinguishing features among trinitarian members of a sort supposedly precluded by the no differentiating property argument, which thus fails.

true.

It should not be thought that my argument here strictly requires (G4) For any maximal proposition P that describes a positive world, there is a maximal proposition Q such that Q is more positive than P, though for simplicity of illustration and starkness of contrast I have included (G4) in its statement. Suppose there is a best possible world but that three lesser worlds tie, and that each trinitarian member finds a different one of these three worlds in some manner preferable to the other two. Or, utterly independent of whether there is a best possible world, perhaps there are some specific(uncreated) possible worlds that one trinitarian member more enjoys contemplating than does the others and this is so for each trinitarian member. Or, from knowledge by description to knowledge by acquaintance, perhaps each trinitarian member most enjoys observing and/or acting in different portions of the actual world. Any of these situations would do as well for my purposes as a creation situation partially defined by G4).

(O3) While X is omnipotent, there is no proposition that X de facto can make true.

It might be suggested that it is logically impossible that there be two omnipotent beings (whether individuals or parts). I have no doubt that there are definitions of |omnipotent’ on which this is so. For example, consider this rough definition (I shall assume throughout that X is omnipotent entails X is omniscient) : (O1) X is omnipotent if and only if for any proposition P, if it is logically possible that X make P true, then X can make P

Suppose that X and Y both are omnipotent in this sense. Then presumably neither can make a proposition true unless the other is willing that it be true. That is, it seems true that: (O2) Not even an omnipotent being can make true a proposition that an omnipotent being is not willing to allow to be true. (Logically necessary propositions are irrelevant here; there can be no such thing as making a logically necessary proposition true.) Suppose, then, that X and Y are so related to one another that for any proposition P such that X can make P true provided Y does not object, Y does object, and for any proposition Q such that Y can make Q true provided X does not object, X does object. Any proposition that it is logically possible that an omnipotent make true presumably is one that she can make only true if no other omnipotent being, if any, opposes. One might say that X and Y are related by omnipotent paralysis. If X and Y are related by omnipotent paralysis, it is the case that:

One might suspect (O3) Of being self-contradictory. The principle behind this suspicion seems something like this: (O4’) It is logically impossible that any being restrict the power of an omnipotent being. On this analysis, what makes (O3) SO suspicious is that it is true precisely because some being distinct from X has severely restricted X’s power. I confess to thinking (O4’) false. The truth rather is that: (O4) It is logically impossible that any non-omnipotent being restrict the power of an omnipotent being. If (O4) is true, then so far as I can see there is no reason to think that (O3) is self-contradictory. Of course, putting the idea very crudely, one might think of an ultimate composite, etc., being that had two parts, A and B, and think of power as divided exhaustively and exclusively in terms of AC-power and BC-power, holding that A has all and only AC power and B all and only BC power. Then this ultimate composite, etc., being would be omnipotent by virtue of having necessarily internally connected essential parts that together are omnipotent so that this being is omnipotent though none of its parts are. But I have no analysis to plug into the variables marked AC’ and BC’ and

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The most brutal and inexcusable error in counting?: trinity and consistency. suspect that there are none; further, I doubt that this model would yield anything much like orthodox trinitarianism.

SG: The Son is part of the Godhead. HG: The Holy Spirit is part of the Godhead.

I stick, then, to a rough analysis of omnipotence expressed by (O1), (O2), and (O4), on which (O3) is non-contradictory. Morally perfect omnipotent beings, after all, will not be related by way of omnipotent paralysis. Two morally perfect omnipotent, omniscient persons will not reduce each other to impotence. Hence from the fact that an omnipotent being might be related to another omnipotent being by way of omnipotent paralysis it does not follow that this is a danger for the members of a trinitarian deity. I turn now to our second anti-trinitarian argument. THE PRODUCTION-OF-A-CONTRADICTION ARGUMENT

The |P’ and |G’ triads express orthodox claims regarding the trinity. The |I’ triad does not. From the |P’ and |G’ triads, one cannot derive the contradictions that easily are derivable from the |I’ triad. If God is an ultimate composite individual composed only of essential parts which are necessarily internally connected, the ’P’ and |G’ triads (these readings are compatible and complementary) remain possibly true of God, but the |I’ triad is not possibly true of God. Hence if we accept the suggested model for trinitarian deity comprised by the |P’ and |G’ triads, we can escape the production-of-a-contradiction argument. I turn then to our third antitrinitarian argument. THE INDIVIDUALITY AND ENTAILMENT ARGUMENT

Taken as partial expressions of orthodox trinitarianism, the propositions: F. The Father is God.

We may as well start by making things worse. A doctrine of meaning is available that is about as plausible as the doctrines of individuation and entailment that (I) and (E) express:

S: The Son is God. H: The Holy Spirit is God. are not to be read as identity statements. So read, they amount to: FI: The Father is identical to God (and so is all the God there is). SI: The Son is identical to God (and so is all there is to God). HI: The Holy Spirit identical to God (and so is all there is to God). Instead, they are to be read as predications, as structurally analogous to Mark Twain was a funny man rather than Mark Twain is Samuel Clemens. Alternatively, if you wish, the |is’ in the sentences that express these propositions is to be read, not as the ’is’ of identity or of predication, but of inclusion. If we take the predication route, we get: FP. The Father is divine. SP: The Son is divine.

(M) Proposition P differs in meaning from proposition Q if and only if there is some proposition R such that it is false that P entails R if and only if Q entails R. What (M) requires is that difference in meaning is present only in the presence of divergence of entailments. The positive version of (M) reads: (M*) Proposition P has the same meaning as proposition Q if and only if, for any proposition R, P entails R if and only if Q entails R. We noted earlier that if God exists is a necessary truth and God is trinitarian, The Father exists, The Son exists and The Holy Spirit exists also are necessary truths. Then, by (E), each entails the others. Thus, by M*), each is identical in meaning. Hence, along these lines, no distinction can arise between trinitarian members. Similarly, if there really are abstracta, and numbers are among them, then among Two exists and Three exists, and Two is even and Three is odd, each entails every other and so, by M*), all are the same proposition. For that matter, so, on the assumption noted, are God exists and Two is even a single proposition, which is hard on both mathematics and theology. Thus (M) and (M*) are highly suspect.

HP: The Holy Spirit is divine. If we take the inclusion route, we get: FG: The Father is part of the Godhead.

Further, of course, by (1), God and two are the same entity, since if God exists and Two is even entail one another, it is logically impossible that God exist and two not exist. By (I), then, God and two are one, which also is inelegant. These consequences follow without any appeal

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The most brutal and inexcusable error in counting?: trinity and consistency. to (M) or (M*). The relevance of these considerations for our purposes is that there seem to be superb reasons for thinking that something is wrong with the individuality-and-entailment argument. The question remains as to how exactly to set things right. Those uncharmed by the standard definition of entailment that (E) expresses have defined non-vacuous entailment (NVE) as follows: (NVE) P non-vacuously entails Q if and only if (i) P entails Q, (ii) P is not a contradiction, and (iii) Q is not a necessary truth. But the third portion of (NVE) rules out necessary propositions as being non-vacuous entailees; on this definition, nothing can non-vacuously entail a necessary truth, since no necessary truth is permitted to occupy the position of the consequent of a conditional statement and only consequents can be entailees.

what must obtain, or what must exist, if that proposition is to be true. My golden retriever is eating his rawhide is true if and only if he is eating his rawhide. On the present suggestion, necessary truths have (necessarily existing, of course) truth conditions. Thus three’s not being evenly divisible by two is Three is odd’s truth condition, and the Properly of someone’s drawing a rectangle including the property of someone’s drawing a figure is If Walter draws a rectangle, then Walter draws a figure’s truth condition; Three is the sum of two even numbers can have no obtaining truth condition though we can describe (albeit not consistently) what would have to obtain were it true. These reflections suggest a definition for nonvacuous entailment among necessary propositions, the notion of N-nonvacuous entailment. (NVE*) Proposition P N-non-vacuously entails proposition Q if and only if P and Q are necessary truths and Q’s truth condition is all or part of P’s truth condition. Or, if you prefer:

I think that the way to set things right is to develop an account of non-vacuous entailment among necessary propositions. This is worth a paper on its own, but the basic idea can be stated briefly in two ways." Suppose that to each necessary truth there corresponds a necessarily existing state of affairs that makes the necessarily true proposition true. Consider two necessary truths: N.1 Three is odd. N.2 If Walter draws a rectangle, then Walter draws a figure. Consider also the necessary falsehood or contradiction: C1. Three is the sum of two even numbers. The corresponding necessarily existing states of affairs presumably are:

(NVE**) Proposition P N-non-vacuously entails proposition Q if and only if P and Q are necessary truths and the truth condition of not-Q obtaining is identical to all or part of P’s truth condition not obtaining. If we dislike the apparent metaphysical lushness of there being both propositions and states of affairs, one can rely simply on the notion of one proposition contradicting another. Thus the proposition Three is even is contradicted by the proposition Three is not even but it is not contradicted by either If Walter draws a rectangle then Walter draws a figure or by It is false that if Walter draws a rectangle then Walter draws a figure. This notion of not being contradicted by is not extensional; it is intensional. Then we can say: (NVE***) Proposition P N-non-vacuously entails proposition Q if and only if P and Q are necessary truths and not- Q contradicts P.

S1. three’s not being evenly divisible by two S2. the property of someone’s drawing a rectangle including the property of someone’s drawing a figure. The state of affairs that would have to obtain in order for C1 to be true of course is:

Given one of these accounts of N-non-vacuous entailment, we can replace (I). Note that (1) is identical to: (I’) X and Y are distinct individuals if and only if it is false that X exists mutually entails Y exists. Then replace (I) and (I’) by:

S3. three’s being evenly divisible by two. Obviously if S1 obtains, S3 cannot obtain.

(I*) X and Y are distinct individuals if and only if it is false that X exists mutually N-non-vacuously entails Y exists.

The truth conditions of a proposition are constituted by

Or, if you prefer:

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The most brutal and inexcusable error in counting?: trinity and consistency. (I**) X and Y are distinct individuals if and only if either X exists is not contradicted by Y does not exist or Y exists is not contradicted by X does not exist. Given (I*) or (I**). God exists does not mutually N-non-vacuously entail Two exists nor is it contradicted by Two does not exist, so God and the number two are distinct. If we view God as having logically necessary existence, then appeal to I*) will not help us to distinguish between the Father and the Son, for then The Father exists and The Son exists N-vacuously entail one another. Strictly, this entailment is mutual if, as seems correct, it is logically impossible that the trinity be reduced to a binity or the binity to unity - if we assume, that is, that it is a necessary truth that for any two trinitarian members X and Y, X exists if and only if Y exists. I take this claim, which we might call the necessary trinitarian connection thesis, to be a necessary truth; that is, Necessarily, if God is trinitarian, then it is logically impossible that one trinitarian member exist and another not exist. The parts of an ultimate composite necessarily internally connected individual that has only essential parts, if that individual necessarily exists, cannot have parts if (I*) or (I**) is true, for then The Father exists is contradicted by The Son does not exist, and The Son exists is contradicted by The Father does not exist. Hence each entails the other.

Appeal to (I*) will allow us to distinguish between God and any number you like, or between any two numbers. But it will not generate any intertrinitarian distinctions if it is a logically necessary truth that God exists. In one way, this is good; given (I*) and (I**), it remains true that (as orthodoxy requires) the members of the trinity are not distinct individuals. But even given (I*) and (I**), one cannot distinguish between the essential parts of a necessarily existing ultimate composite necessarily internally connected being that has only essential parts, since our argument that (I*) and (I**) do not serve to distinguish trinitarian members also shows that the corresponding versions of (I*) and (I**) that are so stated as to be principles of distinctness among parts will not distinguish among essential parts of necessarily existing composite beings. (The |corresponding versions’ are simple to produce; simply replace the one occurrence of |individual’ in (I*), or (I**), by one occurrence of |part’ to produce their part-relevant successors.) The solution to this problem is easy, though a necessitarian will view it as costly. Consider these definitions: T1. X has logically contingent existence if and only if X does not exist is not a contradiction and X exists. Then consider this claim:

Suppose that [as many necessitarians hold] Necessarily, if x is a necessarily existing being, then if X has property P, then necessarily X has P; suppose that necessary beings only have properties that it is logically impossible that they lack. Then for any property P that the Father has, The Father exists entails The Father has P, and for any property Q that the Son has, The Son exists entails The Son has Q. Thus if The Father has P is true, the proposition The Father lacks P entails The Son does not exist and if The Son has Q is true, the proposition The Son lacks Q entails The Father does not exist. In sum, any true property-ascribing proposition about the Father is contradicted by the denial of any true property-ascribing proposition about the Son, and any true property-ascribing proposition about the Son is contradicted by the denial of any true property-ascribing proposition about the Father. Assuming that any true proposition about the Father or the Son is property-ascribing [or purely existential - i.e. of the simple form X exists - if existence is not a property], any true proposition about the Father mutually N-non-vacuously entails any true proposition about the Son. (I take it that |property’ can be unproblematically construed so that this assumption is true.) Then even our newer criterion for individuation will allow for no distinctions among trinitarian members.

T2. God is trinitarian, is an ultimate composite necessarily internally connected individual that has only essential parts, and has logically contingent existence. Suppose that T2 is true. Note that if (i) X is composed only of A, B and C; (ii) X has logically contingent existence, (iii) X is necessarily internally connected, then it follows that (iv) each of A, B and C have logically contingent existence. Even given T2, the Father, the Son and the Holy Spirit are not distinct individuals. It is a necessary truth that if God is trinitarian, then the Father exists if and only if the Son exists and the Son exist if and only if the Holy Spirit exists. Further, if it is true that If God exists, then God is trinitarian then it is true that Necessarily, if God exists then God is trinitarian. Thus it is true that Necessarily the Father exists if and only if the Son exists and Necessarily, the Son exists if and only if the Holy Spirit exists. So even if God exists is logically contingent, it remains true that The Father exists is contradicted by The Son does not exist, so The Father exists entails (and non-vacuously entails, though it does not N-non-vacuously entail) The Son exists. Thus, by (1) - which is the relevant criterion of individuation among logically contingent items - the Father and Son are

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The most brutal and inexcusable error in counting?: trinity and consistency. not distinct individuals. But then for orthodox theology they are not supposed to be distinct individuals. Consider this criterion for distinctness of parts: (IP1) It is logically possible that part A of X is distinct from part B of X, even if A and B are essential parts of X and X is necessarily internally connected, provided X exists is logically contingent and if is false that for any property P A has P mutually entails B has P. (IP2) If A and B are essential parts of X, X is necessarily internally connected, and X exists is logically contingent then A is distinct from B if and only if there is some property P such that of A and B, one has it and the other lacks it. By appeal to (I*) and (I**), one can distinguish between such propositions as Necessarily, if God exists then God is trinitarian and Necessarily, two is even. But if it is true that Necessarily, God exists then one cannot appeal to (IP1) and (IP2) to distinguish between Father and Son as members of the trinity. Any trinitarian member will necessarily exist, and the proposition that it does not exist contradicts the proposition that each other trinitarian member exists. By appeal to (IP1) and (IP2) one can distinguish between trinitarian members as parts, provided God exists is logically contingent. (I assume that Necessarily, God exists entails For any property P that God has, it is necessarily true that God has P.) One cannot distinguish between trinitarian parts as individuals by appeal to any of these claims, but that is not something that a trinitarian theologian wants to do. CONCLUSION There are various standard criticisms of trinitarian monotheism. One is that it is not monotheism. Monotheism holds that there is one individual that is God who is omnipotent, omniscient, Creator, Providence and the like. Nothing in the view that God is an ultimate composite necessarily internally connected being that has only essential parts, each part of which is omnipotent, omniscient and morally perfect, each part having its own distinct positive world preference profile, entails that there is more than one divine individual. So it is monotheistic. Another criticism is that trinitarianism monotheism really is polytheism. Polytheism is the view that there is not one individual who is God, and that there are various divine or quasi-divine beings all of whom lack omnipotence, omniscience, full creatorhood and full providentiality; they

divide the world between themselves with each taking care of part of it, or of all of certain processes in it, or the like. Trinitarian monotheism denies that more than one individual is God, that the beings closest to being creators and providences lack omnipotence and omniscience, that the world is gerrymandered among finite caretakers under no omnicompetent supervision. So it is not polytheistic. Obviously trinitarian monotheism as here construed is not monistic since it regards God as omnipotent and omniscient, and hence as personal. Neither is it pantheistic. Suppose that God creates a lime tree. The lime tree depends for its existence on God. But it is not a part of God, for there is no part of God the existence of which depends on the existence of the lime tree. The parts of Deity are necessarily internally connected. The lime tree bears no internal connection to any trinitarian member. I grant that one variety of monotheism holds that God is an ultimate incomposite individual. I add that another variety of monotheism holds that God is an ultimate composite individual. Neither sort holds that there is more than one ultimate individual. Both hold that only one individual is God. That is what the trinitarian view that I have outlined here holds. Hence it is robustly monotheistic. Monotheists who hold that God was incarnate in Jesus Christ presumably should hold that God is an ultimate composite individual. I conclude by noting that my purpose here is modest. I have attempted to provide one metaphysical model that shows promise as the logical skeleton of a consistent version of trinitarian monotheism. Obviously before it could parade as a robust doctrine of the trinity, considerable theological flesh would have to be put on these dry bones. Further, I have done nothing whatever here to argue that trinitarian theology is true. Finally, there may well be any number of other ways of developing a model that would serve my purposes here, perhaps including necessitarian ones. Thus I have not claimed to show what the metaphysical structure of trinitarian deity is, if there is such. My purpose has not been to develop here a detailed account of trinitarian doctrine, but only to show that certain arguments do not demonstrate that the doctrine of the trinity is self-contradictory. (1) Cf. John Leith, ed., Creeds of the Churches (New York: Doubleday Anchor, 1963), p. 266. The Thirty Nine Articles were formulated in 1563. (2) Published anonymously in 1687, this work is ascribed to John Biddle; italics are in the original. The passage is quoted in Leonard Hodgson, The Doctrine of the Trinity (New York: Charles Scribner’s Sons, 1944), p.219. (3) Joseph Priestly, Tracts (London: printed and published by the Unitarian Society, 1791), vol. 1, 182; italics in the original. This formulation of the problem suggests the reply

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The most brutal and inexcusable error in counting?: trinity and consistency. that, as Theresa, Doris and Harriet may be three persons but share the feature being human so the Father, Son and Holy Spirit may be three persons but share the feature being divine. The passage is quoted in Hodgson, loc. cit. (4) The Trinitarian Controversy Reviewed: or a Defense of the Appeal to the Common Sense of all Christian People (By the Author of the Appeal, London, 1791), p. 338. Quoted in Hodgson, loc. cit. (5) Philosophically sensitive accounts of trinitarian doctrine can be found in Ronald J. Feenstra and Cornelius Plantinga, Jr., eds., Trinity, Incarnation, and Atonement: Philosophical and Theological Essays (Notre Dame, Indiana: University of Notre Dame Press, 1989) and David Brown, The Divine Trinity (La Salle, Illinois: Open Court Publishing Company, 1985). (6) I have not discussed omnibenevolence here. Thomas V. Morris, in The Logic of God Incarnate (Ithaca, NY: Cornell University Press, 1986) deals with omnibenevolence in one way, and in Thomas V. Morris, ed., Divine and Human Action (Ithaca, NY: Cornell University Press, 1988, |Divine Necessity and Divine Goodness’, and ’Some Problems for Tomistic Incarnationists’, International Journal for Philosophy of religion, XXX (1991), 169-82, I deal with it in another. My own view is that it is logically impossible that any being, divine or human, have necessary omnibenevolence as a property, since being omnibenevolent entails being a moral agent, being a moral agent entails having libertarian freedom, and having libertarian freedom is incompatible with possessing necessary omnibenevolence. (For the purists: property P entails property Q if and only if X has P entails X has Q.) These matters are somewhat pursued in the concluding chapter of my The Epistemology of religious Experience (Cambridge: Cambridge University Press, 1993). I see no reason to think that the same sorts of strategies followed in this paper will not do as nicely for omnibenevolence as they do for omniscience and omnipotence. (7) On Christian Doctrine 1, 5, 5. (8) Identity and Trinity’, Journal of Religion (1975), 170. (9) Peter Van Inwagen, |And Yet They Are Not Three Gods But One God’, in Thomas V. Morris, ed., Philosophy and the Christian Faith (Notre Dame, Indiana: University of Notre Dame Press, 1988), 24I-78, explains relativized identity and powerfully argues that if one relativizes identity one can create a logically consistent skeleton which can support the flesh of a full trinitarian doctrine. As is appropriate for a single essay, he does not do more; he does not actually develop a specific and detailed doctrine of the trinity, apparently (and rightly) taking what he does to be enough for one paper. I assent to his conditional while remaining unpersuaded of the wisdom of relativising identity. (10) I have further developed the notion of non-vacuous entailment among necessary truths in the final chapter of The Epistemology of Religious Experience (Cambridge: Cambridge University Press, 1993)

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