Is The Doctrine of the Trinity Logically Coherent? (Peter Lupu)

In this installment, Peter Lupu, atheist, defends the logical coherence of the doctrine of the Trinity.  My critical comments follow in blue.

It may be somewhat of an astonishment to those who know me well that I should venture to defend the doctrine of the Trinity. I am not a Christian; I am not religious; I am an atheist; and I have at least on one occasion privately expressed to Bill my reservations about the coherence of the Trinity doctrine. Nevertheless, there is a question here that deserves exploring. What is the question?

Bill asks: ". . . . is it unproblematic to say that God is one in respect of his nature (or substance) but three in respect of his Persons?"

The question, then, is not whether the Trinity doctrine is true tout court, but whether it is possible: i.e., whether it is a logically coherent doctrine. And despite all my sins listed in the opening paragraph, I wish to know the answer to this question.  Our problem is that the following two doctrines appear to be logically inconsistent:

1) On the one hand, we have the doctrine of the absolute unity of God. Thus, if God exists at all, then God must be one absolutely unified individual: nothing can be identical to part of God without being identical to the whole of God. The principle of the absolute unity of God implies that for any two entities x and y, if x is identical to God and y is identical to God, then x and y are absolutely identical . So, clearly, the absolute unity of God is to be interpreted in terms of the notion of identity. In order to render this explicit I shall call this the Absolute Identity Doctrine (AID).

2) On the other hand, we have the doctrine of the Trinity. What is this doctrine? Well, this doctrine is also interpreted as involving essentially the notion of identity. How so? Well, the way the doctrine of the Trinity is interpreted  is roughly along the following lines: there are three absolutely distinct entities (regardless of how they are named or described) x, y, and z such that each of these absolutely distinct entities x, y, and z is identical to God. So here the doctrine of Trinity involves essentially the notion of identity. I shall call this interpretation of the doctrine of Trinity the Identity Interpretation of Trinity (IT).

3) Of course, it should be immediately apparent that AID and IT cannot be both true. This is the paradox of the doctrine of the Trinity.

4) Father Gratry's solution (as cited in Bill's post) relies upon distinguishing between "absolute unity of nature" vs. "absolute trinity of persons". Thus, with respect to God's nature, God is absolutely identical to one and only one thing and, hence, absolutely unified. However, with respect God qua person, God is absolutely identical to three different persons. What sort of a distinction is being made here? It would be natural to interpret the distinction Father Gratry relies upon for his solution as presupposing a  notion of relative identity. Relative to God's nature, God is one; relative to God as a person; God is many (i.e., three).

5) Bill does not buy Father Gratry's solution:

"Either the divine nature is an individual entity or it is not. If it is an individual (unrepeatable) entity, then each Person can be God only by being identical to God. But this implies that there is one person, not three. If, on the other hand, the divine nature is a multiply exemplifiable (repeatable) entity, then each Person can be God only by exemplifying the divine nature. This, however, implies that there are three Gods."

I suspect that Bill rejects Father Gratry's solution because he thinks that whether or not relative identity makes sense in general, it certainly makes no sense when it comes to God. If God's very nature is to be absolutely unified; absolutely one, then there cannot be some other respect in which God could be many. It is precisely this sort of relativity that is excluded by maintaining that God's unity is absolute by his very nature. Therefore, the possibility that there is some other respect in which God could be many is excluded by the very notion that God's unity is an inherent part of God's nature. What else could AID mean?

6) I think that Bill's intuitions are correct and I agree with him on this point. But perhaps there is a different way of interpreting Father Gratry's solution. Suppose we do not interpret Father Gratry's distinction between "absolute unity of nature" vs. "absolute trinity of persons" as a form of relative identity. Suppose that instead we interpret it as distinguishing between two senses of `is'. God's nature is such that for every two entities x and y, if x is identical to God and y is identical to God, then x and y must be identical. We do not need to reinterpret AID as relative identity. However, once we insist upon interpreting AID in this manner, we no longer can interpret IT as a claim about three absolutely distinct entities being identical to God: i.e., we simply cannot interpret IT as involving also the notion of identity. I suggest that we should not think about the doctrine of Trinity as involving identity at all. Rather we should interpret the `is' in the claims: person x is God; person y is God; and person z is God as the `is' of instantiation or rather as primary instantiation. While God is absolutely unified by his very nature, God has three primary instantiations in three absolutely distinct persons x, y, and z.

7) This proposal takes a page from Plato's solution to the problem of the One and the Many. By the very nature of forms, there is one and only one unified form of horsehood: there cannot be several (within Plato's metaphysics this is easily provable). However, the form of horsehood can have none, one, or many instances. Similarly, by God's very nature, there can be only one absolutely unified God. But God can be exemplified qua persons in several different ways. In this case I suggest that the proponents of the doctrine of the Trinity should maintain that there can be three and only three absolutely different primary instantiations of God qua person. So Father Gratry's distinction between "absolute unity of nature" vs. "absolute trinity of persons" can now be interpreted as a distinction between the sense in which God by his very nature is absolutely unified and hence necessarily one (analogous to Plato's forms) vs. the possible primary instantiations of God in the manner of persons of which there can be only three absolutely distinct such instantiations.

8) If we allow this distinction, then the Absolute Identity Doctrine and the Trinity Doctrine are logically compatible because while the former is about (absolute) identity, the later does not involve identity at all: the doctrine of Trinity is about the possible primary instantiations of God in the form of persons. Hence, the two doctrines do not conflict.

9) None of this proves, of course, that the doctrine of Trinity is true; only that it is possible.

Response

The problem of the Trinity, to put it schematically, is to prove the consistency of the following set of propositions while avoiding tritheism:

a) P1 is numerically distinct from P2.

b) P2 is numerically distinct from P3.

c) P1 is numerically distinct from P3.

d) P1 is G.

e) P2 is G.

f) P3 is G.

If the 'is' in the last three propositions is the 'is' of identity, then a contradiction is easily derivable given the Absoluteness of Identity and the Transitivity of Identity. (Verify this for yourself.)

On Peter's suggestion as I understand it the solution lies in the direction of reinterpreting the 'is' as it occurs in the last three propositions as an 'is' of predication. Say what you want about Bill Clinton, he rendered a great service to philosophical logic by insisting that much depends on what the meaning of 'is' is. And he saved his hide to boot!

Reading the 'is' as the 'is' of predication avoids inconsistency but gives rise to a different problem.  Suppose you take 'The Father is God' to mean 'The Father is divine' where the 'is' expresses predication and 'divine' picks out the property of divinity. Then what you are saying in effect is that the Father exemplifies or instantiates divinity. And similarly in the cases of the Son and the Holy Ghost. But if each exemplifies divinity, then each is a god, and the result is tritheism.

The trick is to maintain monotheism while also maintaining the distinctness of Persons. Can this be done without major surgery on standard logic? Perhaps it can be done if it can be maintained that identity is sortal-relative. For then one can say the following: 'The Father is the same god as the Son, but a different person,' 'The Son is the same god as the Holy Ghost, but a different person,' and 'The Father is the same god as the Holy Ghost, but a different person.' Thus we would avoid such inconsistent triads as the following: The Father = God; The Son = God; The Father is not identical to the Son.

But is the sortal-relativity of identity sound logical doctrine?   That's a separate post.

Comments

[Account Deleted]

Correction to my main post:

In the original #2 there is an error. It says:
"there are three absolutely distinct entities (regardless of how they are named or described) x, y, and z such that each of these absolutely distinct entities x, y, and x is identical to God."

The last occurrence of 'x' should be replaced with an occurrence of 'z' to read:

"there are three absolutely distinct entities (regardless of how they are named or described) x, y, and z such that each of these absolutely distinct entities x, y, and z is identical to God."

[Account Deleted]

Reply to Bill,

Let us take Bill's presentation (a)-(f) of the problem of the Trinity as the standard and ad to it the Absolute Identity (unity) Doctrine (AID): i.e., God must be one absolutely unified individual and, therefore, nothing can be identical to part of God without being identical to the whole of God.

We have three options here:

(1) Clearly, we cannot interpret the 'is' throughout (a)-(f) as the is of identity because then we get a contradiction. I am unhappy with simply conceding this conclusion and noting that therefore the solution is inscrutable to us because it is a mystery.

(2) Interpret the 'is' in (d)-(f) as relative identity, as Bill seems to propose in his Reply. I am unhappy with this solution because it forces giving up AID. Thus, God is no longer absolutely unified. God could be identical to x relative to one aspect but not identical to x relative to some other aspect. I think preserving AID is essential in solving the problem of the Trinity.

3) Interpret the 'is' in (d)-(f) as instantiation, along the lines I suggested. This proposal requires a response to Bill's objection.

Note: I am unhappy with Bill's shift from instantiation to predication because the later is a relation between a linguistic item (term) and a set of objects. My proposal is to view the 'is' here as a relation between a Form in Plato's sense and its instances. Note that instantiation need not be a relation between a form and physical instances only: it can be between a Form (e.g., even number) and other abstract objects (e.g., 2, 4, 6, etc.,).

3.1) Bill's objection against the instantiation proposal is that it results in at least three divinities, each of which instantiates God. Since each divinity is a God, we get that there are three Gods, precisely the sort of result we wished to avoid in the first place. Thus, if the Father, the Son, and the Holy Spirit each exemplify God, then they are all divine and, hence, gods. Therefore, we got three distinct gods.

3.2) How does Bill get this result? Let us take the example of a horse called Double. Double exemplifies the Form or Property of *horsehood* or of *being a horse*. Now, Double exemplifies horsehood insofar as Double is a horse. But it does not follow from the fact that Double exemplifies horsehood that Double enjoys *all* the properties of the Form horsehood. For instance, the form or property of horsehood is indestructible, unchanging, and unique. But clearly Double the horse has none of these properties: Double is destructible, constantly changing, and certainly not unique. So we must beware of assuming that instantiation endows the things that instantiate all the properties of the thing instantiated. How do we guard against such unwarranted inferences? We can make it explicit that the instantiation relation between Double and the form of horsehood pertains only with respect to being a horse.

3.2) Now, Bill's objection assumes that because the Father, the Son, and the Holy Spirit all exemplify God, it then follows that they feature all the properties of God. But we can guard against such a conclusion by making it explicit that the exemplification relationship holds only with respect to certain features: e.g., the feature of being a *divine person*.

3.3) Plato quite explicitly assumes that the world of Forms is hierarchical. There are lower forms and higher forms, the highest of which is truth, beauty, and goodness. For instance, all forms share the property of being unchangeable. So 'unchangeability' is a form that is higher than the forms of horsehood, cathood, doghood, etc. Not everything exemplifies the high form of unchangeability: e.g., double does not.

3.4) So how do we resolve Bill's example about "The Father is divine", "The Son is divine" and "The Holy Spirit is divine". If divine means 'being a god' then we got three gods. But we do not need to think about these propositions in this way. We may instead view them as stating that all three exemplify God's divine-personhood. However, we do not thereby conclude that anything whatsoever that exemplifies divine-personhood is itself an absolutely unified individual such as God, just like we do not conclude that Double is indestructible from the fact that it instantiates the form of horsehood and the form of horsehood is indestructible.

4) Once we relativize the 'is' of instantiation in the manner stated, recognize a hierarchy of forms or properties along the lines described above, and guard against the sort of unwarranted inferences illustrated above, I think we can avoid Bill's objection and accommodate both the doctrine of the Trinity as well as AID.

[Bill Vallicella]

Peter,

First of all, it makes no sense to speak as you do of something "exemplifying God." God is an individual, and no individual can be exemplified. What you have to say is that something exemplifies deity (deitas, Gottheit, Godhood). But, clearly, if x exemplifies deity, then x is a god just as, if you exemplify humanity (the property of being human), then you are a man.

It's a dilemma: If you say that the Father is (identically) God, then you get a contradiction. You see that. But if you read the 'is' as an 'is' of predication and take the Father to exemplify deity, then the result is that the Father is a god. Similalry with the other Persons. Next stop: tritheism.

[HTB]

Bill,

I would like to interject a little if you do not mind. I think the triad you mentioned is a misunderstanding of the doctrine of the Trinity. As I understand it, it is not affirmed that Jesus=God, the Father=God, and the Holy Spirit=God. But rather something like Jesus=one person of the triune God, the Father=one person of the triune God, and the Holy Spirit=one person of the triune God, whilst God=the three persons of the trinity.

If one considers your triad, for example, it can be easily seen that the "is" is not one of identity. For the reversal would be false. One could not say, for example, that God=Jesus in the same sense that one could say Jesus=God, because God includes the three persons of the trinity, whereas Jesus does not. But, if a=b, does not b also equal a?

How to avoid tri-theism? I must confess I am out of my league. But, perhaps it might help to challenge your intuition that an "is" of predication exemplifying deity entails that the predicated is a deity, in the sense of complete ontological distinction. I do not see why this need be true, and it seems to beg the question. It relies on the assumption that to be God means to be God in entirety.

But why assume this? Why assume that if "is God" predicates divinity, it somehow also entails complete ontological distinctness? Could it not be that the three person of the trinity are all divine, and yet that the deity is triune? That no one of the persons is the triune deity, but that the triune deity is all three of the persons?

The problem it seems to me is not with "is" so much as with "God". In one sense "God" means the triune deity. And in this sense, Jesus is not God. In another sense, "God" means to be a member of the triune deity, and in this sense Jesus is God. Does this clarify the doctrine of the trinity? Probably not, but I don't think your objection to the doctrine's coherence is successful, as it relies on a false dichotomy. The options given are 1. That the "is" is one of predication rather than identity, and that if the same predication of deity is made to multiple persons, then a plurality of Gods follows, and 2. that the "is" is one of identity, meaning that Jesus just is God, or that God contains nothing more than Jesus (and likewise with the Father and the Holy Spirit).

The first, I think, would be outright contradicted by the doctrine, and cannot simply be presupposed. The second is not affirmed at all. Why not a third? 3. That deity is something which can be predicated of persons without entailing complete ontological distinction, such as would be the case if The Deity were a trinity of persons.

[Bill Vallicella]

HTB,

In your second sentence, you bring Jesus into it, but that is a mistake. The Trinity and Incarnation doctrines, though connected, are logically distinct. You give the impression of not understanding the Trinity doctrine. It is not that there is one God in three divine persons, the Father , Jesus, and the Holy Ghost. The connection between the 2nd Person, the Logos or Word, and Jesus is contingent: the 2nd Person might not have been incarnated in Jesus of Nazareth. The triune God could exist without the the Incarnation of the 2nd Person, but the triune God could not exist without the 2nd Person.

"And the Wird became flesh and dwelt among us." That does not mean that Jesus became flesh and dwelt among us. A man does not need to become flesh, he already is, qua man.

By the way, I understand that some Muslims think the Trinity is God, Jesus, and Mary!

The rest of what you say shows that you understand neither the doctrine nor the logical problems that it gives rise to.

[HTB]

Bill,

I am neither a theologian nor a philosopher, and it is quite likely that I have missed some important subtleties. By my second sentence, I haven't meant to include explicitly or implicitly the doctrine of the incarnation. My use of "Jesus" wasn't to refer simply to the incarnated Christ, but rather to the second person of the trinity. I agree that Jesus did not take on flesh, but the Word did, and this peron of the trinity is now both God and Man for all eternity. Or, in other words, the second person of the trinity, as I understand it, is Jesus Christ. You can read my meaning to be the pre-incarnated Word if you would rather and I will speak accordingly.

This said, I still have the problem I mentioned above. I am not a theologian, but I do have some college level theology under my belt, and if I have made a mistake, I think it can be corrected without me wasting too much of your time. If, in another time, I might well have sat before the Dominicans for what I have said, I should like to know and correct it. Allow me to restate my point.

No serious theologian, so far as I can tell with what background in theology and philosophy I have, has ever said that the Word is God, that the Father is God, or that the Holy Spirit is God, and meant the "is" to state an identity. The reason for this is because they are not identical. God is a trinity, the Word is not, an neither are the Father or the Spirit. They are members of the trinity, but not the trinity. God=the Father, the Son, and the Holy Spirit, but the Word does not equal the Father, the Son, and the Holy Spirit. Thus, they cannot be identical.

It would seem problematic to me if the doctrine were that 1. God=the three persons of the trinity, 2. each one of the persons=God in this same sense of the word, and 3. The three persons of the trinity are non-identical. But I do not think this is the doctrine. Your argument, it seems to me, presupposes that each person must be identical to God (in this case, meaning that one person of the trinity is identical to the trinity), or that there are a plurality of Gods.

This is the dichotomy you present. But, is it not also the dichotomy rejected by the doctrine? Does the doctrine not claim both a plurality and a singularity, though in different respects? That there can be three persons united in a single God, but also that none of these persons is identical with the others, or the Trinity?

[Account Deleted]

Reply to Bill,

(a) Consider the following two pairs of propositions:

1) John acted Presidential in this debate.
1)* John is the President.
2) John is a short basketball player.
2)* John is short.

In each of the two pairs of propositions above, the (*) proposition does not follow from the corresponding premise. In the case of (1)-(1)*, the reason is that the term ‘presidential’ means roughly ‘acting with the dignity and manner expected from the occupier of the President’s office’ which does not entail that whoever acts in this manner actually occupies the office. We can make this more explicit by saying instead of (1): John’s manner of debating was President-like. Here the phrase ‘like’ modifies the term ‘president’ to form a predicate that is not equivalent in meaning to the term so modified, although it is systematically related to it. Let us call any predicate such as ‘presidential’ that can be converted into a modified predicate that involves the modifier ‘like’ in the manner just described a *kinship-predicate*. Kinship-predicates express properties that are related in a systematic way to the properties expressed by their kin predicates, but they are not equivalent to them.

In the case of (2)-(2)*, the term ‘short’ modifies ‘basketball player’ and, therefore, cannot be detached as a stand-alone predicate such as in (2)*. In each of the above cases we have phrases that include modifiers, implicitly as in (1) and explicitly as in (2), which prevents us from drawing inferences in which the modified predicate stands alone.

(b) Keeping these points in mind, let us examine your two objections. I concede Bill's first objection: since God is an individual, one cannot strictly speaking say that x exemplified God. So let us instead say that x exemplifies Godhood. We shall consider the predicate ‘Godhood’ as the archetype predicate expressing the property of Godhood: i.e., any predicate that properly expresses the property Godhood must be equivalent in meaning to the predicate ‘Godhood’.

Bill's second objection is this:

“But, clearly, if x exemplifies deity, then x is a god just as, if you exemplify humanity (the property of being human), then you are a man.” So the full force of your argument relies upon the assumption that the predicate ‘divinity’ acts in the present context as an independent, unmodified, stand-alone predicate equivalent in meaning to ‘Godhood’. Thus, if the Son exemplifies divinity, then the Son is divine; namely, exemplifies Godhood. The same goes for the Father and the Holy Spirit and, thus, we have the dreaded tritheism.

(c) Given the above discussion, it should be fairly obvious how I am going to respond to Bill’s second objection. I deny the conditional Bill assumes: i.e., “if x exemplifies deity, then x is a god” because the mere use of the term ‘deity’, ‘divinity’ or ‘divine’ does not mean that it is used as equivalent in meaning to the predicate ‘Godhood’. We are not warranted to conclude in general that x is god from the proposition ‘x is divine’ or ‘x exemplifies divinity or deity’ unless we are assured that the terms ‘divine’, ‘divinity’ or ‘deity’ in these contexts are not used as kinship-predicates or even in some other non-literal or metaphorical way.

(d) Thus, in order to counter Bill’s objection I propose to think of the term ‘divine’ in the context ‘x is divine’ as a kinship-predicate; where ‘is’ is interpreted in the sense of predication or exemplification. We can make this explicit by rephrasing ‘x is divine’ into ‘x is divine-like’ or ‘x is a divine-like person’. Now, just like from the proposition that ‘John’s manner is president-like’ it does not follow that ‘John is the president’; similarly from the proposition ‘The son is divine-like’ it does not follow that ‘The Son is divine’. The same holds regarding the Father and the Holy Spirit. Construed as a kinship-predicate the use of ‘divine’ in all of these cases does not warrant the inference that all three are gods from the fact that they are divine. Hence, tritheism is avoided.

(e) At this point Bill might be already thinking to unleash the following objection. Consider:

(3) God is divine.

Surely, in (3) the term ‘divine’ is not a kinship-predicate or a modifier, for in this case we do really mean that ‘God’ exemplifies the property Godhood. Moreover, monotheism tells us that there is exactly one entity that exemplifies Godhood and that this is the entity to which we refer by the term ‘God’. So the following question arises:

How do we know in any given context ‘x is divine’ whether the term ‘divine’ is used to mean ‘x exemplifies Godhood’ or it is not so used, as in the case of kinship-predicates or modifiers?

(f) Consider this:

(4) This chicken soup is divine.

Clearly we do not use the term ‘divine’ in (4) to mean that this soup exemplifies Godhood. In (4) the term ‘divine’ is used metaphorically. How do we know that? Well, we know that from the context; i.e., we infer that the use of ‘divine’ in (4) is used metaphorically from the nature of the entity to which the term ‘divine’ is attributed in this context. We simply cannot literally mean that this chicken soup exemplifies the property Godhood because soups are not the sort of entities that can possibly exemplify this property. Therefore, the question of whether the term ‘divine’ is used in any given context ‘x is divine’ metaphorically or literally is determined by examining the sort of entity for which ‘x’ stands in a given context. The same goes for the question of whether the term ‘divine’ is used in any given context ‘x is divine’ as a kinship-predicate or as equivalent in meaning to ‘Godhood’: we examining the nature of the entity to which the term is attribute in that context.

(g) Thus, we know that the term ‘divine’ in

(5) The Son is divine.

is used as a kinship-predicate rather than as equivalent to ‘Godhood’ because the contrary assumption leads to a contradiction (the contrary assumption will be designated by a ‘*’):

(i) There is exactly one entity which instantiates the property of Godhood (Monotheism);
(ii) Everything that exemplifies the property of Godhood is a god;
(iii) God and the Son are not identical;
(iv) God exemplifies Godhood;
(v) God is a god;
(vi) If the term ‘divine’ in (5) is not used as a kinship-predicate; i.e., if we interpret it as being equivalent to the predicate ‘Godhood’, then it follows that the Son exemplifies the property of Godhood;
(vii)* The term ‘divine’ is not used in (5) as a kinship-predicate;
(viii) If the Son exemplifies the property of Godhood, then the Son is God;
(ix) The Son exemplifies the property of Godhood;
(x) The son is a god.
Therefore,
(xi) There are at least two gods.

Similar arguments can be devised regarding the Father and the Holy Spirit and their combined force leads to denial of monotheism. The culprit in the above argument, I maintain, is (vii)*, which proclaims that the term ‘divine’ is not used in (5) as a kinship-predicate. Once we exclude this assumption no contradiction is forthcoming.

(h) The only remaining question is this: what content does the predicate ‘divine’ has when it is used as a kinship-predicate in a contexts such as ‘The Son is divine’, ‘The Father is divine’, or ‘The Holy Spirit is divine’? Since this is no longer a logical or quasi-logical question, I shall defer this question to scholars of theology who know much more than me about how to answer it.

[Account Deleted]

Addendum,

The problem of the Trinity cannot be solved by logical form alone. It will not do simply to reinterpret the ‘is’ in the relevant contexts not as the ‘is’ of identity but rather as the ‘is’ of instantiation or as composition or in some other manner. A solution will require the combination of at least three levels: logical form, semantics/pragmatics, and theological considerations.

In my original post I made the mistake of offering a solution based merely on logical form: I proposed to interpret the ‘is’ in the relevant contexts as the ‘is’ of instantiation. This made the proposal vulnerable to Bill’s subsequent objections. Bill’s objections forced me to recognize that logical form alone will not do. In the last post I have supplemented the original proposal based upon logical form with semantic/pragmatic considerations.

Now even if the logical form proposal together with the semantic/pragmatic considerations together offer a reasonable line of defense of the Trinity, they are still not enough. They need to be supplemented with theological considerations along the lines indicated in (h) in my last post. It is this last component that will determine whether a proposal along the lines I suggested is viable.

[HTB]

Bill,

I said in my first post that I thought the issue lay more with "God" than "is". I think, perhaps, I should have said that my issue lay more with "God" than "is". I have been using more or less equating God with the trinity, and so have felt that to use an "is" of identity is to deny the distinctness of persons. From what I understand of historical orthodoxy, this would be a mistake, as a distinction is made between the persons and the being of God. The trinity of persons are distinct in their relations to each other, but are not ontologically distinct, and I thought your dichotomy rested on the assumption that this cannot be. However, I think I might have mistaken your use of "God", or missed something along the way.

As I said, I am out of my league. Thanks to both you and Peter for the educational discussion. I hope my commentary hasn't been entirely without value, and if you wouldn't mind correcting my confusion, I would appreciate it.

[Bill Vallicella]

Peter,

I am having a hard time understanding what you are driving at. You write, "I deny the conditional Bill assumes: i.e., “if x exemplifies deity, then x is a god” because the mere use of the term ‘deity’, ‘divinity’ or ‘divine’ does not mean that it is used as equivalent in meaning to the predicate ‘Godhood’. This makes no sense because 'divine' is an adjective whereas 'Godhood' is a noun.

If the Father is divine, then the Father exemplifies divinity (assuming we are not nominalists). Divinity is the property of being a god. So if the Father is divine, then the Father is a god. The same goes for the other two persons, and tritheism results.

Now can you explain in no more than five sentences why you disagree with that?

[Account Deleted]

Bill,

According to you then, the following holds:

1) This soup is divine.
Therefore,
2) This soup is a god.

If it does not, then why not?

[Bill Vallicella]

Peter,

(2) follows from (1) in the presence of the auxiliary premise 'Every divine substance is a god.'

I hope you realize that at this stage of the discussion we are taking identity to be absolute, not sortal-relative.

HTB,

Here is a very clear paper that will help you understand the problem. A. P. Martinich, "Identity and Trinity," The Journal of Religion, April 1978.

[Account Deleted]

Bill,

But surely "Every divine substance is a god" is false if it certifies the inference from (1) to (2), because (2) is false. Identity, relative or absolute, is not involved in either proposition (1) or (2): in both cases the 'is' is that of instantiation.

[HTB]

Bill,

I'm sorry to keep interrupting, but I really would like a response to one of my initial questions. I looked up some points of the debate, and while I have been made aware of issues I had neglected, I am convinced that I was far afield in my response. Since it seems Peter and I are challenging the same intuition (though differently) I would like to restate my question again. Here it is in a nutshell.

You said:
"Divinity is the property of being a god. So if the Father is divine, then the Father is a god. The same goes for the other two persons, and tritheism results."

This is precisely the intuition I tried to challenge. You seem to be saying something like the following:

1. Any person exemplifying divinity is a god.
2. The Father exemplifies divinity, therefore, the Father is a god.
3. The Word exemplifies divinity, therefore, the Word is a god.
4. The Spirit exemplified divinity, therefore, the Spirit is a god.
5. Therefore, there are three gods: the Father, the Word, and the Spirit (if it is given that these are three distinct persons).

Now, I do not see how this follows. It does indeed follow from being divine that the person is a god, but does it follow that it is A god? Here's where your position begs the question, it is simply a denial that one can divide the person without dividing the substance. Your use of "a" in "a god" smuggles in the whole notion of ontological distinction. In smuggles in the notion of one ontologically distinct individual among many. The problem, as I see it, is with the first premise. It seems to assume that personhood is a complete ontological distinction. Thus the "a" in "a god". A person=a god. 3 persons=3 gods. And so on.

This is further demonstrated in your last post to Peter where you posit the auxiliary premise, "Every divine substance is a god". Yes, but the doctrine of the trinity does not divide the substance, only the persons.

So, if the doctrine of the trinity is correct, then one can divide the persons without dividing the substance. All three of the persons, though relationally distinct, are only one being. They can only be said to be multiple gods if they are divided in substance, and the only way I have seen you do this is by inferring it from the attribution of divinity to a person. In other words, a divine person is a God. Three divine persons are three gods.

However, I do not see how an attribution of divinity entails ontological distinction, nor do I see how this takes the claims of the doctrine seriously.

As I said, I'm sorry to keep interrupting, and I am perfectly willing to be corrected on this issue, but I do not think I have strayed from orthodoxy and the question seems valid to me. Thank you for the paper references, I will read it ASAP, and I apologize I am asking questions that could have been answered by reading it first.

[Account Deleted]

HTB,

Bill's point is that

(i) if there are three distinct entities, x, y, and z; &

(ii) if 'x is divine' and 'y is divine' and 'z is divine'; &

(iii) if each occurrence of the predicate 'divine' in a context '...is divine' entails that '...is a god',

(iv) then it follows that 'x is a god', 'y is a god' and 'z is a god'.

I am not sure which premise you are denying. Also I am not sure what distinction you are drawing with a capital 'A' vs. a small 'a'?

My own objection denies (iii) because I maintain that there are occurrences of divine in contexts such as 'such-and-such is divine' which cannot entail the conclusion that 'such and such is god': e.g., this soup is divine.

You say: "All three of the persons, though relationally distinct, are only one being." What do you mean by the phrase 'relationally distinct'? Are you using here a relative identity notion: i.e., relative to being a substance x, y, and z are the same: relative to being persons, x, y, and z are distinct. If so, then we have addressed this proposal earlier and you should counter the arguments made there against the relative identity proposal.

[Bill Vallicella]

Peter writes, "But surely "Every divine substance is a god" is false if it certifies the inference from (1) to (2), because (2) is false. Identity, relative or absolute, is not involved in either proposition (1) or (2): in both cases the 'is' is that of instantiation."

No. (1) and (2) are both false. As you well know, a valid argument can have a false premise and false conclusion

[Bill Vallicella]

Peter,

Now I think you are joking. 'Divine' can be used in all sorts of loose ways. But so what?

HTB,

Here is the problem of the Trinity in a very simple form:

(T1) Each person of the Trinity is distinct from each of the others.

(T2) Each person of the Trinity is God.

(T3) There is exactly one God.

These three theses appear to imply that three distinct beings are each identical with one being, which is logically impossible.

To solve the problem one has to explain how (T1)-(T3) can all be true but without abandoning the orthodox doctrine and falling into a heresy.

Several solutions have been attempted. My present point is only this: the problem cannot be solved by interpreting the 'is' in (T2) as the 'is' of predication.

[Account Deleted]

Bill,

Do you mean that if the term 'divine' in (1)--'This soup is divine'-- is used literally, then (1) is false? I agree. But my point is that the reason we judge it false is precisely because soup is not the sort of thing that can be divine in the sense of exemplifying Godhood. Therefore, 'divine' in the context of (1) must be used metaphorically.

So my point is that we judge whether a given use of 'divine' in the context of '...is divine' is used literally or metaphorically by its context: i.e., the kind of entity that replaces '...'.

I suggest that we use the same policy regarding 'The Son is divine'. Since we know that the Son cannot exemplify Godhood, since the Son is not identical to the one and only one God that exists, we should think of the term 'divine' in this context not as expressing the property of Godhood, but some other property. I call such a use a kinship-predicate. If the term 'divine' is used in this context as a kinship-predicate, then it does not follow from 'The Son is divine' that 'The Son is a god'.

Or to put the same point differently: since the inference from "The Son is divine" yields the falsehood 'The Son is a god', it follows that 'The Son is divine' is false when the term 'divine' is interpreted literally: i.e., as expressing the property Godhood. Therefore, we must interpret the term 'divine' in this context differently, just like in the soup-example.

[HTB]

Peter,

Thank you for the clarification. In your summary of the argument, I would contest iii. Also, I used the capital 'A' rather than the lower case because I knew no other way to emphasize it. The problem for me, is that "if x is divine, then x is a god" seems to conflate personhood and being, and as I underdstand it, orthodox theology has always maintained a distinction here. Let's say that x is the person of the Son, y the person of the Father, and z the person of the Spirit.

So far there is no problem, but then the inference is made that a divine person is a god. It seems here that Bill is taking a person to be a singular distinct being. Thus, the inference is made that if x is a god, y is a god, and z is a god, then there are three gods. That quantity of persons translates into quantity of beings. However, as I said, I think the orthodox perspective denies this and holds that the trinity is a plurality of persons in a unified being. That quantity of persons does not necessarily translate into equal quantity of beings. Thus, if there are three divine persons, and divinity entails godhood, it still would not follow that there are three gods. It could be that there are three divine persons in one God. What I have argued against is the inference from "x is divine" to the conclusion that x is ontologically distinct from y and z, and an ontological distinction seems to be what Bill has in mind when he says "a god".

About relational distinction, I'm afraid I may lack the ability give what I mean a title. The way I understand the orthodox position is this, the Son is relationally distinct from the Father in that he is a person standing in a certain relation to the Father; that of being begotten. The Spirit, likewise, stands in a certain relational position to the Father and (depending on whether one follows the Western or the Eastern view)the Son; that of proceeding from the Father or the Father and the Son. Thus, they cannot be identified with each other. The Catechism of the Catholic Church states this:

"254...They are distinct from one another in their relations of origin: "It is the Father who generates, the Son who is begotten, and the Holy Spirit who proceeds."88 The divine Unity is Triune.

255 The divine persons are relative to one another. Because it does not divide the divine unity, the real distinction of the persons from one another resides solely in the relationships which relate them to one another: "In the relational names of the persons the Father is related to the Son, the Son to the Father, and the Holy Spirit to both. While they are called three persons in view of their relations, we believe in one nature or substance."

I take it from your response that I missed arguments against this stance. Were they in this thread? I missed them and would be happy to give them a look.

[Account Deleted]

HTB,

If you deny the inference from 'The Son is a divine person' to 'The son is a god' on the grounds that you deny something like

--Everything that is a divine person is a god;

then you will have to also deny the inference from 'God is a divine person'; therefore, 'God is a god'. (the term 'God' here is a name). But surely the later inference is sound. So a solution that meets Bill's objection must show why the later inference holds whereas the former does not.

Relative identity as a solution is mentioned in my original post in this thread and bill also discusses it briefly in his response and I believe at least on one other occasion. Read through this thread and you will find it.

Now, the next issue is the crux of the matter. Please pay attention. You say:

"...if x is a god, y is a god, and z is a god, then there are three gods. That quantity of persons translates into quantity of beings. I think the orthodox perspective denies this and holds that the trinity is a plurality of persons in a unified being."

Bill and others who worry about the doctrine of the Trinity *know* that orthodoxy holds roughly what you said above. But merely holding something and saying it does not make it coherent. I can say the following to you: "I have a friend who is his own father" or that "John is taller than Mary and Mary is taller than Ron and Ron is taller than John." These sentences are perfectly grammatical in English and in some sense they even have a meaning. But surely there is something wrong with them. There is a sense in which neither *could* be true, even though they are meaningful.

The same goes regarding the doctrine of the Trinity and your statement of it. In order to ascertain that this doctrine *could* be true, some philosophical analysis must be performed. Why? Because on the face of it: if x, y, and z are distinct individuals, then if x is (absolutely) identical to w, then y and z *must be* (absolutely) distinct from w. This is simply a logical principle governing the notion of (absolute) identity and difference.

So it appears that this is the problem that the doctrine of the Trinity faces. On the face of it, the doctrine says that the Father, the Son, and the Holy Spirit are distinct individuals; It also says that each of the three is identical to God. But if so, then the three are both distinct as well as identical to each other. And this violates the logical principle of identity. This is the paradox as it initially presents itself to us.

So there is a problem. You maintain that the orthodoxy contains a solution. What is it? Well, you say that the three are distinct with respect to being persons, but unified with respect to *being*. But this raises the following question: what it is for x and y to be identical with respect to being and distinct with respect to person? For instance, you and I are distinct persons. Nevertheless, we can say that while you and I are distinct persons, we both have being (roughly, we both exist). But, then, all that this solution means is that even though the Father, Son, and Holy Spirit are distinct individuals, they all exist. Surely, this is NOT what the Trinity means.

Therefore, it is not obvious what the notion of "being united in being" means and whether what it means is coherent. It is the burden of those who adhere to the orthodoxy to give an account of this phrase that is not just grammatically correct and is meaningful in some sense, but also that its meaning is such that we can discern how the doctrine of the Trinity is made possible. And this must be done without violating obvious logical principles.

[Bill Vallicella]

Gentlemen,

I can see that there is no point in discussing this further until both of you understand both the doctrine of the Trinity and the logical problems that it gives rise to. So I suggest you study very carefully the excellent article by Richard Cartwright, "On the Logical Problem of the Trinity." http://eyring.hplx.net/Eyring/Notes/trinity.html

[Bill Vallicella]

And please note that a solution must remain within the bounds of orthodoxy. One must show the consistency of the doctrien without falling into Arianism or Sabellianism or Patripassionism, etc.

I note that the Cartwright article has some scanning errors in it.

[Bill Vallicella]

HTB,

I fully endorse what Peter said is his last response to you, in particular, this part:

>>Bill and others who worry about the doctrine of the Trinity *know* that orthodoxy holds roughly what you said above. But merely holding something and saying it does not make it coherent. I can say the following to you: "I have a friend who is his own father" or that "John is taller than Mary and Mary is taller than Ron and Ron is taller than John." These sentences are perfectly grammatical in English and in some sense they even have a meaning. But surely there is something wrong with them. There is a sense in which neither *could* be true, even though they are meaningful.<<

We who question the logical coherence of the Trinity doctrine know the verbal formulas, the creedal statements. Therefore, merely repeating the formulas doesn't solve the problem. Thus it does no good to say, "There is one God in three divine persons."

[Account Deleted]

Bill,

just read the Cartwright article, without the errors (I have his collected works). Indeed, very good. I think I agree with what he says there (particularly regarding Geach's relative identity solution). we will talk more tomorrow.

[Bill Vallicella]

Peter,

There is a response to you in the last murder and souls thread. He is a guy who teaches philosophy in a California college.

[ocham]

I turn my head for an instant and then this thread pops up.

It's some time since I looked at Cartwright's excellent paper. Agree that everyone should read this first - I will have a look again.

In the meantime:

1. Jane is reading 'Lord of the Rings'
2. John is reading 'Lord of the Rings'
3. Jack is reading 'Lord of the Rings'
4. They are reading different copies of the book
5. They are reading the same book.
6. Three copies, one book.

This does not address the problem of the inconsistent statements that Bill highlights above. However, it would have to be shown that that Bill's statements are consistent with the theology, and that depends what the theology is. This is where Cartwright's paper comes in (he looks at one of the creeds - the Athanasian, no?).

The problem is that the unproblematic

(*) Each copy is a copy of the same book

is not of the same form as the problematic

(**) Each person is God

[ocham]

(Update) I have read Cartwright again. Here are his seven difficult propositions expressed in a different way, but with identical 'logical form'.

(1) My copy is "Lord of the Rings"
(2) Your copy is "Lord of the Rings"
(3) Her copy is "Lord of the Rings"
(4) My copy is not your copy
(5) My copy is not his copy
(6) Your copy is not his copy
(7) The "Lord of the Rings" is one book

These all seems consistent to me. (Substitute 'my copy' for 'the Father', 'your copy' for 'the Son', 'his copy' for 'the Holy Ghost' and ' "The Lord of the Rings" ' (note the double set of quotes on the final expression) for 'God'

[Bill Vallicella]

Ocham,

Now that is a very stimulating and helpful comment. But first, with respect to the first of your two comments, I want to draw your attention to a distinction Cartwright makes between the doctrine of the Trinity and the theology of the Trinity. We find the doctrine in the Athanasian creed and in other documents. But the theology, strictly and narrowly speaking, of the Trinity is what we find in, say, Geach when he explains the logic of the doctrine and how it could be true. (That it is true, I take it, is a matter of revelation, and the theologian takes revelation as given, as his data the way a philosopher of science takes scientific theories and practices as his data.) Contra what you seem to be suggesting, the theology is not the doctrine, but the attempt to get at the logic of the doctrine, and though it, to the logic of God. Theology is not just talk about God but the logic of talk about God. (I borrow the last point from A. P. Martinich.)

[Bill Vallicella]

Ocham,

It seems you are proposing a model whereby we can see that the Trinity doctrine is consistent. Now although the seven statements making up your model are consistent (can all be true), I rather doubt that the model actually models the Trinity. Note that the 'is' in the first three starements is not the 'is' of identity, but instead expresses what 'is entitled' expresses. To give it a bad name we could call it the 'is' of entitlement. But the 'is' in the second three statements is the 'is' of identity. In the Trinity doctrine, however, the 'is' of the first six statements is the 'is' of identity.

[Bill Vallicella]

Ocham,

To elaborate. There is a book entitled "The Lord of the Rings" of which there are many copies. Any three copies are numerically distinct among themselves. But the relation of the book to one of its copies is not the relation of God to one of his Persons. The book is not identical to any of its copies. But God is identical to each of his Persons. The book-copy relation is a type-token relation; but the God-Person relation is not type-token but something else. If it is standard absolute identity, then incoherence is the upshot. And that's the problem.

[HTB]

A final comment.

I was leaving this discussion since my point was not being understood and I had no further desire to clarify it, or, for that matter, confidence in myself that I could. However, Bill's latest post on the trinity (which has closed comments) strikes me as doing some disservice. I assume that part of what provoked Bill's criticisms there were the contributions of myself and Mr. Sullivan. Afterall, Mr. Sullivan's point and mine were much the same, though mine lacked the terminology. Furthermore, Peter's response to me (which was seconded by Bill) also closely resembles Bill's response to Mr. Sullivan and Bill's criticisms in the later post. If my own comments played any part in Bill's impression that verbal formulas were merely being repeated, then I should like to respond to Peter's implication that this was so in my own case, and thus, indirectly to Bill's accusations of the same.

First, a few misunderstandings. I was not using "being" in the sense of existence, but more in the sense of existent. I was refering to an ontologically distinct entity, an existent thing identical with itself and distinct from everything else. I take this to be something like what we mean by a human being. We do not mean human existence, but a distinct existent which happens to be human.

Now, the thrust of my point wasn't simply to repeat verbal formulas, though this seems to be all the meaning I could convey. Rather, my point was to say that there is a distinction made by the doctrine and the theology of the trinity which Bill has effectively missed. The verbal formula that the trinity consists of three distinct persons in one being, if taken seriously, entails that persons are not necessarilly ontologically distinct. That is, it entails that quantity of persons does not necessarilly translate into an equal quantity of beings.

However, Bill ignores this distinction in his dichotomy, wherein he states that 1. There are three divine persons, entails 2. There are three gods. This inference presupposes that persons are ontologically distinct, and therefore, that the quantity of divine persons equals the quantity of divine beings. This, it seems to me, begs the question. It is to assume the falsity of a central component of the doctrine in order to proceed in proving the doctrine false.

Thus, I asked Bill to support this inference. Was my commentary unhelpful? Perhaps so. Have I mistakenly accused him? Perhaps, though no one bothered to show me my mistake. Was I merely repeating a verbal formula, or providing novice solutions to the problem (such as that the three persons are distinct as persons but all equally exist)? I think it clear that I was not. Neither can I determine how such mistakes were made aside from rather uncharitible presumptions concerning my competence. I do not think Mr. Sullivan's replies were so hollow as this either. And this leaves me with a question. Who, might I ask, was Bill referring to then?

[aresh v.]

Peter,

According to your strategy, It would be much easier to interpret the 3 Persons as properties of God
instead of considering God as a property of the 3 Persons.
That approach would lead us to the following translations:
1) God is the Father -> the individual God exemplifies the property of "being the unbegotten Father"
2) God is the Son -> the individual God exemplifies the property of "being the begotten Son"
3) God is the Holy Spirit -> the individual God exemplifies the property of "being the proceeding Holy Spirit"
4) the Father is not the Son -> the property of "being the unbegotten Father" is not the same as the property of "being the begotten Son";
5) the Son is not the Holy Spirit -> the property of "being the begotten Son" is not the same as the property of "being the proceeding Holy Spirit";
6) the Holy Spirit is not the Father -> the property of "being the proceeding Holy Spirit" is not the same as the property of "being the unbegotten Father";
7) There is only one God -> there is only one individual that is God
This claim would be coherent but, if I'm not mistaken, unorthodox precisely because by applying the notion of "Person" one has to refer to individuals and not to properties. If that is the case, then Bill's objections are still compelling