The Logic of the Trinity Revisited

Our question concerns the logical consistency of the following septad, each limb of which seems entailed by the dogma of the Trinity as set forth in the Catechism of the Catholic Church.  How can the following propositions all be true?  My concern is whether the dogma in its Roman Catholic form can be expressed in such a way as to satisfy the exigencies of the discursive intellect.  The prime exigency or requirement is that it not violate the Law of Non-Contradiction. The question is not whether the dogma can be known to be true by reason unaided by revelation; it can't. The question is whether the dogma can be rendered rationally acceptable to intellects of our sort.  Can it be expressed in such a way as to make logical sense to us?

1) There is only one God.
2) The Father is God.
3) The Son is God.
4) The Holy Spirit is God.
5) The Father is not the Son.
6) The Son is not the Holy Spirit.
7) The Father is not the Holy Spirit.

If we assume that in (2)-(7), the 'is' expresses absolute numerical identity, then it is clear that the septad is inconsistent.  (Identity has the following properties: it is reflexive, symmetric, transitive, and governed by the Indiscernibility of Identicals).  For example, from (2) and (3) taken together it follows that the Father is the Son by Transitivity of Identity.  But this contradicts (5).

To spell it out: if the Father is God, and the Son is God, and these are identity statements, and identity is symmetric and transitive, then the Father is the Son, which contradicts (5).

So what we have above is an inconsistent septad each limb of which appears to be a commitment of orthodoxy.  The task is to remove the contradiction without abandoning orthodoxy.  There are different ways to proceed.

One way is to invoke the standard distinction between the 'is' of identity and the 'is' of predication, and construe (2), (3), and (4) as predications rather than as statements of identity.  Well, suppose we do this.  We get:

1)There is only one God.
2*) The Father is divine.
3*) The Son is divine.
4*) The Holy Spirit is divine.
5) The Father is not the Son.
6) The Son is not the Holy Spirit.
7) The Father is not the Holy Spirit.

But this implies that there are three Gods, which contradicts (1).  The trick is to retain real distinctness of Persons while avoiding tritheism.

Matthew Kirby in correspondence suggests the following:

1K) There is only one Divine Nature.
2K) The Father hypostasises the fullness of that Divine Nature (as Source/Lover).
3K) The Son hypostasises the fullness of that Divine Nature (as Logos/Form/Image/Beloved).
4K) The Holy Ghost hypostasises the fullness of that Divine Nature (as Spirit/Gift/Loving).
5K) The Father is not the Son, but gives him fully his essence.
6K) The Son is not the Holy Spirit, but shares with him fully the very same essence.
7K) The Father is not the Holy Spirit, but gives him fully his essence.

Unfortunately, Fr. Kirby does not explain what he means by 'hypostasises,' but I think I know what he means. He means that the Father, the Son, and the Holy Ghost are each subjects of the divine nature.  One nature, three hypostases/persons.  Compare the Incarnation: One hypostasis, two natures. Thus the Son has two natures, one human, the other divine. In the Trinity, however, we have one divine nature in three divine persons.

Well, are we in the clear now?  I can't see that we are. For Fr. Kirby's septad is just a variation on the second one we examined. If the Father, Son, and Holy Ghost are each subjects of the divine nature, then we have three Gods, when the dogma clearly implies that there is exactly one God in three divine persons.

Comments

[Fr Matthew Kirby]

One of the problems with I see with my septad is that I used essence and nature as synonyms, sliding from one to the other, and thus obscuring the logical structure. However, this does not address your point.

In my correspondence I noted that the first proposition had correct and incorrect interpretive versions. "There is only one divine person" was one of the incorrect ones. Thus God's unity in Trinitarianism does not refer to singularity of personal subject.

You say that if each Person is a distinct divine subject of the divine nature/essence, there are three Gods. But the assumption only proves there are 3 divine personal subjects in itself, which Trinitarians admit. It only further implies 3 Gods if we make another assumption, that is:

In the case of Divinity, to say multiple persons share the same essence means the same thing it would among hypothesized identical created, material persons. That is, it is used improperly to express the fact that there are really 3 cases of essence-made-concrete, the unity of essence referring purely to exact similarities intelligible by abstraction only. In other words, the threeness is concrete, the oneness is abstract. 2 of the persons may be exact copies of the other, such that the one abstract Form is particlarised in 3 separate real entities, but that is exactly parallel to separate matter individuating form among us.

But that assumption is not only not accepted, it is denied at a radical level in Christian theism. For a start, God transcends the distinction between abstract and concrete, and there is nothing for or in him parallel to actualization by matter. More to the point, the unity of essence between the 3 divine persons is not conceived as abstract and due to copying but as substantial and due to procession and co-inherence.

[Lukáš Novák]

Bill,

I say that your

But this implies that there are three Gods, which contradicts (1).

is a non sequitur.

In order to validly infer that, you would need a premise stating something to the effect that the non-identity of the persons ((5),(6),(7))implies non-identity of the shared essence. Which is not universally true because it is not the case in God, where the divine essence is not multiplied in the persons as though it were a universal but remains one and individual. There is simply no logical law requiring the number of natures to match the number of subjects. It is an ontological fact about finite beings, but even there it might be difficult to prove, as the persistence of ultrarealism about universals in the history of philosophy witnesses.

(Do you consider Platonism about universals evidently inconsistent? I suppose not. Then think of divine nature as though it were a Platonic (but inherent) universal (which, according to the Aristotelians, would not be a true universal precisely because not multiplied in its instances). It is a very good approximation of what is meant.)

Or maybe by "there are three Gods" you just mean "there are three subjects/persons each of which is God" which is true and not in conflict with the dogmatically intended meaning of (1), which is: there is just one individual divine nature.

(Well: now I see that most of what I have written coincides with Fr Kirby's reply...)

[BV]

Lukas,

Greetings, and thanks for the comments. They are penetrating as usual.

Me, you, and Matthew are human. We are three numerically distinct persons/subjects, but we share human nature. It follows that we are not only three different subjects, but three different men. If you said that we are three subjects but one man, that would make no sense.

You say it is different with God. The divine nature is like a Platonic universal which is inherent in the divine persons but is not multiplied in them. So while there is one divine nature in the three persons there is only one God.

No doubt this is what the dogma affirms. The precise question, however, is whether it makes sense to the discursive intellect. I say it makes as little sense as the claim that me, you, and Matthew are three subjects but one man.

I am claiming that the dogma is unintelligible to us, not that it is false or that it is contradictory in itself. Nor am I claiming that there is no reality toward which it 'points.' One could take it as a Christian koan, a form of words meditation on which might trigger a glimpse into a reality lying beyond the discursive intellect.

Or one might take a mysterian line with respect to the dogma.

And isn't it traditionally called a mystery? What do old-time Catholic theologians mean by 'mystery'?

[Fr Matthew Kirby]

Dr Vallicella,

I think we should distinguish between what is unimaginable and what is inconceivable. This is a traditional distinction, nicely discussed, from memory, in R. Machuga's In defense of the soul. He uses the old example of the chiliagon, I think. However, in this example, I suspect that it might even be possible for a human mind of sufficient genius in the area of geometric mental imagery (or an alien with such capabilities) to actually form a true mental image of a 1000-sided polygon. But, beyond this, there are, I would argue, examples of unimaginability which involve qualitative rather than quantitative insufficiency of human mental power, so to speak.

It is not possible for us to imagine fully how one Divine substance/essence can have three personal subsistences, since all attempted analogies will be drawn from a created realm of composited or divided realities. Thus the division of abstract and concrete therein means that a nature/essence can only be "common" to different particular subsistences abstractly. The composition of form and matter therein, along with distinctions such as that between substance and accident, means that differences between individual human persons necessitate both imperfect commonality of form and actualisations of form that must be individuated by separation of matter, thus differentiating those person's substances in 2 ways. So, any such analogy falls short and cannot illustrate both unity of substance and distinction of person adequately.

Other analogies would fail in the other direction, by using a real substantial unity from creation which has a merely abstract or conceptual distinction of subsistences (that each depend on that whole substance) within it, for example, the classic Augustinian example of self-knowledge in the aspects of memory, understanding and will. Indeed, any "3 aspects of one thing" approach risks collapsing into modalism because within Creation the different aspects are either purely conceptual, or purely externally relational because they have the subjective aspect existing outside the one object considered.

Nevertheless, knowledge of divine simplicity (which is also not "imaginable") can logically show us precisely where the analogies fail and why, and logical analysis can also show that there is no formal contradiction, once the necessary qualifications are made.

Therefore, while the doctrine is conceivable, it is not imaginable, and Thomist epistemology and anthropology show us why. The mystery you mention lies, then, not in logical inconceivability or unintelligibility, but in unimaginability and the failure of all analogies due to the need for all such mental "pictures" to rely on that which is, unlike God, ontologically complex.

[BV]

Fr. Kirby,

I have used the chiliagon example many times. It comes from Descartes. I use it to show that the conceivable and the imaginable are not the same. I can easily conceive of a chiliagon, but I cannot come close to imagining such a polygon.

But what does this have to do with the Trinity? We are trying to conceive it, not imagine it. I define conceivability as follows:

X is conceivable =df x is thinkable without formal-logical contradiction.

I grant that what is inconceivable by us might nonetheless be really possible in itself. Just as conceivability does not entail possibility, inconceivabilty does not entail impossibility.

Before proceeding, please tell me how imaginability comes into this at all.

[Vlastimil]

Bill,

On various theological senses of 'mystery', see my diss., fn. 190 on pp. 79-80. http://www.kfil.upol.cz/doc/pgs/vohanka/Disertacni_prace.pdf?lang=en

I rewrote that diss. for my book on the epistemology of the Trinitarian belief. Lukáš had disliked the diss. initially, but then I placated him and he helped me to publish it. The main thesis was a bit skeptical, but not as much as your position: roughly, philosophy cannot _prove_ the Trinity doctrine to be conceptually possible (I say 'logically possible' in the diss.), even if philosophy can render the doctrine intelligible, and even reasonable.

[Vlastimil]

By the way, I cite you and Lukáš a lot, both in the diss. and in the book.

[Fr Matthew Kirby]

Dr Vallicella,

Sorry for the delayed reply. While I thought you would know about the example of the chiliagon, I have not been following your blog closely for long and did not realise you had used the same example, and thought it best not to assume anything but argue my case as fully as reasonably possible. I apologize if it seemed I was trying to teach my grandmother to suck eggs!

The reason I think the issue of conceivability vs imaginability is relevant is this. When Dr Novak and I pointed out that multiple hypostases do not logically necessitate multiple actualised essences, undermining the claim of formal contradiction in the qualified septads, you did not respond with a formal argument based on the definition of the terms. Instead, you appealed to an analogy based on material created entities. Once you did this, I believe an admixture of different epistemomlogical criteria came in, criteria that, as I hope I showed above, are deficient when thinking about Absolute Being.

Basically, I do not see how you can posit the formal contradiction you identify within the qualified septads unless you assume certain extra intuitions which are wholly or mostly based on abstraction from experience of or mental pictures about finite physical entities. The mystery you are refrring to lies not in logical inconsistencies, it seems to me, but in the non-intuitive ontology, one which is never adequately "visualizable" in any one finite analogy.