0. Introduction. In “The Inconsistency of the Doctrine of (the Distinction of Divine Persons and so That of) the Trinity with Monotheism,” my post of April 4, 2014, I presented what I take to be a rigorous proof of, as its title says well enough, the inconsistency of the classical Christian doctrine of the Trinity with the equally classical Christian doctrine of monotheism. Since then, I have taken up the reading of Réginald Garrigou-Lagrange, O.P., Reality. A Synthesis of Thomistic Thought,* because, as I noted in my “Two Questions re Thomistic Metaphysics. A Plea for Their Answers” of June 4, 2014, I have begun a “process of preparing myself, and hardly for the first time, for an effort at coming to a determination of whether the arguments for the existence of God set forth by Thomas Aquinas in the Summa Theologiae are valid and sound, valid but unsound, or simply invalid.”

Unable, characteristically, to discipline myself and keep to my intention of reading and rereading the earlier chapters of Reality as part of that process, I have allowed myself to delve into the book’s “Third Part: The Blessed Trinity” in a search for further light on the doctrine of the Trinity. I have found therein what could be taken as a reply to the proof mentioned just above. The primary aim of the present post is then to examine that reply.

1. Before, however, turning to that examination, I want to briefly take note of a wonderfully concise statement by Garrigou-Lagrange, in Ch. 16, “The Divine Persons,” in Reality’s “Third Part: The Blessed Trinity,” of the conjunction of the thesis of the identity of the divine persons with God with that of the distinction of the persons from each other. It reads (p. 124):

[W]hile we say: The Father is God, the Son is God, the Holy Spirit is God, we also say: the Father is not the Son, and Holy Spirit is not the Father, and the Holy Spirit is not the Son. In this sentence the verb “is” expresses real identity between persons and nature and the negation “is not” expresses the real distinction of the persons from each other.

This conjunction, as “The Inconsistency of the Doctrine of (the Distinction of Divine Persons and so That of) the Trinity with Monotheism” makes evident, leads to absurdity.

2. Turning now to the primary purpose of this post and so to what Garrigou-Lagrange might take as an escape from that absurdity, we find Garrigou-Lagrange telling us in Ch. 15 of Reality, “The Divine Relations” (p. 122), that:

If there are real processions in God, then there must also be real relations. As in the order of nature, temporal generation founds two relations, of son to father and father to son, so likewise does the eternal generation of the Word found the two relations of paternity and filiation. And the procession of love also found [sic] two relations, active spiration and “passive” spiration.

Garrigou-Lagrange next states (Ibid.), again with admirable concision, the two theses, that of the distinction of the divine persons and that of monotheism the conjunction of which, again, is proven inconsistent in “The Inconsistency of the Doctrine of (the Distinction of Divine Persons and so That of) the Trinity with Monotheism.”

Those divine relations which are in mutual opposition are by this very opposition really distinct one from the other. The Father is not the Son, for nothing begets itself. And the Holy Spirit is not the Father nor the Son. Yet the Father is God, the Son is God, the Holy Spirit is God. Thus, by increasing precision, we reach the formula of the Council of Florence: In God everything is one, except where relations are opposite.

3. Garrigou-Lagrange now (Ibid.) provides, still with admirable concision, the obvious objection:

Here enters the saint’s [i.e., Aquinas’s] response to an objection often heard. The objection runs thus: Things which are really identified with one and the same thing are identified with one another. But the divine relations and the divine persons are really identified with the divine essence. Hence the divine relations and the divine persons are identified with one another.

The principle to which Garrigou-Lagrange has here given recognition is a variation on the principle known classically as that of “Triple Identity.” It is one to which Aquinas too has given recognition, in Book One, Lecture 3, Comment 22 of his Commentary on Aristotle’s Physics,** where he says:

[T]hings which are identical with the same thing are identical with each other.

It is also a principle which devotees of contemporary logic will recognize as a variation on the principle of the Transitivity of Identity, which variation can be stated as:

For any existent x, any existent y, and any existent z, if x is identical with z and y is identical with z, then x is identical with y.

or, more briefly:

(x)(y)(z)((Ixz & Iyz) –> Ixy)

4. Garrigou-Lagrange believes there is a solution at hand, saying (op. cit., p. 123):

The solution runs thus: Things which are really identified with one and the same third thing are identified with one another; yes, unless their mutual opposition is greater than their sameness with this third thing. Otherwise, I must say No. To illustrate. Look at the three angles of a triangle. Are they really distinct one from the other? Most certainly. Yet each of them is identified with one and the same surface.

This is, frankly, astonishing. First, the illustration: though it is true that the three angles of a triangle are really distinct one from the other, it is just false that each of them, indeed that any one of them, is identified with that surface.

The problem, however, runs deeper than the illustration. Let us examine the statement that:

Things which are really identified with one and the same third thing are identified with one another; yes, unless their mutual opposition is greater than their sameness with this third thing.

In the “Things which are really identified with one and the same third thing are identified with one another,” all is well and good: he there presents the variation at hand of the principle of triple identity as a thesis without restriction of scope, that is, as a universal affirmative proposition, even if it lacks an explicit expression of some version of the universal quantifier. But then, however, he removes from the scope of that thesis those purported things whose “mutual opposition is greater than their sameness with” a third thing.

Garrigou-Lagrange has then both affirmed the variation at hand of the principle of triple identity as a thesis without restriction of scope, that is, as a universal affirmative proposition, and then, contradicting himself, denied its universal applicability.

5. Yet Garrigou-Lagrange proceeds (Ibid.) to critique the solution given, he tells us, by Francisco Suarez to the difficulty raised for the Trinitarian thesis by the variation at hand of the principle of triple identity.

He solves it thus: The axiom that things identified with one third thing are identified with one another—this axiom, he says, is true in the created order only, but not universally, not when applied to God.

But, Garrigou-Lagrange goes on to say immediately (Ibid.)

Thomists reply. This axiom derives without medium from the principle of contradiction or identity, and hence, analogically indeed, but truly, holds good also in God, for it is a law of being as such, a law of all reality, a law absolutely universal, outside of which lies complete absurdity.

6. Thus, on the one hand, Garrigou-Lagrange affirms the axiom at hand in its full universality, and yet, when faced with the difficulties posed by Trinitarian doctrine, has to retract that affirmation. In its denial of the axiom’s full universality, his theory of identity does not differ from that of Suarez. I take this as confirmation, though none is really needed, of the incompatibility of the classical Christian doctrine of the Trinity with the logic of identity.

Until next time.

Addition, June 20, 2014. I failed to notice, at the time of the original posting, that the next to the last paragraph of Chapter 15, “The Divine Relations,” shows Garrigou-Lagrange once again contradicting himself. Let’s see how.

First, however, that paragraph will only make sense if we understand that, as Garrigou-Lagrange says in Chapter 16, “The Divine Persons” (p. 124):

A divine person, then, according to St. Thomas and his school, is a divine relation as subsistent. Elsewhere the saint gives the following definition: A divine person is nothing else than a relationally distinct reality, subsistent in the divine essence.

In, then, that next to the last paragraph of Chapter 15, Garrigou-Lagrange tells us:

Real relations in God are four: paternity, filiation, active spiration, “passive” spiration. But the third of these four, active spiration, while it is opposed to passive spiration, is not opposed to and hence not really distinct from, either paternity or filiation.

Now, if active spiration is not really distinct from either paternity or filiation, it is identical to both. Thus:

Active spiration is identical with paternity and active spiration is identical with filiation.

According, however, to the variation at hand of the principle of transitivity of identity:

For any existent x, any existent y, and any existent z, if x is identical with z and y is identical with z, then x is identical with y.

or:

(x)(y)(z)((Ixz & Iyz) –> Ixy)

So, applied to the present case:

If active spiration is identical with paternity and active spiration is identical with filiation, then paternity is identical with filiation.

Assuming, then, as Garrigou-Lagrange does, that:

Active spiration is identical with paternity and active spiration is identical with filiation.

one is committed to the conclusion that:

Paternity is identical with filiation.

But, we are told in Chapter 16 (p. 125):

These three opposed relations, then, paternity, filiation, and passive spiration, belong to related and incommunicable personalities.

As paternity and filiation are two of the three opposed relations; therefore:

Paternity is not identical with filiation.

Here too, therefore, with the conjunction:

Paternity is identical with filiation and paternity is not identical with filiation.

the Thomistic Trinitarian doctrine of Garrigou-Lagrange finds itself in contradiction, as indeed it must.

* Réginald Garrigou-Lagrange, O.P., Reality. A Synthesis of Thomistic Thought, translated by Patrick Cummins, O.S.B. (Ex Fontibus, 2006-2012)

* Thomas Aquinas, Commentary on Aristotle’s Physics, translated by Richard J. Blackwell, Richard J. Spath, and W. Edmund Thirlkel, introduced by Vernon J. Bourke, and with a foreword by Ralph McInerny. (Notre Dame, Indiana: Dumb Ox Press, 1999), originally published by Yale University Press, 1963.