Collect: O Blessed and Holy Trinity, who called your servant Fr. Garrigou-Lagrange to the defense of the coherence of the mysteries of the faith against the enemies of the true religion, grant that, by his intercession, I may partake of that same light with which he was illumined and militantly defend this mystery now under attack from your enemies, through Jesus Christ our Lord. Amen.
The Logical Problem of the Trinity attempts to refute the Trinity by attempting to show an incoherency in the Catholic Dogma of the Trinity by pointing to the law that “those things which are equal to a third are equal to each other.”
I will construct this syllogism from this principle:
The Father is God
The Son is God,
Therefore, the Father is the Son.
By a sober analysis of the doctrine of the Trinity, the nature of syllogism, and the nature of distinction, it will be demonstrated that such argumentation, while rhetorically powerful, does nothing more than mangle the sense of the Catholic teaching.
To the objection, I distinguish, those things which are MENTALLY EQUAL and without MUTUAL OPPOSITION are equal to a third, I concede. Those things which are NOT MENTALLY EQUAL and have MUTUAL OPPOSITION, such as the Trinity, I deny.
A thing may be distinct either before the consideration of the mind (a real distinction) or after the consideration of the mind (a distinction of reason). When considering the identity of the Father/Son with God, clearly it could not be a real distinction (otherwise, the identity would not be verified). Thus, the distinction must be one of reason.
Now, a distinction of reason can be distinguished into two types depending on the type of identity present. There are two types of identity, formal and material. Formal identity is verified when there is an identity of definition present. Material identity is verified when there is an identity of entity present.
For example, when I say “Donald Trump is a rational animal,” there is a material identity present between “rational” and “animal” in that they share the same entity. Yet, “rational” is not “animal” formally speaking, for, they verify different aspects of Donald Trump and are thus formally distinct, yet materially identical.
In this we can make a twofold distinction and thus form some tertium quid between a purely reasonable distinction, i.e., formally and materially identical, and a purely real distinction, i.e., formally and materially distinct, and posit that a certain thing can be materially identical (i.e., share one entity), yet be formally distinct (that one entity considered under a different formal aspect). This is called a “virtual distinction” or “distinction of reason reasoned.” The difference in formal aspect being called a fundamentum in re.
In the response, it is distinguishing based on this formal identity, i.e., we deny that such a rule follows where there is a distinction between the formal identity of two subjects, yet we affirm that such a rule follows where there is formal identity.
St. Thomas gives a similar response, “According to the Philosopher (Phys. iii), this argument holds, that whatever things are identified with the same thing are identified with each other, if the identity be real and logical; as, for instance, a tunic and a garment; but not if they differ logically. Hence in the same place he says that although action is the same as motion, and likewise passion; still it does not follow that action and passion are the same; because action implies reference as of something from which there is motion in the thing moved; whereas passion implies reference as of something which is from another. Likewise, although paternity, just as filiation, is really the same as the divine essence; nevertheless these two in their own proper idea and definitions import opposite respects. Hence they are distinguished from each other.” (ST.I.Q28.A3.Rep1)
To illustrate, the argument would follow in such a case (where there is only a merely rational distinction):
The tunic is a garment,
The tunic is red,
Therefore, a garment is red.
This distinction is theologically powerful and is a bulwark against all heresies De Deo Uno et Trino. For, a similar case happens concerning Divine Simplicity (which helps illustrate the case), “it is only materially true to say that the divine mercy and the divine justice are the same, because they are not really distinct, and by reason of their subject or matter they are in a sense the same…it does not belong to the divine mercy to punish; the divine mercy pardons, condones, and it is the divine justice that punishes, although these two perfections are really the same, that is, materially the same but not formally.”
Now, applying this analysis to syllogisms. The laws of syllogisms are not verified except in formal identity. For, the object of logic is being as existing in our intellect, i.e., mental terms, which represent things in themselves. Thus, in our reasoning, we must compare two terms based on the formal aspect under which it is being considered. Otherwise, whatever term we are considering under two different formal aspects will be two terms, not one terms, i.e., we will break the first law of syllogisms and commit an equivocation.
To illustrate, it would be false if we said “Donald Trump is rational, Donald Trump is animal, therefore, animal is rational,” for, “Donald Trump” is being considered under two different formal aspects and thus there are four terms, i.e., “rational,” “animal,” “DT considered under the formal aspect of rationality,” and “DT considered under the formal aspect of animality.”
Fr. Lagrange applies this to the example above, “the following argument is not valid because the major is only a material predication: in God mercy is the same as justice; but justice is the principle of punishment; therefore God inflicts punishment through His mercy. The argument is false because in God mercy and justice are not the same formally although they are the same materially.”
Now, how does this apply to the example of the Trinity? It is conceded that they share the same entity, yet it is denied that they are formally identical. For, the Father is God considered under the formal aspect of paternity. The Son is God considered under the formal aspect of being begotten. They are relatively opposed due to the Father’s position as terminus a quo of begetting and the Son’s position as the terminus ad quem of that immanent act. Yet, there is not that same relative opposition between the persons and the essence, thus there is material identity present. Yet, as we have established, not only a material identity, but a formal identity is needed in order to draw a syllogistic conclusion, thus the syllogism “This God is the Father, but this God is the Son, therefore the Son is the Father” cannot be drawn.
“It is truly meet and just, right and for our salvation, that we should at all times, and in all places, give thanks unto Thee, O holy Lord, Father almighty, everlasting God; Who, together with Thine only-begotten Son, and the Holy Ghost, art one God, one Lord: not in the oneness of a single Person, but in the Trinity of one substance. For what we believe by Thy revelation of Thy glory, the same do we believe of Thy Son, the same of the Holy Ghost, without difference or separation. So that in confessing the true and everlasting Godhead, distinction in persons, unity in essence, and equality in majesty may be adored.”