Fr. Réginald Garrigou-Lagrange, O.P., says, in Le Sens du Mystère et le Clair-Obscur Intellectuel: Nature et Surnaturel p. 128 fn. 1 (Engl. transl. p. 142 fn. 41):
Jamais saint Thomas n'aurait admis comme Suarez que le principe de contradiction ne s'applique pas dans la Trinité; il s'y applique selon un mode éminent qui nous reste caché, et nul ne peut montrer que ce mystère implique contradiction.
St. Thomas never would have admitted like Suarez that the principle of contradiction is not applied in the case of the Trinity. It is applied there according to an eminent mode that remains hidden to us, and nothing can show that this mystery implies a contradiction.
Where did Suárez write that the principle of non-contradiction does not apply in the Trinity?
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Suárez discusses the applicability to the Persons of the Trinity of this form of the principle of non-contradiction:
The objection might be made that this argument is based on the principle gathered from Aristotle, Metaphysics, Bk. IV, text. 3,56 that things which are the same as a third thing are the same as each other — a principle which has no place in the Trinity; otherwise we should infer not only that one relation cannot exist without another, but that it is this other.
Dices, hoc argumentum fundari in illo principio Aristotelis, IV Metaph., text. 3: Quæ sunt eadem uni tertio, sunt eadem inter se, quod in Trinitate locum non habet; alioqui non solum inferretur unam relationem non posse esse sine alia, sed etiam esse aliam
56. The axiom is nowhere explicitly formulated in Metaphysica, IV, text 3. Junta VII fol. 31 vb. 32–58. Cf. Metaphysica, IV, 2, 1003b 22–34. But it is an obvious application of the principle of contradiction, which Aristotle discusses throughout this book.
and in the last section of this disputatio:
Finally, we can gather from the foregoing doctrine the meaning of an axiom enunciated by Aristotle in the fourth book of the Metaphysics:72 Things which are the same as a third thing, are the same as each other. Due proportion must be observed in applying this principle. If two things are in reality identical with a third thing, they will also be identical with each other in reality, although they may be diverse in concept. And if they are identical with a third thing both in reality and in concept, they will be identical with each other in the same way. In creatures and in finite things this principle avails absolutely. But in an infinite thing, such as is the divine essence, the maxim is not verified, absolutely speaking, since on account of its infinity the divine essence can be identical with opposite relations which, because of this opposition, cannot be identical with one another, except in the essence alone. But we have dealt with this problem on another occasion.73
Ultimo potest ex dictis colligi, quomodo sit intelligendum illud axioma quod Aristoteles posuit IV Metaph.: Quæcumque sunt eadem uni tertio, sunt eadem inter se; intelligendum est enim cum proportione, nam si sunt eadem re uni tertio, simili modo erunt eadem re inter se, poterunt autem esse ratione diversa; si autem re et ratione sint uni tertio eadem, erunt eodem modo eadem inter se. Sed hoc principium in creaturis, et in rebus finitis simpliciter tenet; in re autem infinita, qualis est divina essentia, non verificatur illa maxima absolute loquendo, quia propter suam infinitatem potest esse idem relationibus oppositis quæ propter oppositionem inter se idem esse non possunt nisi tantum in essentia; de quo alias.
72. See note 56.
73. De Sanctissimo Trinitatis mysterio, Lib. IV, cap. 3; in Vol. I of the Vivès edition.
In De Sanctissimo Trinitatis mysterio, Lib. IV, cap. 3, Suárez discusses St. Thomas's solution in Summa Theologica I q. 28 a. 3 "Whether the relations in God are really distinguished from each other?" arg./ad 1.
St. Thomas's solution:
Objection 1: It would seem that the divine relations are not really distinguished from each other. For things which are identified with the same, are identified with each other. But every relation in God is really the same as the divine essence. Therefore the relations are not really distinguished from each other.
Videtur quod relationes quæ sunt in Deo, realiter ab invicem non distinguantur. Quæcumque enim uni et eidem sunt eadem, sibi invicem sunt eadem. Sed omnis relatio in Deo existens est idem secundum rem cum divina essentia. Ergo relationes secundum rem ab invicem non distinguuntur.
Reply to Objection 1: 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.
Ad primum ergo dicendum quod, secundum philosophum in III Physic., argumentum illud tenet, quod quæcumque uni et eidem sunt eadem, sibi invicem sunt eadem, in his quæ sunt idem re et ratione, sicut tunica et indumentum, non autem in his quæ differunt ratione. Unde ibidem dicit quod, licet actio sit idem motui, similiter et passio, non tamen sequitur quod actio et passio sint idem, quia in actione importatur respectus ut a quo est motus in mobili, in passione vero ut qui est ab alio. Et similiter, licet paternitas sit idem secundum rem cum essentia divina, et similiter filiatio, tamen hæc duo in suis propriis rationibus important oppositos respectus. Unde distinguuntur ab invicem.