How has Aquinas not proved the Trinity?

St Thomas holds that we cannot know by natural reason that God is a Trinity. However, he also endorses a version of St Augustine’s account of the Trinity, on which God has a mental Word or concept of himself that he generates mentally, and then there is a Love that is responsive to that Word. Why is this not a proof by natural reason?

On this point, Thomas is sadly brief in the Summa Theologiae: “Again, the similarity with our intellect does not sufficiently prove anything about God, since the intellect is not found univocally in God and in us.”

But Aquinas thinks that we can literally talk about God, even if we do so by means of analogy. He has argued, by reason, that God exists and has all perfections. One of these perfections is knowledge of everything, and thus of himself. Does this not commit Aquinas to being able to say on the basis of natural reason that God generates his self-knowledge, a self-knowledge that, by divine simplicity, must then be God himself rather than a mere creature? And does not God love himself under the description that this knowledge provides?

I think Aquinas would (with perhaps minor cavils) endorse all the claims in my previous paragraph as knowable by natural reason. How is this not a proof of the Trinity? I think the answer is this. Focus on the generation of the Son—the case of the Holy Spirit will presumably be similar. We do not know by reason whether the relation of generating self-knowledge is a real relation in God. If it is a real relation it will individuate the knower from the knowledge, thereby ensuring that there are at least two persons in God. But it needs to be a real relation in God, rather than a merely conceptual one. And here Thomas’s brief remark about univocity seems apposite. Aquinas thinks that what makes our language about God analogical rather than univocal is that the grounding of claims about God is radically different from the grounding of similar claims about creatures. Thus, when we say Socrates is wise, this is grounded by the inherence in Socrates of an accident of wisdom, while when we say God is wise, this is grounded by the identity between God and his wisdom. Because of this, even if it turns out that in us the generation of self-knowledge is a real relation (but not one between persons, since we are not simple, and hence our self-knowledge does not need to be of one essence with us), since the grounding structure of claims about God is radically different, as far as unaided human reason goes, it may not be grounded in a real relation in God—though it might be. We need God’s revelation to know if it is a real relation or not. And indeed God has revealed that it is.