Moreover, that the principle does not apply to the infinite is evident from the very enunciation and meaning of the principle. Things which are identical with a third are identical with each other. In the enunciation and in the meaning, the principle supposes a plurality, and, consequently, a distinction; for the gist of the principle is to compare a multiplicity to a unity. Now, who does not see that, if there were not a supreme identity and a supreme multiplicity beyond the sphere and subordination of this principle, the principle itself would be destroyed?
For if it be asked, what is the origin, the cause, and the supreme expression of plurality and distinction, which this principle supposes, we must rise to a supreme and typical distinction and identity, not subject to the principle; else we could never account for the existence of the principle.
The infinite is the supreme identity and the supreme multiplicity, the cause of all distinction and identity, and consequently, to it the principle cannot apply.
We conclude, therefore, that the first law governing the genesis of God's life is the law of opposition of origin, and that this law accounts both for the unity of essence and the trinity of persons in God.
We pass to the second law, which is as follows: In the infinite, there must be a person who does not proceed from anything, and who is neither begotten nor made, but who subsists by himself. The metaphysical reason of this law is, that there must be a first principle in everything, both in the ontological and in the ideological orders.
In the ontological order, because if every principle of reality, if every cause called for the existence of another to explain its existence, it is evident that there would be a process ad infinitum without explaining anything. For an infinite number of causes, each requiring another cause to explain their existence, would multiply, ad infinitum, the necessity of first cause, existing by itself and containing in itself the reason of its existence.
In the ideological order, because every science must have a principle which is not derived from any other, and which must be taken for granted, otherwise science would become impossible. Ask a proof and a demonstration for every principle, say of mathematics, and you will never be able to learn it.
Thus, in the genesis of infinite life, there must be a first person who subsists by himself, otherwise the life of the infinite becomes impossible.
But, besides this general reason which requires a first person underived from anything, there is a particular reason, more closely allied to the subject, which demonstrates it. Because, if there were not a first person in the infinite, not proceeding from any other thing, it would originate either from the essence or from another person. Now, it could not originate from the essence; because between the principle and its product there is a real opposition of origin; therefore, in the supposition, there would be a real opposition between the essence of the infinite and the first person. Now, the essence in question is infinite, and only the finite can be opposed to it. The first person, therefore, proceeding from the essence, would be finite and not infinite; that is, he would be a creature. Moreover, it would be impossible that the first person should proceed from the essence, because the essence without subsistence is an abstraction, and an abstraction could not originate a reality.