That it does not consist of three persons, or of any other number of persons, is as easily demonstrated, as that the whole is bigger than a part, or any other proposition in mathematics.
We will premise, that the three persons in the supposed Trinity are either finite or infinite; for there cannot in the scale of being be a third sort of beings between these two; for ever so many and exalted degrees in finiteness is still finite, and that being who is infinite admits of no degrees of enlargement; and as all beings whatever must be limited or unlimited, perfect or imperfect, they must therefore be denominated to be finite or infinite: we will therefore premise the three persons in the Trinity to be merely finite, considered personally and individually from each other, and the question would arise whether the supposed Trinity of finites though united in one essence, could be more than finite still. Inasmuch as three imperfect and circumscribed beings united together could not constitute a being perfect or infinite, any more than absolute perfection could consist of three imperfections; which would be the same as to suppose that infinity could be made up or compounded of finiteness; or that absolute, uncreated and infinite perfection, could consist of three personal and imperfect natures. But on the other hand, to consider every of the three persons in the supposed Trinity as being absolutely infinite, it would be a downright contradiction to one infinite and all comprehending essence. Admitting that God the Father is infinite, it would necessarily preclude the supposed God the Son, and God the Holy Ghost from the god-head, or essence of God; one infinite essence comprehending every power, excellency and perfection, which can possibly exist in the divine nature. Was it possible that three absolute infinites, which is the same as three Gods, could be contained in one and the self-same essence, why not as well any other number of infinites? But as certain as infinity cannot admit of addition, so certain a plurality of infinites cannot exist in the same essence; for real infinity is strict and absolute infinity, and only that, and cannot be compounded of infinities or of parts, but forecloses all addition. A personal or circumscribed God, implies as great and manifest a contradiction as the mind of man can conceive of; it is the same as a limited omnipresence, a weak Almighty, or a finite God.
From the foregoing arguments on the Trinity, we infer, that the divine essence cannot consist of a Trinity of persons, whether they are supposed to be either finite or infinite.
The creed-mongers have exhibited the doctrine of the Trinity in an alarming point of light, viz.: "Whoever would be saved before all things it is necessary that he hold the Catholic faith, which faith, except every one doth keep whole and undefiled, without doubt he shall perish everlastingly." We next proceed to the doctrine, "The Father is eternal, the Son is eternal, and the Holy Ghost is eternal, and yet there are not three eternals but one eternal." The plain English is, that the three persons in the Trinity are three eternals, individually considered, and yet they are not three eternals but one eternal.
To say that there are three eternals in the Trinity, and yet that there are not three eternals therein, is a contradiction in terms, as much as to say, that there are three persons in the Trinity and yet there are not three persons in the Trinity.
The first proposition in the creed affirms, that "the Father is eternal," the second affirms that "the Son is eternal," the third affirms that "the Holy Ghost is eternal," the fourth affirms that "there are not three eternals," and the fifth that there is "but one eternal."
The reader will observe, that the three first propositions are denied by the fourth, which denies that there are three eternals, though the three first propositions affirmed, that there were three eternals by name, viz. the Father, Son and Holy Ghost. The fifth proposition is unconnected with either of the former, and is undoubtedly true, viz. "but there is one eternal." "The Father is God, the Son is God, and the Holy Ghost is God, and yet there are not three Gods but one God." Here again we have three Gods by name, affirmed to have an existence by the three first propositions, by the fourth they are negatived, and the fifth affirms the truth again, viz. that there is "but one God."
Admitting the three first propositions to be true, to wit, that there are three Gods, the three could not be one and the same God, any more than Diana, Dagan and Moloch may be supposed to be the same; and if three Gods, their essences and providences would interfere and make universal confusion and disorder.
"The Father is Almighty, the Son is Almighty, and the Holy Ghost is Almighty, and yet there are not three Almighties but one Almighty." Here we have three Almighties and at the same time but one Almighty. So that the point at issue is brought to this simple question, viz. whether three units can be one, or one unit three or not? Which is submitted to the curious to determine. Our creed further informs us, that the three persons in the Trinity are co-eternal together and co-equal, but in its sequel we are told that one was begotten of the other; and when we advert to the history of that transaction, we find it to be not quite eighteen hundred years ago, and took place in the reign of Herod, the King of Judea, which faith except "we keep whole and undefined," we have a threat, that "without doubt we shall perish everlastingly."