Arithmetic of Boethius | Book I

interpretation: The text suggests that the arithmetical concepts of unity, equality, and connection serve as evidence to prove the eternal unity of the exceedingly high Trinity.

Arithmetical unity, equality, and connection serve to prove the eternal unity of the super-eminent exceedingly high Trinity through equality and connection. Whether these points carry weight is something we shall dwell on more fully in the following sections. To return to the author, it seems almost superfluous to review what the ancients said about the substantia substance of numbers and their principles, especially since Aristotle has touched upon these more than enough in the thirteenth and fourteenth books of his Metaphysics original: "supernaturalium," referring to the books on things beyond nature.

A structured table summarizes various philosophical opinions on the substance and elements of numbers. The left side of the table has a vertical header reading "Opinions on the substance of number and its principles, from the 13th and 14th books of the Metaphysics, where they are mostly refuted." The table classifies views from Plato, the Platonists, Pythagoreans, the Reals, the Nominals, and Aristotle across columns for "Substance of numbers," "Material Elements," "Formal Elements," and "The Composite."

The substances of numbers are separate according to some, or sensible according to the numerical Realists, or Pythagoreans, or as we and others hold.

It must at least be noted that numbers are not substances, whether separate (as the Platonists want) or immersed in sensible things according to the decrees of the Pythagoreans. This is made known by the reasons through which Aristotle refutes both views in the aforementioned books. Instead, numbers are true accidentia attributes of our mind. They have such a close affinity with the soul that some philosophers have said the soul is a number moving itself. Indeed, just as the sight distinguishes its own object and grasps it with its own cognition through a visible form, so the reason discerns things themselves by number. Thus, if the discretion and number of the mind were taken away, the things themselves would not be distinct or defined by any number, just as color is not actually visible when the cognition of the visual power is missing.

However, for those searching accurately, number presents itself as twofold. We previously noted that Boethius intended this in the first book, fourth chapter of On the Trinity. Specifically, there is the number by which we count, which is called the counting number numerus numerans, and the number which is in the things to be counted, which is identical in subject with the things themselves. Furthermore, that same counting number is in one sense an exemplar an ideal pattern and in another sense a craft of our own mind. Boethius speculates on the nature and principles of both equally.

Indeed, each is a discernment of things. For if we look toward God, the plurality of things comes from the Divine Mind. But if we look toward our own mind, which is the excellent image of that infinite mind, discerning and numbering each individual thing, then the plurality of things will be judged to come from our mind. But this is not measured on an equal scale: for the discernment of the Divine Mind is the creation of things, whereas ours is by no means so. Furthermore, the mind alone knows how to number and discern. If you take the mind away, you likewise take away discernment and harmony, and the entire heap of things immediately collapses.

Hence, number is rightly called the primary exemplar of things. For as long as the Divine Mind understands one thing in one way, and another thing

Twofold number: Number as it is meditated upon, and the counting number. In which the exemplar of things is clear in one way and through modes of distinction.

differently, a plurality of things has arisen. This can be said, not without reason, to be the mode of understanding of the Divine Mind. To that extent, number is weighed as the first footprint leading into wisdom. There is no other reason why distinct things respond harmoniously to one another except through the divine discernment and number, just as we ascribe the distinct plurality to our own number through the craft of our mind. If we raise our mind to divine matters, it will be established that what Boethius brings forward here differs in no way from the opinion of the Pythagoreans.

The faith of the Three the Trinity through logic or the principles of arithmetic, by which number is the same in weight, both one and distinct.

Indeed, among the Pythagoreans there were three principles of things: namely the Infinite, the One, and Number. The Infinite was said to be that which contains the essences of all things that can be produced, as well as the universe, its properties, the differences of accidents, as well as what is proper and the connections. Nothing can be said or thought of as prior to it, especially since each thing exists insofar as it was able to be. It is surely that in which all things lay hidden, eternally and without beginning. For because things were able to exist, they subsequently obtained their being. Driven by this very reasoning, Anaxagoras asserted that the universe was in that principle. In this, he comes close to the opinion of Empedocles and Anaximander: the discernment of creatures and the mass of the deity, distinguished by a full light.

Because it contains all things, therefore it is one and does not flow; nothing is infinite in this scale.

And since it contains all things—subsistent, sensible, rational, intellectual, both those that currently are and those that are not—they rightly called the divine idea and essence "infinite." Plato called the One, which is also the principle of number, the father of the gods. From this, the binarius the number two or dyad of divine unity first arises.

Plato calls the one and the same principle of number the father of the gods.

Furthermore, since nothing is found in the divine essence that is not the same as itself, it is established that the One and the number two are one and the same God. In this way, it is also explored that the number of the Divine Mind rejects all composition from other things; therefore, it consists of itself. It is immutable, eternal, and remains continually the same, existing as the exemplar of all things, as the oracle clearly brings forth.

The Divine Mind is composed of these; it creates from itself and in reality.

"By the word of the Lord the heavens were made firm, and by his spirit, all their power." To such an extent, that number two—the fruitfulness of the fatherly hypostasis divine person or substance—existed as the exemplar and idea from which came the entire harmony, distinction, and state of the world. Since the truth of the order and state of things is the same, it is immutable and remains in the same species. For take away the distinction of things, and disorder remains, to which "otherness" is joined. Indeed, disorder was called the cause of otherness by some philosophers. But from where else does the distinction of things come, if not from the number of the Divine Mind, as that from which all things are, and are distinct?

From this, distinction is seen.

Take away the number of the Divine Mind, and distinction perishes, and with it, the state of things. Since, therefore, the state that is in things comes from and is preserved by that number of the Divine Mind, it is established that this number does not change from its substance but is immutable. If you express that divine and super-immense essence—which is supremely undivided, one, most simple, the idea of all ideas, and the form of forms—as "odd" impar based on the perspective of its indivisibility and lack of distinction (just as in the craft of our mind, Unity receives the name of oddness, but never evenness), and if you make the divine properties and the distinctions of the divine persons "even" par because of their personal division and difference, then you will recognize the Trinity as the ideal and exemplary number, consisting of itself and nothing less than the even and the odd.

Unity is the name of oddness; evenness is the power of two.

Consequently, because these possess their own opposites, they are yet more simple than any simple composition. For that thrice-blessed Trinity consists of the divine essence as the odd, and the divine properties as the even. To such an extent, from that eternal unity, the even and the odd flowed into one melody, and indeed a super-immense one, by the miraculous and ineffable craft of the divine Trinity. And since the Father, Son, and Holy Spirit are nothing other than that essence, and likewise those divine properties are nothing other, we can rightly conclude that the divine and super-immense number consists of itself, and nothing less than the even and the odd. Because these receive different properties, they are called opposites. Even refers to division and distinction. Odd, truly, refers to unity and lack of distinction. You see, therefore, that all things correspond in every way: essence causes lack of distinction, while divine properties cause distinction. And so in the Trinity, there is the highest unity in distinction, and division absorbed in the highest unity. This divine essence and these immense properties remain, flourishing by the reason of immutable substance for the substance of the exemplary number. But perhaps I have said more than is proper regarding the substance of the exemplary number. Nevertheless, some things can be deduced from these which present an understanding not to be despised: such as that in that divine number resides all harmony, distinction, order, and finally all consonance. You will grasp this most easily if you express the immense essence by the unity of our mind, and the three divine distinctions by the first three numbers of our mind. By this paradigm, you will apprehend in that essence the enfolded essence of all things, and in that distinction, every enfolded distinction. And this is as in a symbol within the craft of our mind. For in unity and the first three numbers, every number and distinction, and every harmony, is enfolded, as is clear from this description.