The Ascent to the Intelligible

[readoldthings]

Here is how Plato described the purpose of mathematical studies in the Republic:

All number has also an elevating effect; it raises the mind out of the foam and flux of generation to the contemplation of Being.

And:

Let our second branch of education be geometry... The use of geometry, to which I refer, is the assistance given by it in the contemplation of the Idea of Good, and the compelling the mind to look at true Being, and not at generation only.
 

Now, it was of course obvious to him that these studies had practical uses, and he especially singles out their uses to the general in war. Agamemnon, he notes, would have been a rather poor general if he'd been unable to count his feet, let along his soldiers; the uses of geometry in war are also obvious. 

Of course, Arithmetic is also very useful in the art of making money. Plato dismisses this: 

to our higher purpose no science [than arithmetic] can be better adapted; but it must be pursued in the spirit of a philosopher, not of a shopkeeper. It is concerned, not with visible objects, but with abstract truth

And has little patience for the use of geometry as simply a tool for art and construction:

the present mode of pursuing these studies, as any one who is the least of a mathematician is aware, is mean and ridiculous; they are made to look downwards to the arts, and not upwards to eternal existence. The geometer is always talking of squaring, subtending, apposing, as if he had in view action; whereas knowledge is the real object of the study. It should elevate the soul, and create the mind of philosophy; it should raise up what has fallen down, not to speak of lesser uses in war and military tactics, and in the improvement of the faculties.

This is one of the challenging things that modern people face when we begin to study the Platonic tradition. We are used to a kind of nested hierarchy of sciences in which Psychology can be reduced to Biology, Biology to Chemistry, Chemistry to Physics, and Physics to Mathematics. And we are used to both assuming this scientific hierarchy as an a priori, and to the belief that it somehow works as a proof of Materialism. Somehow proponents of this point of view never get around to asking what the height of the number 2 is, or its breadth, its mass, or its location in space, how long it has lasted and when it might be expected to conclude. 

The ancient view of Mathematics, passed on by Pythagoras to Plato and then forward through the whole tradition of ancient philosophy, is also the more realistic. Mathematical objects are not material objects. They have no dimensions, no location, and no duration. They have no existence in matter. And yet they constantly act upon the material world, defining and delimiting it. We are able to interact with them through the medium of the physical world-- by writing a problem on a chalkboard, or by practicing the classical art of the geometer with a stake in the ground. In this way, Mathematics serves as a bridge between the Sensible World-- that is, the world we grasp with our ordinary five senses-- and the Intelligible World, what we might ordinarily think of as the world of spirit, pure Mind. 

Proclus described it thusly, in his commentary on the Elements of Euclid. 

Mathematical being necessarily belongs neither among the first nor among the last and least simple of the kinds of being, but occupies the middle ground between the indivisible realities and divisible things characterized by ever variety of composition and differentiation. The unchangeable, stable, and incontrovertible character of the propositions about it shows that it is superior to the kinds of things that move about in matter. But the discursiveness of mathematical procedure, its dealings with its subjects as extended, and its setting up of different prior principles for different objects--- these give to mathematical being a rank below that indivisible nature that is completely grounded in itself. 
 

For the ancients, Mathematics had an anagogic function. That is, it elevated the soul, allowing it to function on higher levels of being. The objects of mathematics exist at a level between the perfectly simple Ideas and the material world. They are not the only such objects. Logical formulae also serve this purpose, and the syllogism functions as well as the geometrical theorem in elevating the mind. But love, too, has an anagogic power, and so does music, as Plato shows in the Symposium and Phaedrus.  

In the writings of Proclus, Plato is regularly given the epithet "Divine." "The Divine Plato" teaches this, "As the Divine Plato writes," and so on. Not only Plato is given this title. Plotinus, Iamblichus, and others are also Divine. "Divine" was rather like "Saint," a word which simply means "Holy." But when Proclus mentions Aristotle, he refers to him instead as Daemoniacal. Because I find Aristotle irritating, I like to pronounce this "demoniacal" and to treat it as its English homonym. But of course, that isn't what Proclus means. The daimones, as I've discussed many times here, are intermediaries between humans and the gods; in the Symposium. They elevate human souls to the divine, and distribute the energies of the divine into matter. 

Traditionally, one began the study of Aristotle with the Organon, a collection of logical treatises beginning with the Categories. In later centuries (that is, after about the year 200) one began first with the Isagoge or Introduction of Porphyry, which then became the standard introduction to logic during the Middle Ages. One then proceeded through Aristotle's physical, metaphysical, and ethical works, and only then began to study Plato. Aristotle's works functioned as a sort of Outer Initiation, preparing the mind for the Inner Initiation of Plato. 

The great philosopher of the Catholic Church in the Middle Ages was Saint Thomas Aquinas. Aquinas was an Aristotelean. In his work he refers to Aristotle simply as "The Philosopher," and rarely disputes with him on anything. With Plato, on the other hand, he is constantly quarreling. This was a reversal of a longstanding tradition. Augustine, the Catholic Church's first great theologian, was a Platonist strongly influenced by Plotinus and Porphyry. Aquinas's great contemporary, Saint Bonaventure, was a Platonist, as Augustine had been, but in the end Aquinas ended up carrying the day. His Dominican Order's Thomistic theology provided the intellectual grounding for the Roman Church, with Bonaventure's Franciscans providing a kind of minority report. 

I'm wondering if this wasn't the great error of the Western world, and I wonder if it doesn't ultimately amount to prefering the Daemoniacal to the DIvine.