CT 18: The Infinity of God According to Essence

In Chapter 18, we learn that there are different kinds of infinity. As a mathematician I’m not surprised by this; and I’m rather comforted to hear Thomas speak this way. He says:

This leads to the question of God’s infinity. God is not infinite by way of privation, according to which infinity is a passion of quantity; in this sense whatever lacks limits, but is nevertheless capable of having limits by reason of its genus, is said to be infinite. Rather, God is infinite negatively, in the sense that a being that is unlimited in every way is infinite.

It’s always nice when Thomas defines his terms; in this case, though, I’m finding the terms in which he defines his terms to be reasonably opaque. Let’s start with privation. I’m familiar with this term in the context of the privation theory of evil, that evil is not a positive quantity in and of itself, but a privation, a lack, at times even a perversion of goodness. Pride, for example, is a lack of humility, a disorder of the self. So in the first sense, something is infinite because it could in principle be limited in some way, but isn’t. It lacks limits. That’s clear enough, though it’s the opposite of how I would have thought about it; but on reflection it makes sense. Finitude we can grasp. And the very word “infinite” means “not finite”.

I’m not at all sure what Thomas means by “a passion of quantity”.

Anyway, God is clearly infinite in a more powerful sense: He cannot be limited, even in principle. An arbitrary integer x could be infinite, in the sense that we’ve not limited it; and given any specific integer x one can always find a larger x+1. You can build up to any amount you like in this way. But God isn’t infinite in this “we can build it as large as we like” sense. OK; I’m not sure I’ve really got it, but I’m ready to move on.

No act is found to be limited except by a potency that is receptive of the act; thus we observe that forms are limited in accordance with the potency of matter. Hence, if the first mover is an act without any admixture of potency, as not being the form of any body or a force inhering in a body, it must be infinite.

I’m not sure what a “potency that is receptive of the act” means, precisely. But it’s clear that the new forms that matter can take on are limited by the potency of matter. An apple can be made into applesauce; it cannot be made into a lounge chair. (Although, I suspect Thomas means the potency of matter to take on forms in general rather than the potency of this particular bit of matter to take on the particular forms it can take on.) The giving of a form, bringing the form into actuality, is act; and the acts that can occur are limited by the potency of the matter to be acted upon. Thomas claims that this is the only limit on act that there is, and so since there is no potency in God, it cannot be limited in any way and must be infinite.

I can half-way see my way clear to that, but it’s been a long day.

The very order perceived in things is a proof of this. The higher the position occupied in the scale of being, the greater are things found to be in their own way. Among the elements, nobler things are found to be greater in quantity, as also in simplicity. Their generation demonstrates this: as the proportion of the respective elements is increased, fire is generated from air, air from water, and water from earth. And a heavenly body clearly exceeds the total quantity of the elements. Necessarily, therefore, that which is the first among beings and which has nothing above it, must in its own fashion be of infinite quantity.

I love St. Thomas dearly, but when he starts talking about the elements and using them as examples, my eyes start to glaze over. Possibly I’m being too impatient with him.

Nor is there anything to wonder at if what is simple and lacks corporeal quantity is said to be infinite and to exceed in its immensity all quantity of body. For our own intellect, which is incorporeal and simple, exceeds the quantity of all bodies in virtue of its knowledge, and embraces all things. Much more, then, that which is the very first of all exceeds the universe of beings in its immensity, and embraces them all.

Aristotle taught, if I recall correctly (and if I understood it properly) that our intellect learns by extracting form from bodies and keeping it. Our intellect can bring in and retain an arbitrary number of forms; yet our intellect is immaterial, incorporeal. It can embrace all forms regardless of their size, and hence is larger than any. The Divine Intellect embraces all forms (having caused them, I guess) and thus has a reasonable claim at being larger than any.

I think that’s what’s going on in this last bit. I have some notion of the division of our wits into intellect, sense, and so forth, and how it’s all supposed to work, but I don’t remember the details all that well.

Oh, well; it’s late.

6 Responses to “CT 18: The Infinity of God According to Essence”

  1. I was going to write this to you the other day because it seemed relevant, but I held back. Now I guess I’ll lend what help I can.

    God is pure act, and in St. Thomas’s language that means that He possesses every perfection. In Aristotle, form was considered finite, and matter was considered infinite. The Greeks hated the concept of infinite, because the infinite was unintelligible. Thus, form was the limiting principle of matter, giving it definite shape and perfecting previously formless matter. The reasons why the heavenly bodies where spherical and moved in a circle is because the circle/sphere was considered the perfect shape: perfection existed in the finite, imperfection in the infinite.

    This whole idea got reversed with Thomas, making a move that perhaps started with Plotinus. Thomas thinks God is infinite, which no longer means that he is completely perfect, but possessive of all perfections. He is fond of saying that unreceived act is unlimited. In other words, since God is His own act of existing, He is unlimited. To receive act is to give act to something which does not necessarily possess act. Thus, every essence outside of God receives act because they receive their existence/act from God, i.e. they aren’t there own act of existing. Essence serves as a limiting principle of existence. For example, horseness possesses several traits which imitate the perfections found in God, but horseness lacks other perfections. To use a crude analogy, existence/act is like a waterfall, and essences/potency are like clay jars. The existence is infinite, but the clay jar can only hold so much of that infinite.

    Furthermore, matter serves as a further limiting principle of essence. In this case, essence/form is the actuality and matter is the potency, the limiting principle. This is because matter further limits act, making it a particular thing which is unable to exhaust a genus. So a particular horse is a horse, but it is not horseness itself.

    So again, for Thomas act is not the limiting principle, but matter is. Existence/act is infinite if it is not received, but it becomes finite when it is received by a particular potency: so existence is limited by essence at the level of essence, and essence is further limited by matter.

    I hope that helps.

  2. Correction:

    “Thomas thinks God is infinite, which no longer means that he is completely perfect, but possessive of all perfections.”

    That should read, “…which no longer means that he is completely imperfect…”

  3. Will says:

    Wow. Yes, that helps quite a bit. I’d already picked up the notion that God possesses all perfections, and that created things resemble God in possession some of those perfections; but Thomas’ notion of infinity vs. the Greeks was completely off of my radar. I’m going to have to ponder your comment a bit, but it fills in a few more of the ground rules. Outstanding.

    Thanks very, very much.

  4. Ian says:

    Infinity Is the essence, I think we are here in this creation this temporary state of Defined infinity to gain knowledge of our self, our essence the Infinite that life is that God is, that we are not separate from but through the appearance or illusion if you will of this separation ..this illusion of Definition through this experience, in defined infinity in such forms as time and space & Matter which makes up the physical world we exist in we learn about the Infinite through the definite …the same way one learns about “up” by experiencing “down”

  5. Will says:

    Ian, I’m not at all sure what you mean.

  6. Ian says:

    I guess it would take a bit more explaining :)

    not the best at putting my thoughts down on paper