The Infinity of Existence, and of God

As I have argued, Thomas proposes that every actual being has its own act of existence (actus essendi). An act of existence is a real being, although it is not a substance. In this sense, the act of existence is something like an accident, since accidents are also real but non-substantial beings. Nonetheless, an act of existence is not an accident of its substance, since it is causally prior to that substance. The act of existence gives the substance actual existence. Substances do have (by virtue of their essences) a kind of being (potential being) that is independent of the act of existence. It is potential beings that make up the structure of mere possibilities (including Leibniz's 'possible worlds').
 
Do acts of existence themselves exist, and, if so, do we face an infinite regress, with each act of existence requiring a further act to give it existence? I think acts of existence do exist, but they exist in a way that is different from the way that substances and accidents exist. They exist simply by being acts of existence, while substances and accidents require distinct acts to give them actual existence. Substances and accidents can have potential existence, which is why they can be contained in mere possibilities. Acts of existence cannot have potential existence: they are intrinsically actual. Hence, no mere possibility contains any act of existence.
 
An act of existence must give whatever actuality a thing has. Hence, acts of existence, as such, are infinite, while all substances and accidents are finite. If acts of existence as such were finite in any way, then there would be possible entities that could not be actualized. But that is a contradiction in terms: to be a possible entity is to be possibly actualized. Hence, acts of existence must have the power to actualize everything, to the outermost limits of possibility. They must be intrinsically infinite.
 
Furthermore, if any act of existence were finite as an individual, then this finitude would define a particular kind of being. In other words, the act of existence would have a kind of essence built into it. But if the act includes such an essence, then it would make sense for the act to exist only in potentiality. But, as we've seen, this is impossible. Every act of existence must be actual.
 
Finally, existence itself can have no limit, since a limit implies some possible thing beyond the limit, but nothing can exist “outside” of existence. A limit is something that receives existence, and that limits the existence it receives. Existence itself cannot be or have a limit.
 
God is a pure act of existence, without any associated essence. Hence, God is absolutely infinite. He must possess every possible perfection without any limit whatsoever.
 
Now, infinity seems to be something negative—the lack of finite boundaries or limitations. However, when infinity is combined with God’s perfection, we do get something positive. God must have each perfection to a greater degree than any possible creature.
 
Infinity is, for Thomas, a complicated matter. For Aristotle, infinity is generally a bad thing. Being not-finite means lacking sharp boundaries. A non-finite thing is somewhat amorphous and shapeless, lacking any sharp definition. Shadows, clouds, or crowds would all be examples of in-finite, somewhat vague entities. Clearly none of this applies to God. God is definitely what He is, with no vagueness or amorphousness.
 
In addition, Aristotle generally associates infinity with potentiality. Nothing in the material world is ever actually infinite. A real line segment (say, one on the surface of a box), for example, does not contain an actual infinity of points. Instead, each of its internal points exists only potentially, since the line segment can be divided in any of an infinite number of quantitatively different ways. Similarly, the future is potentially but not actually infinite. We will never reach a day that is infinitely many days after this one. God, in contrast, is pure actuality. So, it seems that God’s essence and infinity should be incompatible.
 
But, of course, God’s infinity is not a quantitative infinity. He is not infinite by having an infinite number of parts, or by filling (in a physical way) an infinite volume of space or an infinite duration of time. The kind of finitude that material substances have is itself foreign to God. My form is made finite by my matter, since my matter is quantitatively limited prior to my generation. At the same time, my matter is also made finite by my form, since it is form that gives a definite size and shape to my matter. Thus, finitude emerges in the cooperation of matter and form.
 
There is nothing corresponding to matter in God. Hence, there is nothing that can put a limit to His “form”. And, conversely, there is nothing that could be limited by His form. Hence, God is in-finite.
 
When we turn to article 2 of Question 7, we see that creatures can be “relatively” infinite, but only God can be absolutely infinite. Matter, for example, is relatively infinite, in the sense that it is capable of taking on any substantial form for a material substance. A material substance can be relatively finite with respect to its possible accidents, like shape. Angels have no matter, and yet they too can be only relatively infinite, since their being (esse) is “received and contracted into a determinate nature.” Only God is pure, absolute being, and so only He can be absolutely infinite.
 
God’s infinity is an infinity of active power and maximum nobility. He and He alone has the full power of being itself.
 
In the Summa Contra Gentiles, I I.43, Thomas talks of God having an infinite “spiritual” magnitude. We shouldn’t read too much into the word ‘spiritual’ (spiritualis). The term is used in two quite different ways in scholastic philosophy. It can mean purely intellectual substances, like God, the angels, and the separated soul. But it can also mean the more ethereal and subtle aspects of the physical world. Light, for example, is sometimes classified as spiritual. So too are the ‘animal spirits’ which scholastic philosophers took to be circulating through the body (like our modern electrical impulses of the nervous system).
 
Thomas identifies two dimensions of spiritual magnitude: active power, and the goodness or completeness (perfection) of one’s nature. Clearly, God is infinite in both these respects.
 
In natural magnitudes, as we’ve seen, infinity is a kind of privation, a lack of definition and form. In God’s case, it is a pure, non-primitive negation, a simple absence of boundaries and limits, without any implication that those boundaries and limits ought to be there.
 
Things that have limits have those limits either due to the definition of their nature (reflected in their genus and species) or from something into which they are received. So, anything whose existence and essence are distinct must have a limit: the essence will have limits due to its definition, and the act of existence will be limited by being received by something limited (the essence). God has no definition or genus, and His existence is not received into any distinct nature. Hence, God’s existence is infinite.
 
Thomas also argues that God is infinite in the sense that He cannot be exceeded by anything else. Since He has no passive potentiality, nothing can be more actual than He is. (SCG 1.43, paragraphs 6-7, 9-11) He argues, in somewhat Platonic fashion, that nothing could be better than a being that is its own goodness (par. 9). He appeals to something like Anselm’s conception of God as the greatest conceivable thing in par. 10, arguing that there must be a greatest of all intelligible beings. These are interesting, but they fall short of showing that God is infinite, as opposed to simply the greatest of all finite beings.
 
In par. 11, Thomas argues that we can think of something greater than any finite being, and yet our intellect cannot think of something greater than its own cause. So, God (our intellect’s cause) must be infinite. (This is close to one of Descartes’ arguments for God in the Meditations, a sort of hybrid of the cosmological and ontological arguments.)