As part of our series on how God exists and the divine essence we delve into two articles on the infinity of God. This is the first of those two articles on His infinity. On the divine essence, we learned so far about the simplicity of God, His perfection, and His goodness. Today, in Question 7 of Part 1, Thomas digs into God’s infinity, whether there can be an infinite magnitude, and whether there can be an infinite multitude.
Whether God Is Infinite
God is infinite, Thomas says, and here’s how he demonstrates this:
- Matter is made finite by form. Form is made finite by matter.
- Matter is first potential to many forms, but when it receives a form it is made finite by that form.
- Form is common to many, but when it is received by a particular matter it is then made finite.
- Infinite matter, before it is made finite by form, is imperfect because matter without form is formless matter.
- Form is contracted, and not made perfect, by matter. Form is infinite when not contracted by matter and thus has the nature of something perfect.
- Being is the most formal of all things.
- God is a divine being not received in anything, but is his own subsistent being. Therefore, God is infinite and perfect.
Thomas answers objections
The first objection says that, according to Aristotle, everything infinite is imperfect since it has parts and matter. But God cannot be infinite because He is perfect.
In his response, Thomas discusses how mistaken the ancient philosophers were in asserting that the first principle was a material being. There in the demonstration above, however, Thomas shows that form is infinite before it is contracted by matter, so that when it is the being made of form and matter it becomes finite. Therefore, it is impossible for something containing matter to be infinite. God, too, on the other hand can’t be material because when matter is without form it is imperfect and when matter contains a form then it becomes finite, and thus loses a certain nature of perfection. God, as we discussed previously, is simple. He is not a composite of form and matter. So, God is a formal being. He is His own subsistent being and therefore He is perfect and infinite.
Another objection is that finite and infinite are quantities, but God is not a quantity because He is not a body. Therefore, God cannot be infinite.
Since God is not matter, and the infinite of quantity is the infinite of matter, this type of infinity cannot be attributed to God, Thomas replies.
Still another objection is God is finite according to place. He can be one place and not another. He is also finite according to substance. He can’t be something else, such as a wood or stone.
Thomas says that God is self-subsisting, not received in any other, and is infinite. He is distinguished from all other beings and all others are apart from Him. This is something we’ll study more in our next blog titled, “The Essence of God in Things.”
Whether Anything but God Can Be Essentially Infinite
Nothing besides God is essentially infinite because everything is from God, who is the first principle. What is infinite has no beginning.
Thomas here speaks of absolute infinity versus relative infinity. Now, relative infinity seems to be a contradiction in terms, but let’s examine this.
Everything that actually exists contains form, and this form determines matter. Once we have the form determining matter, we have the latter determined by the former, which means that matter is finite. Matter now “remains in potentiality to many accidental forms” and is now relatively infinite, though absolutely finite. Thomas shows how wood, for example, is in potentiality to an infinite number of shapes.
Forms are in now way infinite once they are contracted to matter. However, there are some forms that are self-subsisting. So are they absolutely infinite, such as the angels? They are not because their being is derived from something else. They are not their own being. They are not the first principle.
Thomas answers objections
It seems that God has infinite power and therefore can produce an infinite effect.
Thomas answers that it is not possible for a made thing to have the same essence and existence. Subsistent being is not a created being. A made thing cannot be absolutely infinite. God cannot make a thing to be not made, so He cannot make a created thing be absolutely infinite.
The created intellect has infinite power for it can dwell upon the universal which has an infinite number of singular things.
The created intellect could be one of two things, according to Thomas. The intellect could be a form separate and apart from matter as is the case in the substance of angels. Or it is the case that it is the human soul, which is apart from an organ in the body.
Primary matter is apart from God and we have seen previously that it is infinite.
Primary matter does exist in nature since it is only in potentiality and not in actuality. It is relatively infinite because it only extends to natural forms.
Whether an Actually Infinite Magnitude Can Exist
Next, we move on to a very difficult topic — the infinity of magnitude and whether it can exist. I say this topic is difficult due to the objections and their replies.
First, let’s begin with Thomas’ initial response. Every body has a surface and that surface is the term of a finite body. This applies to a line as well. Therefore, nothing is infinite in magnitude.
Thomas points out a difference between something that exists in essence and something that exists in magnitude. He grants that something such as fire or air can exist in magnitude, but never in essence “because its essence would be terminated in a species by its form, and confined to individuality by matter.”
Having said this, Thomas goes on to determine whether any creature can be infinite in magnitude either naturally or mathematically.
First, he considers whether any natural body can be infinite in magnitude. It cannot be actually infinite, Thomas says.
“Every natural body has some determined substantial form.” We have seen how matter is not infinite when joined with a form and how form is contracted when it is assigned to a particular matter.
”Since therefore the accidents follow upon the substantial form, it is necessary that determinate accidents should follow upon a determinate form; and among these accidents is quantity.”
“So every natural body has a greater or smaller determinate quantity. Hence, it is impossible for a natural body to be infinite.”
Thomas goes on to demonstrate that an infinite body could not have any movement. It would be impossible for an infinite body to move because it occupies every place and could in no possible way move from one place to another.
An infinite body could not move circularly either. Lines drawn from the center would be infinite and they could never reach each other.
Mathematical bodies are not infinite either, according to St. Thomas. If we imagine a mathematical body actually existing, we would imagine it as having some form. The form for quantity is figure, which would show that a body is finite since it is “confined by a term or boundary.”
Thomas answers objections
Mathematics uses infinitude in magnitude, and, as Aristotle says, there is no deceit in that discipline. A geometrician would say in a demonstration, “Let this line be infinite,” and so forth.
Thomas replies that a geometrician doesn’t need to assume that a line is infinite, but rather simply calls a line infinite.
Another objection is that it does not go against the nature of magnitude to infinite. Finite and infinite belong to quantity.
Thomas says that “although the infinite is not against the nature of magnitude in general, still it is against the nature of any species of it.” It’s impossible to have an infinite bicubical or tricubical magnitude.
A third objection is that since magnitude is infinitely divisible, and since addition is opposed to division, and addition goes up while division goes down, it seems that we are reaching infinity through increase and decrease of numbers.
Thomas says that while we divide we are nearing matter. While we add we are nearing the whole, which has the aspect of form. Here we have form and matter. We especially note the form, which has a term or border.
The fourth objection is that “movement and time have quantity and continuity derived from the magnitude over which movement passes,” according to Aristotle. “Every determinant indivisible in time and circular movement is both a beginning and an end.” Therefore, there is an infinity of magnitude.
Thomas replies that movement and time are potentiality mixed with actuality. The infinite of quantity refers to matter, which is in potentiality, not in an infinite magnitude.
Whether an Infinite Multitude Can Exist
It is not possible for an infinite multitude to exist, whether it be absolutely infinite or accidentally infinite.
An absolutely infinite multitude cannot exist because a multitude is said to be absolutely infinite “when an infinite multitude is necessary that something may exist.” But this is impossible because for that something to exist it would have to be generated through an infinite medium.
Others, however, argued that something can be accidentally infinite as when “its existence is such is not necessary, but accidental.” Thomas says that for a carpenter, there is art in the soul, movement of the hand, and a hammer. But say that an infinite number of hammers are required because they keep breaking and that the work would be carried on for an infinite amount of time. In this way, we are dealing with an accidentally infinite multitude. (I don’t see the difference between this and absolutely infinite multitude.)
But Thomas says an accidentally infinite multitude is impossible as well. “Every kind of multitude must belong to a species of multitude.” Each species of multitude belongs to a species of number and this would be impossible because there can only be one multitude more than an another in actuality, not an infinity in actuality. Something, however, can be potentially infinite whether that number of multitude be divisible or added. As it is divided it nears matter, as we discussed previously.
Thomas answers objections
An actually infinite multitude is possible because potentiality can become actuality and number can be multiplied to infinity.
Thomas responds that things become actual successively and not all at once. A full day, for instance, becomes actual successively instead of all at once. So too does a larger multitude becomes actual over that of another.
Another objection is that it is possible for there to be an infinite number of actual species. “The species of figures are infinite.”
Thomas states that as an infinite of number is not all reduced to one act, neither is an infinite number of figures.
The final objection is that if we were to suppose that a multitude of species exist, there would be many others that would coexist and that can lead to infinity.
Thomas says that there would be one single species opposed to another if there were an infinite multitude of species.