There is One God

By delaying this issue until Question 11 in the First Part of Summa Theologiae (and chapter 42 in the SCG, I), Thomas is indicating that it is easier to prove that there is at least one God than it is to prove that there is no more than one. It is also important to realize that the ‘one’ that we appeal to in proving God’s unity is not the number 1, but the concept of oneness that is convertible with being. God is supremely one precisely because He is supremely a being. We don’t count gods in the same way that we can count apples or doors. As we shall see, the nature of God excludes the very possibility of there being two or more gods. At the same time, since the oneness involved is not that of the numerical one, Thomas is leaving open the door for God’s being, in some sense, a plurality or multitude. This will help in working through both the problem of God’s ideas  and the Trinity.
 
In Summa Theologiae I, Q11, article 1, Thomas explains that the focal meaning of ‘one’ in ‘there is one God’ is that of being undivided. God is supremely indivisible, and this follows from His simplicity. Thomas argues that if oneness were not convertible with being, an infinite regress would result. If oneness is not equivalent to being, then it would have to be something that is added to being. But then we can ask what makes this addition one addition, and an infinite regress follows.
 
But what about multitudes, like crowds of people? If they exist, they must also be one. And, indeed, a crowd is one crowd. But how can something be both one and many? Isn’t that inconsistent? Thomas anticipates here an answer given much later by the German logician Gottlob Frege. A multitude is one in one way, and many in another. It is, for example, one crowd but many people. Thomas elaborates this point in article 2, again distinguishing between one as the principle of number and one as convertible with being. We can ask for the number of a crowd, and this question must appeal to some way of dividing the crowd—into families, or individuals, or human cells.  At the same time, a crowd must be, like anything that exists, in some more basic sense one thing. Some more recent metaphysicians, following the work of American logician George Boolos, have suggested that multitudes can exist without being one thing at all. Very large proper classes, like the class of all sets, for example, seems to be a real multitude that is not in any sense one thing. If this is right, it could create some difficulty for some of Thomas’s proofs (in article 3) for God’s oneness. Or, it might simply point to the fact that the oneness of God is consistent with His comprising a kind of multiplicity, so long as these things are not parts or attributes of God.
 
In objection 4, Thomas addresses the problem of the definition of one as undivided. Being undivided is a negative notion, signifying the absence of division. But being is perfectly positive. So, how can being be convertible with oneness? Thomas replies that division is prior to one only in the order of our understanding. Ontologically, being undivided is prior to being divided. It’s just that we are first aware of composite things before we are aware of their simple parts.
 
In article 3, Thomas offers three arguments for the oneness of God. The first argument appeals to God’s simplicity. God is made to be God by His divine nature, and that divine nature also makes Him exist as a particular being. For there to be two gods, there would have to be two divine natures, each of the same species. But for two natures to exist with the same species, there would have to be something responsible for making each distinct from the other. So, for example, two men can be two by virtue of being combined with two packets of prime matter. Two packets of prime matter have no actual nature of their own, and so they can be fundamentally or primitively distinct. The divine nature is an actual nature (it is maximally actual), and so two divine natures cannot be fundamentally distinct. Since God is identical to His own nature, there cannot be two instances of the divine nature, just as there cannot be two instances of a single angelic species.
 
In the second argument, Thomas appeals to God’s infinity. (This is a new argument, not present in the SCG.) In fact, he appeals to the infinity of God’s perfection, by which he means that nothing can be superior to God in perfection. Suppose that there were two such maximally perfect beings. In this argument, Thomas concedes (for the sake of argument) that there could be two distinct species of god. If there were two such species, something would have to differentiate them. One would have to have something that the other did not have. But this means that one would have to have some form of perfection that was lacking in the other. But God has all perfections. So, in fact, this argument actually appeals to God’s perfection, rather than His infinity.
 
Third, Thomas appeals to the apparent unity of the world. This is one of the relatively few cases in which Thomas appeals to some form of the Fifth Way—pointing to God as the cause of the world’s systematic harmony, the fact that the active and passive powers of the world’s created substances fit together in order to make a stable, scientifically intelligible universe. Thomas gives a more detailed version of this argument in Summa Contra Gentiles 1.42, paragraph 7.
 
In Summa Contra Gentiles 1.42, paragraph 5, Thomas also appeals to some details of Aristotle’s natural philosophy, especially the assumption that the movement of the heavenly spheres are regular and continuous. It’s not clear to me whether any of this can be salvaged, given the falsity of Aristotle’s astronomy.
 
In paragraph 8, Thomas argues that if there were two gods, at least one would have to be composite. But no composite being could be necessary through itself (as established in the Third Way). It’s not obvious here why one of the gods would have to be composite, but the two arguments that Thomas gives in the Summa Theologiae support this premise: either the two gods would belong to the same species, in which case each would have to have a part that individuates it from the other, or they would belong to two species, in which case each would have to add some differentia to their common genus.
 
Paragraphs 9-11 contain another interesting argument that appeals to God’s necessity of being. This argument involves a complex dilemma: if there were two necessary beings (each necessary per se), then either (1) the two differ by something required for the completion of the necessity of being, or (2) not.
 

• Assuming (2). (Paragraph 9) If not, then they are different by something accidental. This accident must have a cause (since all accidental additions must be caused), which is either (a) the essence of the necessary thing, or (b) some external thing. We can rule out (a), since both necessary beings would have the same accident, if it is a proper accident determined by their common essence. If (b), then the existence of two necessary beings depends on the action of this third thing. But then the existence of each thing would also depend on the third thing, and so neither could be necessary in itself.
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• Assuming (1). (Paragraph 10) That which differentiates the two necessary beings would be either (a) something included in the common nature of necessary being, or (b) something that differentiates the two natures into two species. Case (a) is impossible because in that case, the factor will be present in both necessary beings. In case (b), the common nature must be made actual by each of the two differentiae, in which case, each necessary being would derive its existence from something else. Hence, the two things cannot be necessary in themselves, nor could each be simple and identical to its own act of existence. This complex argument seems to be mirrored in the first two arguments in the Summa Theologiae. The SCG helps us to see that these are really two parts of a single argument, based on a dilemma (either one species of god or two).

 
Paragraph 12 involves a very simple argument, based on the thesis that God is identical to His nature and to His act of existence. If there were two gods, then each god would have the same divine nature. But this divine nature would then have to be identical to two distinct acts of existence. But nothing can be identical to two distinct things.
 
Paragraphs 13 and 14 contain another complex argument.
 

1. If x is a per se necessary being, then x’s necessary being belongs to x insofar as it is x. That is, the necessity of x is grounded by x’s being x.
2. Suppose there were two per se necessary beings, x and y. Then x’s being x would also consist in x’s not being y, since if x and y are distinct, x’s being x depends on its not being y.
3. Consequently, x’s necessity would belong to it insofar as x is distinct from y.
4. This means that x’s necessity depends on the existence of y.
5. Consequently, x’s necessity would not be per se. Contradiction
6. So, there cannot be two per se necessary beings.

 
Thomas defends premise 1 in paragraph 14. If x’s necessary being depends only on x, then x’s necessary being must belong to x insofar as it is x.
 
In paragraph 18, Thomas appeals to the fact that God is supreme being. Since being is convertible with oneness, God must be supremely one, and so undivided. This applies equally well to the divine nature.
 
Thomas also appeals in paragraph 20 to the superiority of monarchy as the form of government. Since God is the perfect governor of the universe, God must be one.