An Argument from Uniqueness
The following argument occurred to me the other day. I do not know if anything similar has been argued (please let me know in the comments, if you are aware of something similar). I call it an argument from uniqueness. Basically, the argument is:
1. If God does not exist, necessarily it is not the case that there is an essential property, uniqueness, that is exemplified.
2. Possibly, the essential property, uniqueness, is exemplified.
3. Therefore, God exists.
A defense of the premises:
I argue that (1) is true, given that I am understanding “God” in the Thomistic sense (I am appealing to concepts specified by Thomas in the Summa Theologiæ). Now, Uniqueness is attributed to God in many theistic traditions, but let me stipulate what I think Thomas means, and why I think (1) follows from it.
Some theists understand the “uniqueness” of God to mean that only God has all perfections, i.e. there is no other being that is omniscient, omnipotent, and morally perfect. But, I take Thomas to be saying something a bit more radical than that. For, the God Thomas describes is said to be the exemplification of Being itself:
God is His own essence, as shown above (Article 3) if, therefore, He is not His own existence He will be not essential, but participated being. He will not therefore be the first being–which is absurd. Therefore God is His own existence, and not merely His own essence. (ST. I 3.4).
So, the first point is that God is the only being that is its own act of existence. All other sorts of beings are participated being, which is to say that they receive the act of being from without and not per se. What’s more, since God’s essence is existence, God does not belong to any genus. Thomas provides three arguments for why God lacks a genus, and this relates directly to why God is unique (ST. I.3.5):
First, because a species is constituted of genus and difference. Now that from which the difference constituting the species is derived, is always related to that from which the genus is derived, as actuality is related to potentiality. For animal is derived from sensitive nature, by concretion as it were, for that is animal, which has a sensitive nature. Rational being, on the other hand, is derived from intellectual nature, because that is rational, which has an intellectual nature, and intelligence is compared to sense, as actuality is to potentiality. The same argument holds good in other things. Hence since in God actuality is not added to potentiality, it is impossible that He should be in any genus as a species.
Secondly, since the existence of God is His essence, if God were in any genus, He would be the genus “being”, because, since genus is predicated as an essential it refers to the essence of a thing. But the Philosopher has shown (Metaph. iii) that being cannot be a genus, for every genus has differences distinct from its generic essence. Now no difference can exist distinct from being; for non-being cannot be a difference. It follows then that God is not in a genus.
Thirdly, because all in one genus agree in the quiddity or essence of the genus which is predicated of them as an essential, but they differ in their existence. For the existence of man and of horse is not the same; as also of this man and that man: thus in every member of a genus, existence and quiddity–i.e. essence–must differ. But in God they do not differ, as shown in the preceding article. Therefore it is plain that God is not in a genus as if He were a species. From this it is also plain that He has no genus nor difference, nor can there be any definition of Him; nor, save through His effects, a demonstration of Him: for a definition is from genus and difference; and the mean of a demonstration is a definition. That God is not in a genus, as reducible to it as its principle, is clear from this, that a principle reducible to any genus does not extend beyond that genus; as, a point is the principle of continuous quantity alone; and unity, of discontinuous quantity. But God is the principle of all being. Therefore He is not contained in any genus as its principle.
So, since God is not in any genus, there cannot be other beings that have the same essence, or other kinds of beings that are their own act of existence. Hence Thomas writes (ST. I.11.3):
First from His simplicity. For it is manifest that the reason why any singular thing is “this particular thing” is because it cannot be communicated to many: since that whereby Socrates is a man, can be communicated to many; whereas, what makes him this particular man, is only communicable to one. Therefore, if Socrates were a man by what makes him to be this particular man, as there cannot be many Socrates, so there could not in that way be many men. Now this belongs to God alone; for God Himself is His own nature, as was shown above (Question 3, Article 3). Therefore, in the very same way God is God, and He is this God. Impossible is it therefore that many Gods should exist.
To say that God does not exist is to say that the “being who is its own act of existence” does not exist. But, if such a being were to exist, necessarily it would exist, since there would be no potential in its essence for its non-existence. By contraposition, God’s non-existence entails God’s impossibility—there would be neither the potential nor the actuality of anything being its own act of existence. So, if God does not exist, it is not possible that there is a being who is its own act of existence. And if it is not possible that there is a being who is not its own act of existence, then all beings that do exist would fall under one category of being or another. Thus, if every being falls under one category (highest genus) or another, no being is essentially unique. For, every being would the same at least with respect to other members that fall under the same category, e.g. one quantity would not be uniquely a quantity, since another quantity exists.
Put simply, if God does not exist, everything that exists would be the same as something else at least with respect to the highest genera. Thus, God’s non-existence entails the impossibility of essential uniqueness.
My defense of (2) will be much more brief. There is nothing within the concept of essential uniqueness that implies a contradiction. Therefore, it is not impossible that essential uniqueness is exemplified. In fact, our discussion of the first premise provided a coherent account of how essential uniqueness could be exemplified, namely if a being that is its own act of existence were to obtain. Nothing in that discussion seemed inconsistent, so there is, at the very least, prima facie plausibility that the second premise is true.
From these two premises, the conclusion necessarily follows that God exists. The deduction is as follows:
θx – x is a Thomistically defined divine being
U – Uniqueness
Π – Essential Property
1. ~(∃x)θx → □~(∀x)(∃Π)[Πx & (Π = U) (premise)
2. ◊(∀x)(∃Π)[Πx & (Π = U)] (premise)
3. ~~◊(∀x)(∃Π)[Πx & (Π = U)] (2 DN)
4. ~□~(∀x)(∃Π)[Πx & (Π = U)] (3 MN)
5. ~~(∃x)θx (1,4 MT)
6. (∃x)θx (5 DN)