Here is an argument for Divine Simplicity inspired by this argument formulated by Alexander Pruss. In my argument, I define God as a maximally great being.
1. If God has parts, then either God has an actual infinity of parts or a finite amount of parts.
2. God has an infinity of parts only if there can be an actual infinity of concreta.
3. God has a finite amount of parts only if a finite amount of coconut trees on an island doesn’t prevent it from being a maximally great island.
4. An actual infinity of concreta is impossible.
5. An finite amount of coconut trees on an island prevents it from being a maximally great island.
6. Therefore, God has no parts.
1. This premise is essentially trivially true. It should be noted, though, that I take the claim that God has parts to be a real ontological claim about constituents that jointly compose the divine substance. That is, the denier of divine simplicity cannot fall back onto an anti-realist position about parts (that the parts of God are just ways we conceive of God’s essence) as that would be indistinguishable from the doctrine of divine simplicity.
2. Given that God is a concrete reality, the parts of God would be concrete realities. Hence an actual infinity of parts would be an actual infinity of concrete parts (not too controversial).
3. A common objection to Gaunilo’s lost island, one that I think is quite right, is that an island cannot be maximally great since it must have an finite amount of some constituent parts, e.g. coconut trees or, say, island beauties. But the addition of one more part would be greater, so finite parts are incompatible with maximal greatness. One might insist that the parts of God are not like trees or beauties. But why think that? Suppose you think, for instance, that God is three persons, but you deny that those persons are identical with God (as some theistic personalists are apt to do). Instead, you hold the view that the Father, Son, and Holy Spirit are parts of the Divine Substance. Why wouldn’t you be inclined to think that one more person would be greater? Perhaps you might have some argument about harmony to justify a particular finite set of person-parts, but it isn’t obvious that that sort of “aesthetic” judgment is objectively correct, or, if one is at all concerned with defending Christianity, that three persons achieves that harmony. Or, consider omnipresence. Does it entail that God is present in every spatial location? Some argue that omnipresence is entailed by omniscience, that God is present in all locations in so far as intellect is cognizant of those locations. But those who want to attribute parts to God want to say that God’s Intellect is a different part than, say, God’s will, love, power, etc. If so, it seems that only part of God is omnipresent, namely God’s intellect. But is all of God’s intellect cognizant of a location or only part of God’s intellect? Could more of God’s intellect be cognizant of a location? Could more of God’s parts be present in a given location? Could more locations add to the parts of God’s intellect? If so, it would seem that more parts of the intellect, more intellects, more wills, more love between more persons of the God-head would increase God’s greatness. But then a God with parts cannot be maximally great for the same reason an island, pizza, or human cannot be maximally great. A person who rejects divine simplicity, but holds that God has a finite amount of parts, needs to show that no addition of parts could make God greater. But prima facie, and absent any reason to think otherwise, I think it is reasonable to think that an addition to at least some of the finite sets of divine parts would make a non-simple god greater, which is to say that a maximally great non-simple God is impossible.
4. There are many arguments against an actual infinity of concreta. Consider, for example, Craig’s use of Hilbert’s Hotel and related paradoxes.
5. As mentioned in my defense of (3), there doesn’t seem to be a finite amount of coconut trees (or island beauties) that would be consistent with an island being maximally great. All else being equal, an island with 100 coconut trees seems to make an island greater than some island with 99 coconut trees. We might suppose then that, all else being equal, an island with n coconut trees is less great than an island with (n+1) coconut trees. Therefore, a maximally great island with finite parts is impossible. Given that all islands are necessarily finite, a maximally great island is a logical absurdity, which is why I think most parodies of the ontological argument are ineffectual. They depend upon substituting “God” with something that is implicitly a finite composite. Now, one might say that there are other reasons for why a maximally great island is impossible, e.g. such an island must be a contingent thing given its dependence on space and time. But surely the finitude of great-making island properties are among the reasons such an island cannot be.
I think (1)-(5) are defensible and true. Therefore, I think God has no parts, i.e. God is simple. QED