Simplicity and aseity

He is necessary, self-existent. This means, for example, that God is not composed of elements that are more ultimate, in a logical or metaphysical sense, than he is. 

[Simplicity] denies that God is physically, logically, or metaphysically composite. Non-composition, it is argued, must characterize God inasmuch as every composite is a dependent thing that cannot account for its own existence or essence and stands in need of some composer outside itself. To be composite is to be composed by another and to be dependent upon the parts that enter into the composition. Furthermore, composition signifies the capacity of a thing to change or even be annihilated…no composite entity can be "most absolute" inasmuch as it requires some entity prior to itself to account for the composition and is thus relative to the entity. Also, each composite thing must possess the capacity to come into existence from nonexistence, go out of existence and, in most instances, change while in existence.

George Joyce observes, "The real significance of the notion of Ens a se is to deny that God is, like creatures, caused by another. He is conceived as self-existent in the sense of unoriginated'" 

The basic logic is that if God were composed of parts he would, in some sense, depend upon those parts inasmuch as those parts would be indispensable to the explanation of his existence and essence. James E. Dolezal, God without Parts: Divine Simplicity and the Metaphysics of God's Absoluteness (Pickwick 2011), xii, 31-32, 71-72.

1. It's necessary to explicate and disambiguate all the dubious assumptions in the way Dolezal frames the issue.

2. I'll say more about this, but notions of composition, parts, &c. rely on explicit or implicit paradigm-examples. 

3. What does Dolezal mean when he says that God is devoid of "logical" or "metaphysical" composition? One way to unpack this is to deny "real distinctions" in God. 

4. What is a "part"? Parthood is a comparative concept. A part/whole relation.

5. Consider some definitions of parthood:

• Piece of something

• Subdivision 

• Fraction

• Section

• Smaller unit

6. Parthood is typically a quantitative notion.

7. Parthood is typically based on physical objects, especially spatial objects. 

8. Parthood can be extended to a process, like watching a move or hearing a musical performance. Temporal parts as well as spatial parts. 

9. Physical parts are:

i) Contingent

ii) Detachable

iii) Replaceable

iv) Interchangeable

10. Stock examples of composite objects include:

i) A brick wall

ii) A car (auto parts) 

iii) A Swiss watch

11. Sometimes a part of a system is physically separate from the system, viz. the remote on a radio control airplane.  We might say the remote is a functional component rather than a unit it's made of. 

12. One fundamental issue is whether parthood/composition is still meaningful if we attempt to extend that concept to abstract objects (i.e. timeless, spaceless entities). If we try extrapolate from paradigm examples of concrete objects to abstract objects, does the concept become so attenuated that the comparison is vitiated by equivocation? 

Are abstract properties "parts"? Or is that characterization beset by so many qualifications, compared to the original basal examples, that it's too disanalogous to be an applicable category? 

13. Suppose our starting-point is abstract objects rather than concrete objects. Consider some paradigm examples of abstract complexity:

i) The Mandelbrot set

ii) The number Pi

iii) Modus ponens

iv) Reflection symmetries

Their internal complexity doesn't imply a capacity to change, come into being, or pass out of existence. Their constituent elements aren't contingent, detachable/separable, replaceable, interchangeable. So they're not composite objects in the usual sense. Why aren't some abstract objects a better model to illustrate metaphysical complexity? 

14. There's a sense in which Pi "depends" on having a unique decimal expansion. There's a sense in which the Mandelbrot set "depends" on self-similar iterations. There's a sense in which modus ponens "depends" on the elements of the logical formula. But that doesn't generate the same consequences as composite physical objects. They aren't created by adding or combining smaller units to form them. 

15. God would not be God unless he were omnipotent. So doesn't his existence "depend" on his omnipotence? 

16. In Nicene theology, the Father necessarily generates the Son. In that event, not only does the Son's existence "depend" on the Father, but the Father could not exist apart from the Son. That's a dependence-relation. A mutual dependence-relation, even though its asymmetrical. (I myself don't subscribe to eternal generation, but exponents of Thomistic simplicity typically do.) 

17. If God has real internal relations, how does that imply that God is "caused" by his internal relations? Doesn't causation involve contingent relations and temporal relations? 

18. Even if we grant for discussion purposes that God is "composed" of "parts", yet assuming those are divine "parts", then God isn't composed of something "outside" himself. Even in that case, God isn't caused by "another". 

19. Perhaps Dolezal means "other than" in the sense of "lesser than". "Lesser" in the sense of "smaller" elements–smaller in relation to the whole. 

You might say any finite sequence in the decimal expansion of Pi is less than the entire infinite series. And that's a "real distinction" inasmuch as one numerical sequence differs from another. But how is that a problem? Although any particular sequence is a "subdivision" of the whole, that's not contingent or detachable from the whole. You might say a particular iteration of the Mandelbrot set is a "subdivision" of the whole. Infinite self-similar iterations. But that's not contingent or detachable from the whole. Rather, these are static, necessary internal relations.  

20. In addition, the part/whole framework is misleading. Take reflection symmetries. Each image of the "other" contains the whole image. In paired mirror images, it isn't part of the image; rather, the reflection contains the entire image of what it mirrors. 

Assuming I understand Dolezal's position, I find it hopelessly equivocal and confused. It suffers from impoverished conceptual resources.