I’ll be reviewing and summarizing the book “God Over All: Divine Aseity and the Challenge of Platonism” by William Lane Craig as I work my way through it. The topic this book deals with might be one of the most complex I’ve dealt with on this blog to date. Craig sets out to argue against the existence of abstract objects (like numbers, sets, or properties) since their existence would seem to pose an existential threat to the traditional orthodox understanding of God. Namely, that God exists a se, or that He is self-existent and is the sole ultimate reality (we will see how this robust doctrine has been understood by the biblical authors and early church fathers, and why a belief in abstract objects poses such a threat to it in the review of chapter two).

The first chapter, however, is meant to ground and define the terminology that will be used throughout the book. This will also serve as a helpful resource for readers of this blog to return to throughout this series.

DIVINE ASEITY

Divine aseity an attribute that theologians assign to God in order to describe His self-existence. The word comes from the Latin phrase a se, which means of itself or from itself. God just exists in and of Himself, independently of everything else. He is self-existing.

Craig also notes here that the attributes of God are typically divided into two categories: communicable attributes, and incommunicable attributes. The distinction between these categories is that it would seem some attributes are possessed exclusively by God, while others are shared with His creation to some extent. It is pointed out by Craig that aseity would clearly belong to the category of incommunicable attributes. To say so otherwise would lead to a logical contradiction, for it seems absurd to suggest that God could create something that is self-existant. So Craig asserts that God is the only being that possesses the attribute of aseity, and is thus “the sole ultimate reality.”[1]

PLATONISM

The strongest challenge to the doctrine of divine aseity is the philosophical system called Platonism. Named after the classic philosopher Plato (429-347 BC), he held that there exist uncreated entities other than God. These entities that he spoke of are not a part of our created physical world, but “are part of a transcendent, conceptual realm comprising what Plato called Ideas or Forms.” Though it may be hard to imagine what would inhabit a realm like this, Plato taught that this is where entities like mathematical objects, or geometric figures, like the perfect circle or perfect triangle, could be found. Plato also held that “far from being created by God, these transcendent realities served as God’s model or pattern after which He fashioned the physical world”

Craig concludes this section by noting that contemporary Platonism differs vastly from classical Platonism in different areas, but they both believe that these uncreated abstract objects exist.

ABSTRACT AND CONCRETE OBJECTS

We see from this section of the chapter that contemporary philosophy is somewhat undecided on how to clearly delineate the difference between abstract and concrete objects. Craig works his way through multiple attempts at a clear, accurate, and coherent definition.

1. The distinction between abstract and concrete objects is the same as between material and immaterial.

Although this may seem like the simplest way to form a definition of abstract and concrete objects, it fails almost immediately. For objects like souls and angels, if they exist, are clearly concrete objects rather than abstract. Entities like angels are causally active in our world, directing actions and causing events to happen. So it could be said that all abstract objects are immaterial, but not all immaterial objects are abstract objects. So it would seem this definition fails.

2. Concrete objects, whether material or immaterial, are all spatiotemporal objects, while abstract objects are without exception non-spatiotemporal objects.

Here, the term “spatiotemporal” just means “located in time and space.” So then a non-spatiotemporal object would be an entity that transcends space and time. Again, this definition fails. Because God, if He exists, is most certainly a concrete object rather than an abstract object. Although He currently resides within time and inserts himself into our physical reality, in the absence of creation/the universe God existed eternally without time, and without space.

Craig also points out that certain abstract objects like numbers plausibly exist outside of time, other abstract objects would seem to have temporal relations to the world. Take, for example, properties. “Particular things are constantly changing in their properties, acquiring some and losing others at different times. Properties must therefore exist in time.” So then, this proposed definition would seem to fail.

3. All concrete objects are metaphysically contingent.

Contingent here means that the object owes it’s existence to something outside of itself, as opposed to metaphysically necessary, where the non-existence of the object is impossible. This definition also fails. Since God, if He exists, is uncontroversially a concrete entity. 

By this point, it should be clear that defining the differences between abstract and concrete objects is difficult. But Craig seems to have found an attribute of abstract objects that seems to be unique to them, therefore giving us a clear idea of the distinction needed to advance the conversation.

4. Abstract objects, in contrast to concrete objects, are causally impotent and so are not related to other objects as causes to effects.

Here we see with this definition that abstract objects do not stand in a causal relationship with other objects. For example, if two apples are thrown through the air, they will cause some sort of effect on whatever they come into contact with. But if we remove the apples from the picture, it is absurd to think that the number 2 will cause something to happen. So then, “the criterion of essential causal impotence seems to delineate effectively abstract from concrete objects.”

TERMINOLOGICAL CLARIFICATIONS

Before concluding the chapter, Craig finishes by making a few more clarifications in the terminology that will be used throughout the book. 

Platonism/Anti-Platonism and Realism/Anti-Realism

“Platonism is the view that abstract objects exist, while anti-Platonism is the view that abstract objects do not exist. Sometimes these two views are equated with realism and anti-realism respectively, but this equation is misleading. For, as we shall see, there are anti-Platonists who believe in the reality of mathematical objects, propositions, and so on, but who think that these objects are concrete, not abstract.

For the purposes of this book, Craig suggests we use the term realism to be any view that objects like numbers exist, and anti-realism to describe any view that these objects do not exist. 

Nominalism

Craig needed to address this term here since it is used differently in two different philosophical debates. In the context of this book, the word is used as a synonym for anti-Platonism about abstract objects. Because of the confusion that is posed by a word with multiple philosophical and theological uses, Craig advises that use of “nominalism” should be avoided.

Platonism

Finally, Craig demonstrates that there are in fact two schools of thought in modern day Platonism. First, a type of ‘heavyweight’ Platonism, which says that abstract objects are just as real as the physical objects that make up the universe. Second, a type of ‘lightweight’ Platonism that obscures the reality of abstract objects by thinking of them more as semantic objects. Despite drawing attention to these two schools of thought in the debate, Craig says that the content of the rest of the book will focus on ‘heavyweight’ Platonism.

[1] Craig borrows this phrase from Brian Leftow, God and Necessity.