Introduction: God’s Sovereignty and Abstract Objects

The nature of God and His sovereignty is one of the most profound questions in theology and philosophy. An interesting debate in this regard revolves around how God’s absolute sovereignty interacts with abstract objects like numbers, properties, and mathematical concepts. Can God remain sovereign if there are uncreated, eternal abstract objects? This question has challenged theologians and philosophers alike. In this article, we explore how these abstract objects may threaten God’s autonomy and how various philosophical responses aim to resolve this issue.

Understanding the Challenge of Abstract Objects

At first glance, abstract objects may seem irrelevant to the question of God’s sovereignty. After all, these objects—like numbers or logical truths—exist independently of any physical form. However, their very existence raises a significant question: if these objects exist independently of God, does that undermine God’s claim to be the creator of everything? If these abstract objects are uncreated and eternal, it would seem that something exists apart from God’s will, which contradicts the traditional understanding of God as the self-sufficient being who creates and sustains everything.
This concern is not new, but it became particularly pressing for theologians like William Lane Craig, who first encountered the challenge during a philosophical conference. The concept that abstract objects exist independently and necessarily—much like God—posed one of the most compelling objections to God’s sovereignty Craig had ever encountered. In fact, he found it to be a more powerful objection than traditional challenges, such as the problem of evil.

Platonic Realism and the Existence of Abstract Objects

The view that abstract objects exist independently is known as Platonic realism. According to this view, abstract objects like numbers, properties, and sets exist necessarily and are not contingent upon God. They are timeless, spaceless, and non-physical. This presents a problem for theists who hold that God is the sole necessary being. If abstract objects exist necessarily, they seem to rival God’s self-sufficiency.
The indispensability argument for Platonism is one of the most prominent defenses of this position. This argument states that since abstract objects are indispensable to our best scientific and mathematical theories, we are ontologically committed to their existence. For example, when we say that “2 + 2 = 4,” we are referencing the number 2 as an existing abstract object. If these references are true, then abstract objects must exist.
However, not all theologians or philosophers agree with this conclusion. Some argue that abstract objects could be created by God. Others suggest that these objects don’t exist at all and are simply useful fictions.

Absolute Creation and the Bootstrapping Problem

One proposed solution to the problem of abstract objects is known as “absolute creationism.” This view suggests that abstract objects are not independent of God but are created by Him. In this way, God would retain sovereignty, as all things—abstract and concrete—would depend on Him for their existence.
However, absolute creationism encounters a significant problem, often referred to as the “bootstrapping problem.” This arises when we consider the nature of properties, which are often seen as abstract objects. For example, in order for God to create the property of being powerful, He must already be powerful. Thus, God would need to possess the property before creating it, which leads to a kind of circularity.
Due to this bootstrapping issue, absolute creationism has not been widely accepted as a viable solution. Instead, philosophers have turned to other approaches, such as conceptualism and anti-realism, to reconcile God’s sovereignty with the existence of abstract objects.

Conceptualism: Abstract Objects as Divine Thoughts

Conceptualism is the view that abstract objects are not independent entities but are instead thoughts in the mind of God. Under this theory, numbers, properties, and other abstract objects exist because God conceives of them. This approach aligns well with the traditional theistic view that God is the source of all reality.
In this view, abstract objects are not created in the traditional sense but come into existence as thoughts in God’s mind. This preserves God’s sovereignty because these objects depend entirely on God’s intellect. Thus, God remains the only self-sufficient being, and abstract objects pose no threat to His autonomy.
Conceptualism has been a popular solution among theologians and philosophers, including Alvin Plantinga. It avoids the bootstrapping problem and maintains that God is the source of all existence. However, it does require a strong commitment to the idea that thoughts can have the same ontological status as physical or independent abstract objects.

Anti-Realism and the Fictionalist Approach

Another solution to the problem of abstract objects is anti-realism. Anti-realists argue that abstract objects do not exist independently. Instead, they are useful fictions or mere linguistic conventions that help us make sense of the world. For example, when we talk about numbers or mathematical truths, we are engaging in a kind of “make-believe” that allows us to function scientifically and mathematically without committing to the existence of abstract objects.
Within anti-realism, various sub-theories offer different explanations. One of the most prominent is fictionalism, which suggests that statements about abstract objects are false, but they are useful in helping us understand the world. Fictionalists argue that just as we can talk about fictional characters like Sherlock Holmes without believing they exist, we can talk about numbers or sets without believing they are real entities.
William Lane Craig, after years of study, has embraced a form of anti-realism that he refers to as “neutralism.” Neutralism holds that while statements about abstract objects may be true, they are ontologically neutral, meaning they do not commit us to the existence of the objects they reference. This view allows for the truth of mathematical statements without the metaphysical baggage of admitting abstract objects into our ontology.

Conclusion: Reconciling God’s Sovereignty with Abstract Objects

The question of whether abstract objects threaten God’s sovereignty is a profound one. While Platonic realism presents a challenge, various philosophical approaches like conceptualism and anti-realism offer ways to maintain God’s absolute sovereignty. Conceptualism preserves the existence of abstract objects as thoughts in the mind of God, while anti-realism denies the independent existence of these objects altogether.
After extensive research, William Lane Craig has found philosophical peace with neutralism, a form of anti-realism that avoids ontological commitment to abstract objects while acknowledging the utility of statements about them. This approach maintains that God remains the only self-sufficient being, upholding the traditional view of divine aseity.
If you are interested in diving deeper into this fascinating discussion, I encourage you to watch the full conversation: here.