Introduction: The Dilemma of God’s Sovereignty and Abstract Objects

The relationship between God and abstract objects presents one of the most profound challenges in philosophical theology. Can an omnipotent, sovereign God coexist with uncreated, eternal abstract objects like numbers, logic, and forms? This article delves into the complex issue of God’s sovereignty and how it interacts with abstract objects. Through exploring various philosophical approaches, including platonism, conceptualism, and anti-realism, we’ll unravel the ways theologians attempt to maintain God’s absolute authority while addressing the existence of abstract entities.

Why Abstract Objects Challenge God’s Sovereignty

For many believers, God is the supreme, self-sufficient being, existing independently of anything else. This concept of divine *aseity*—God’s ability to exist entirely by Himself—forms the foundation of Christian theology. However, the existence of abstract objects, such as mathematical truths or logical laws, poses a threat to this sovereignty. If these objects exist necessarily and independently of God, does that mean God is no longer supreme?
This dilemma has deeply troubled Christian philosophers. Dr. William Lane Craig, a prominent theistic philosopher, calls the existence of abstract objects one of the most powerful objections to God’s sovereignty. He argues that if these objects are eternal and uncreated, then they undermine God’s self-sufficiency, posing a greater challenge than even the problem of evil.

The Indispensability Argument for Abstract Objects

One of the main arguments in favor of abstract objects is known as the indispensability argument. According to this view, certain objects—such as numbers, sets, or propositions—are indispensable to our understanding of reality. For example, when we say, “There are five apples on the table,” we implicitly refer to the number “five.” If statements like these are true, then abstract objects like numbers must exist.
The second premise of this argument is that because these abstract objects are part of our everyday language and scientific understanding, they must exist independently and necessarily, just like God. This is where the tension lies: if abstract objects exist as necessarily as God does, how can God maintain His sovereignty over everything?

Realism and Platonism

Realism is the belief that abstract objects exist independently of human thought. One of the most well-known forms of realism is platonism, which holds that abstract objects exist in a realm of their own, separate from the physical world and even from God. This idea, first introduced by the ancient Greek philosopher Plato, suggests that objects like numbers or forms have an eternal, unchanging existence.
For a platonist, mathematical truths or logical principles are not created by God but exist independently and necessarily. This view directly conflicts with the idea of God as the creator of all things, leading many theistic philosophers to seek alternatives.

Conceptualism: Abstract Objects as Divine Thoughts

One alternative to platonism is *conceptualism*, the idea that abstract objects exist as thoughts in the mind of God. Instead of being independent, these objects are creations of God’s intellect. This view preserves God’s sovereignty because it suggests that numbers, logic, and other abstract entities depend entirely on God for their existence.
Conceptualism aligns with traditional theistic views of God as the creator of everything, including abstract concepts. If abstract objects are merely ideas in God’s mind, then they do not challenge His self-sufficiency. This approach has been historically embraced by theologians like Augustine and more recently by Alvin Plantinga, a prominent Christian philosopher.
However, conceptualism faces its own challenges. For example, if God creates abstract objects, does He possess these properties Himself before creating them? This leads to what philosophers call the “bootstrapping problem”—the idea that God would need to possess certain properties in order to create those properties, resulting in a circular explanation.

The Problem of Bootstrapping

The bootstrapping problem arises when we try to explain how God creates properties that He Himself must already possess. For instance, to create the property of “being powerful,” God would need to already be powerful. This creates a kind of explanatory loop, where God must rely on properties that He has not yet created. This circularity makes conceptualism less attractive to some philosophers, who see it as an inadequate solution to the problem of abstract objects.

Anti-Realism: Rejecting the Existence of Abstract Objects

Another approach to resolving the tension between God’s sovereignty and abstract objects is *anti-realism*. Anti-realists argue that abstract objects do not actually exist. Instead, they are simply useful fictions or convenient linguistic tools that help us describe the world. In this view, statements about numbers or logical principles are true in a practical sense but do not commit us to the actual existence of these entities.
One anti-realist theory is known as *pretense theory*, which suggests that when we talk about abstract objects, we are merely pretending that they exist. For example, when we use mathematical language, we are engaging in a kind of intellectual game that helps us understand the physical world, but we are not making any ontological commitment to the existence of numbers themselves.
Another anti-realist approach is *neutralism*, which holds that statements about abstract objects can be true without implying that those objects actually exist. Neutralism avoids the pitfalls of both realism and fictionalism by allowing us to speak about abstract entities without committing to their existence.

Neutralism: A Middle Ground

Neutralism, as championed by philosophers like Jody Azzouni, offers a middle ground between realism and anti-realism. According to this view, statements about abstract objects are true, but they are not ontologically committing. In other words, we can talk about numbers, sets, and propositions without claiming that these things exist independently in some abstract realm.
For theists, neutralism is an appealing option because it avoids the theological challenges of platonism while still allowing us to use mathematical and logical language meaningfully. Neutralism preserves God’s sovereignty by denying the existence of independent abstract objects, yet it acknowledges the practical usefulness of these concepts.

Conclusion: Inspired by Philosophical Inquiry

After exploring these various perspectives, it becomes clear that the question of God and abstract objects is far from simple. From realism to anti-realism, philosophers continue to grapple with how to reconcile God’s sovereignty with the existence of abstract entities. While conceptualism offers a theistic solution, anti-realist views like neutralism provide a way to navigate these issues without compromising God’s supremacy.
I found inspiration in Dr. William Lane Craig’s approach to this complex topic. His deep philosophical exploration has shaped my understanding of this profound issue. If you are intrigued and want to dive deeper, I recommend checking out this insightful video: William Lane Craig Retrospective V: God and Abstract Objects | Closer To Truth. It may challenge and broaden your perspective on God, reality, and the nature of abstract objects.