Introduction: Can Abstract Objects Threaten God’s Sovereignty?

In the realm of philosophical theology, the concept of abstract objects—things like numbers, properties, and logical principles—raises a profound question: can their existence threaten God’s sovereignty? If abstract objects exist independently and necessarily, does that limit God’s authority as the creator of all things? These questions are central to understanding the metaphysical relationship between God and reality. In this article, we explore the philosophical journey of addressing the issue of abstract objects, divine sovereignty, and God’s self-sufficiency, known as aseity.

God’s Sovereignty and the Challenge of Abstract Objects

The idea that abstract objects could exist independently of God poses a significant challenge to traditional Christian theism. The concept of God’s aseity asserts that God is self-existent and that everything else depends on Him for its existence. However, if abstract objects—such as numbers, propositions, or properties—exist necessarily and independently, they seem to be outside of God’s creative control. This notion undermines the idea of an all-sovereign, self-sufficient God who is the creator of all things.
Philosopher William Lane Craig encountered this challenge during his academic career and described it as one of the most powerful objections he had faced. It became clear to him that this issue needed to be addressed seriously to maintain a coherent understanding of God’s sovereignty. The problem is often framed in the context of Platonism, a philosophical position that holds that abstract objects exist independently and eternally, much like Plato’s “world of forms.”

The Indispensability Argument for Platonism

The primary argument in favor of Platonism is the indispensability argument. This argument asserts that abstract objects are indispensable to our understanding of reality, particularly in fields like mathematics and logic. If we use terms that refer to things like numbers or properties, and if we believe those statements are true, then we are ontologically committed to the existence of these abstract objects.
For example, when we say “the number two exists,” or “triangles have three sides,” we seem to be making statements about real objects. The indispensability argument concludes that since abstract objects are referred to in true statements, they must exist independently of our minds or any physical reality.

Facing the Challenge: Platonism vs. Divine Aseity

One way some philosophers attempt to reconcile Platonism with theism is through “absolute creationism,” which suggests that God creates abstract objects by His intellect. However, this approach runs into what is known as the “bootstrapping problem.” In order to create properties like “being powerful,” God would already need to possess that property. Therefore, it seems that some properties must already exist for God to be able to create them, leading to a kind of circularity.
Faced with this challenge, Craig sought to explore alternative ways to maintain God’s sovereignty while addressing the problem of abstract objects. Over the course of 13 years, he studied various approaches to find a resolution that would preserve both divine aseity and the coherence of Christian theism.

The Spectrum of Views on Abstract Objects

In his research, Craig mapped out a broad spectrum of views regarding abstract objects. On one side of the spectrum are realist positions, which hold that abstract objects are real. This category includes Platonism and its variants, such as absolute creationism. If abstract objects exist independently, they could either be uncreated (classical Platonism) or created by God (absolute creationism).
On the other side are anti-realist positions, which deny the existence of abstract objects. These views range from fictionalism, which claims that statements about abstract objects are literally false, to more nuanced positions like pretense theory and conceptualism. Pretense theory suggests that we “pretend” abstract objects exist for practical purposes, but they are not real in an ontological sense. Conceptualism, a view long associated with Christian theism, holds that abstract objects are thoughts in the mind of God.

Craig’s Anti-Realist Position: Neutralism

After much exploration, Craig found that an anti-realist view provided the best solution. He rejected the realist position, which he saw as unnecessary for explaining the world. Instead, he adopted what he called “neutralism.” According to this view, statements about abstract objects, like numbers or properties, can be true without committing us to their existence. For instance, when we say “two plus two equals four,” we are not necessarily claiming that the number two exists as an independent entity. The statement is true in a practical sense, but it does not require an ontological commitment to abstract objects.
Neutralism allows Craig to maintain that God is the creator of all things that exist, without the need to posit independent, uncreated entities like numbers or propositions. This approach preserves God’s aseity and sovereignty while offering a plausible way to account for the utility of abstract language in mathematics, science, and logic.

Other Anti-Realist Alternatives: Pretense Theory and Conceptualism

While Craig ultimately favored neutralism, he also explored other anti-realist views. One such view is pretense theory, which posits that abstract objects are “imagined” as part of a useful fiction. In this view, when mathematicians or scientists talk about numbers, they are engaging in a kind of make-believe that helps explain physical reality but does not commit them to the actual existence of numbers.
Another option is divine conceptualism, which remains a popular view among Christian philosophers. According to conceptualism, abstract objects are thoughts in the mind of God. Numbers, properties, and other abstract entities are not independent of God but exist as part of His perfect intellect. Craig noted that while this view has its merits, he ultimately found that neutralism offered a more compelling solution.

The Relationship Between Truth and Ontological Commitment

An essential aspect of Craig’s neutralism is the distinction between truth and ontological commitment. In neutralism, a statement can be true without committing us to the existence of the objects it refers to. For example, we can truthfully say, “Triangles have three sides,” without assuming that the concept of “three” exists as a separate, independent entity.
This approach is deflationary, meaning it reduces the metaphysical baggage associated with abstract objects while preserving the practical utility of statements involving them. Neutralism offers a way to use abstract concepts without violating God’s sovereignty or introducing unnecessary metaphysical complexity.

Conclusion: Reconciling God’s Sovereignty with Abstract Objects

Through years of exploration, I’ve found a perspective that preserves God’s sovereignty while addressing the challenge of abstract objects. This journey led me to appreciate the nuanced approaches within anti-realism and how they offer solutions that respect both logic and theology. If you’re interested in delving deeper into this fascinating topic, I encourage you to watch this insightful video, which expands on these ideas. You can find it here.