Introduction: The Challenge of Abstract Objects to God's Sovereignty

The relationship between God and abstract objects, such as numbers, forms, and logic, has long puzzled philosophers. For those who believe in a sovereign God who created everything, the existence of abstract objects poses a unique problem. If these objects exist independently, how can God be truly sovereign? Are there things that exist outside of God’s control?
In this article, we dive deep into this philosophical debate, exploring the nature of abstract objects and how they may challenge the traditional view of God’s absolute autonomy.

Understanding Abstract Objects and God's Independence

Abstract objects, like numbers or mathematical truths, are often thought of as timeless and uncreated. Philosophers have debated whether these objects exist independently of God or if God somehow creates them. If they exist independently, it could mean that there is something in reality that even God didn’t create, threatening His absolute sovereignty.
This issue gained significant attention in theological and philosophical circles due to the work of thinkers like William Lane Craig, who has dedicated much of his career to exploring this problem. He considers it one of the most difficult challenges to theism, even more pressing than the problem of evil. For Craig, the central question is: How can God be self-sufficient (what philosophers call *aseity*) if abstract objects exist independently of Him?

What Are Abstract Objects?

Abstract objects refer to things like numbers, logical truths, and properties that don’t exist physically but are often thought to exist nonetheless. They are not part of the material world but are critical to understanding how the world functions. For example, the number two doesn’t exist in the same way a tree or a rock does, but it seems to be a real part of how we describe and interact with the universe. Mathematical truths exist regardless of human minds, which leads to the question of whether these truths are dependent on God or exist outside of Him.
One of the primary concerns in this debate is the concept of God’s aseity. Aseity means that God exists independently, without any need for external factors. If abstract objects like numbers and logical truths exist on their own, then God might not be entirely independent, undermining His sovereignty.

Platonism and the Indispensability Argument

A common view supporting the independent existence of abstract objects is Platonism, named after the ancient philosopher Plato. Platonism holds that abstract objects exist in a realm of their own, separate from both the physical world and God. According to Platonists, these objects exist necessarily and eternally, meaning they cannot be created or destroyed.
The most significant argument for Platonism is the *indispensability argument*, which states that abstract objects are indispensable for making sense of the world. For example, mathematics is essential for physics and other sciences, and without abstract objects like numbers, it would be impossible to describe the natural world. Therefore, if abstract objects are indispensable, they must exist independently of anything else, including God.
This argument poses a direct challenge to the idea of a sovereign God. If these objects are uncreated, how can God be the creator of all things? Does this mean that God is not truly sovereign over everything in existence?

God as the Creator of Abstract Objects: The Absolute Creation View

Some philosophers, such as Tom Morris, have proposed a compromise known as the *absolute creation* view. This perspective holds that abstract objects, like numbers and properties, are not independent of God but are created by Him. According to this view, God is the source of all reality, including abstract objects, which He creates through His intellect.
While this view attempts to preserve God’s sovereignty, it introduces a new problem: the *bootstrapping problem*. To create a property like "power," God would already need to possess the property of being powerful. In other words, creating abstract objects would require God to already have the very properties He is supposed to create, leading to a circular and problematic explanation. This bootstrapping issue has made many philosophers uncomfortable with the absolute creation view.

The Anti-Realist Approach: Rejecting the Existence of Abstract Objects

William Lane Craig has spent over a decade exploring various solutions to the problem of abstract objects, and he has come to favor an anti-realist approach. Anti-realists reject the idea that abstract objects exist in any meaningful way. Instead, they argue that references to things like numbers or logical truths are simply useful fictions or linguistic conveniences, but they do not imply the existence of independent entities.
This anti-realist view allows Craig to maintain that God is truly sovereign and independent. Since abstract objects do not actually exist, there is nothing outside of God’s control. According to this view, when we talk about numbers or logical principles, we are not describing real, independent entities but rather engaging in a useful fiction that helps us navigate the world.
One version of anti-realism is called *pretense theory*, which suggests that we are simply pretending that abstract objects exist to make our mathematical and scientific descriptions work. Another view, known as *neutralism*, holds that statements about abstract objects are neither true nor false—they are simply neutral with respect to reality. In either case, God remains the only truly self-existent being, as abstract objects do not challenge His sovereignty.

Conceptualism: A Middle Ground

While Craig favors an anti-realist approach, he also acknowledges that *conceptualism* could serve as a fallback position. Conceptualism argues that abstract objects are not independent entities but rather thoughts in the mind of God. In this view, numbers, properties, and logical truths are all ideas that exist in God’s mind. This allows God to remain the creator of all things, even abstract objects, without the problems associated with absolute creation.
For many Christian philosophers, conceptualism offers a satisfying middle ground. It preserves God’s sovereignty by making abstract objects dependent on God, while also recognizing their role in mathematics and science. Although Craig leans toward anti-realism, conceptualism remains a viable alternative for those who find it difficult to reject the existence of abstract objects altogether.

Conclusion: Maintaining God's Sovereignty

The relationship between God and abstract objects is a fascinating and complex issue that touches on both philosophy and theology. For believers in a sovereign God, the existence of uncreated, independent abstract objects presents a serious challenge. However, various approaches—ranging from anti-realism to conceptualism—offer solutions that preserve God’s sovereignty while acknowledging the role of abstract objects in our understanding of the world.
William Lane Craig’s exploration of this topic has brought significant clarity to the debate, offering a path forward for those who wish to maintain a robust view of God’s sovereignty. Whether one adopts anti-realism or conceptualism, the goal remains the same: to uphold the belief that God is the self-sufficient creator of all things.
I found this exploration of God's sovereignty and abstract objects deeply thought-provoking. If you're interested in delving deeper into this topic, I encourage you to watch the full discussion on YouTube [here](https://www.youtube.com/watch?v=IYmV5m42HHg).