Is an Infinite Regress of Causes Impossible? A Philosophical and Logical Perspective

Introduction

At the heart of philosophical debates about the existence of the universe and the reason for its origin lies a powerful question:

“If the chain of causes extends infinitely into the past, does that mean the universe could not have existed in the first place?”

This question is rooted in the principle of causality—that every effect must have a cause. However, it collides with the concept of infinity, which is both a mathematical and philosophical challenge. In this article, we explore this question from logical and philosophical perspectives and ask: Is an infinite regress of causes possible? Or does it logically imply the impossibility of existence?

Causality in Philosophical Thought

Causality is the idea that every event has a cause. This principle forms the foundation of scientific reasoning and our understanding of the world. From an apple falling to the formation of galaxies, we explain phenomena through a chain of causes.

But when we ask: “What caused the cause? And what caused that cause?”—we find ourselves facing a potentially infinite chain with no apparent beginning. This raises the central question:

Can this causal chain extend infinitely into the past?

The View That Infinite Regress Is Impossible

Many classical and religious philosophers argue that an infinite regress of causes is logically impossible because:

• An infinite sequence of causes means there is no true starting point.

• If there’s no beginning, then the entire chain could not exist, and thus nothing would exist now.

• Therefore, there must be a first cause—a necessary being or uncaused cause.

Some of the most well-known advocates of this position include:

• Aristotle (The Unmoved Mover)

• Al-Ghazali (Temporal beginning of the universe)

• Ibn Sina (The Necessary Existent)

• Thomas Aquinas (Five Ways to prove God)

The View That Infinite Regress Is Possible

On the other hand, some philosophers argue that an infinite regress is not logically impossible, and is in fact mathematically and conceptually coherent. Their main points include:

1. Infinity is not a number to be reached, but a concept that implies no end—like how negative numbers extend to −∞ without a “first” negative number.

2. As long as each cause in the chain has its own cause, the whole system doesn’t require a first cause.

3. The universe may not have had a temporal beginning—it could have existed in an eternal, infinite sequence.

Prominent thinkers who supported this view include:

• Bertrand Russell

• David Hume

• Certain schools of Buddhist and naturalist philosophy

A Mathematical Insight: What Does (−∞ + ∞) Really Mean?

To understand this idea mathematically, let’s consider the expression:

−∞+∞−∞ + ∞−∞+∞

In mathematics, this is known as an indeterminate form—an expression that is undefined without more context. We cannot say the result is zero or any specific value.

Using Limits:

Imagine two functions:

• f(x)→∞f(x) \to ∞f(x)→∞

• g(x)→−∞g(x) \to −∞g(x)→−∞

Now consider:

lim⁡x→∞[f(x)+g(x)]\lim_{x \to ∞} [f(x) + g(x)]x→∞lim​[f(x)+g(x)]

The result depends entirely on how fast each function grows. The limit might tend toward ∞, −∞, a finite value, or remain undefined.

This is similar to the philosophical discussion:

• Without knowing the nature and structure of each cause in the chain, we cannot logically conclude that an infinite regress is impossible.

• Just like adding ∞ and −∞ requires precise mathematical context, evaluating an infinite regress of causes requires clear philosophical definitions.

Conclusion

The claim that “the universe could not exist if the causal chain were infinite” is not a proven logical necessity—it is a philosophical assumption that can be challenged. The debate over infinity and causality remains open, with respected thinkers on both sides.

Rather than rushing to final answers, perhaps it’s more meaningful to admit that such questions stretch the limits of human reason—and that infinity is not always an impossibility, but sometimes an invitation to deeper reflection.