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Writer's pictureEdward D. Andrews
Nov 59 min read

How Can We Understand the Concept of an Infinite Series in Light of God’s Creation and Existence?

The idea of an infinite series, particularly in relation to the existence of God, poses deep philosophical and theological questions. From the very nature of the universe to the logical implications of causality, the question of infinity raises issues that have significant bearing on the Christian understanding of God's existence, His creation, and the nature of time. In this article, we will explore the differences between mathematical and actual infinities, the impossibility of an infinite regress of causes, and how these concepts are essential in defending the existence of a First Cause, namely, God.



What Is an Infinite Series?


An infinite series can be defined as a sequence of events, points, or causes that either have no beginning, no end, or both. It is crucial to understand that there are two kinds of infinite series: mathematical infinities and metaphysical (or actual) infinities. Mathematical infinities are abstract constructs often used in mathematics and geometry. For example, the number of points between two points on a line can theoretically be infinite. This is an abstract concept that does not necessarily have a bearing on the real world. Actual infinities, on the other hand, refer to concrete entities or events that would exist in reality. These would be actual causes, effects, or moments in time.


An important distinction to make is between a potential infinite and an actual infinite. A potential infinite series refers to something that can continue indefinitely, like counting numbers: you can always add one more number, but you never actually arrive at an infinite number. On the other hand, an actual infinite would be a completed series that contains an infinite number of items. In the metaphysical sense, an actual infinite series of events, causes, or moments in time is impossible, as we will discuss further.



The Impossibility of an Actual Infinite Regress of Events


One of the primary reasons why an actual infinite series is impossible is due to the nature of time and causality. Time, as we experience it, is a sequence of moments that follow one after another. If the number of moments preceding the present moment were actually infinite, it would be impossible to ever reach the present moment. This is because an infinite sequence of past moments would never be fully traversed. The fact that we are at a present moment demonstrates that time had a beginning and is not infinite in the past.


This concept is integral to the Kalam Cosmological Argument, which argues for the existence of a First Cause. The argument can be summarized as follows:


  1. Everything that begins to exist has a cause.

  2. The universe began to exist.

  3. Therefore, the universe has a cause.


The impossibility of an actual infinite regress of moments supports the second premise of this argument. The universe must have had a beginning, for if it were eternal, it would be impossible to reach the present moment. Genesis 1:1 affirms the beginning of the universe: “In the beginning, God created the heavens and the earth.” This biblical truth aligns with the understanding that the universe is not eternal but had a starting point, implying that it was caused by something or someone outside of itself—namely, God.


Moreover, if time had no beginning and was infinite in the past, the present would never arrive because an infinite sequence cannot be fully traversed. Ecclesiastes 3:11 reinforces this idea, stating, "He has made everything beautiful in its time. Also, he has put eternity into man’s heart, yet so that he cannot find out what God has done from the beginning to the end." Time, as created by God, has a definite order and purpose, and its beginning points to the need for a Creator.



The Impossibility of an Infinite Regress of Causes


Just as there cannot be an infinite number of moments preceding the present, so too can there not be an infinite regress of causes. In other words, every effect must have a cause, but if we were to trace these causes back infinitely, we would never reach a starting point. The problem with an infinite regress of causes is that it denies the necessity of a first, uncaused cause, which is essential for explaining the existence of anything at all.


To illustrate this, consider a series of falling dominoes. Each domino falls because the one before it pushed it over. However, if there were no first domino to start the sequence, none of the dominoes would fall. An infinite regress of dominoes, with no initial cause, is impossible. There must be a first cause to begin the chain of events.


Philosophically, the idea of a self-caused cause is incoherent. A cause is ontologically prior to its effect, meaning that for something to cause itself, it would have to exist before it existed, which is a contradiction. Therefore, an infinite regress of causes is impossible. There must be a first cause that is not itself caused by anything else. This uncaused cause is what we understand as God, the Creator of the universe.


The Apostle Paul affirms this truth in Acts 17:24-25: "The God who made the world and everything in it, being Lord of heaven and earth, does not live in temples made by man, nor is he served by human hands, as though he needed anything, since he himself gives to all mankind life and breath and everything." God, as the Creator, is not dependent on anything else for His existence. He is the uncaused First Cause.



Mathematical Infinities vs. Actual Infinities: Why Is This Distinction Important?


The distinction between mathematical and actual infinities is crucial in understanding the impossibility of an actual infinite series of causes or events. In mathematics, infinity can be a useful tool for describing abstract concepts. For instance, the number of points between two points on a line is theoretically infinite, or a series of numbers can continue indefinitely. However, these mathematical infinities are not actual entities. They do not exist in the real world but are only conceptual.


In contrast, actual infinities refer to entities or events that would exist in reality. The problem with actual infinities, particularly in the context of time or causality, is that they are impossible to complete or traverse. This impossibility is best illustrated through what is known as "Hilbert’s Hotel," a thought experiment proposed by the mathematician David Hilbert. In this experiment, a hotel with an infinite number of rooms is always full, yet it can still accommodate more guests by shifting the current occupants. While this is logically possible in the abstract world of mathematics, it becomes absurd when applied to the real world.


Similarly, applying the concept of an actual infinite series to the real world leads to contradictions and absurdities. It would mean that events could occur without a beginning, which contradicts our experience of time and causality. In the real world, everything that exists must have a cause, and there cannot be an infinite regress of causes.



The Theological Implications of a Finite Universe


The impossibility of an actual infinite regress has profound theological implications. It points to the necessity of a First Cause, which is uncaused and outside of the chain of contingent events. This First Cause must be eternal, self-existent, and all-powerful, as it is the source of all that exists. In Christian theology, this First Cause is identified as God, who is described in Scripture as eternal and unchanging.


Psalm 90:2 declares, "Before the mountains were brought forth, or ever you had formed the earth and the world, from everlasting to everlasting you are God." God, as the Creator, is not bound by time or causality. He exists outside of the universe He created, and His existence does not depend on anything else. This is in contrast to everything else in the universe, which is contingent and dependent on something outside of itself for its existence.


The First Cause argument is also supported by John 1:3, which states, "All things were made through him, and without him was not any thing made that was made." This verse emphasizes that God is the Creator of all things, and nothing exists apart from His creative power. The universe, therefore, is not eternal but had a definite beginning, and that beginning was brought about by the will of God.



The Potential Infinite: Can Causes Continue Without End?


While an actual infinite series is impossible, a potential infinite series is possible. A potential infinite refers to a series that can continue indefinitely without ever being completed. For example, the future is potentially infinite because time can continue without end. However, the future is not actually infinite, as there will never be a point at which an infinite number of future moments have been reached. There will always be one more moment to add.


This concept is important when considering the nature of God's eternal reign. While God is eternal and His existence stretches infinitely into the future, the sequence of events within creation is potentially infinite but not actually infinite. Revelation 22:5 speaks of the eternal reign of God, saying, "And night will be no more. They will need no light of lamp or sun, for Jehovah God will be their light, and they will reign forever and ever." The future existence of God’s kingdom is potentially infinite in that it will never end, but it is not an actual infinite because it is a sequence of events that will always have another moment to add.


Addressing Common Objections to the Impossibility of an Infinite Regress


Some argue that an infinite series of events or causes must be possible because the future is infinite and God, being omniscient, must know the infinite future. However, this objection confuses the nature of a potential infinite with that of an actual infinite. While it is true that God knows the future and that the future is potentially infinite, this does not imply that an actual infinite series exists. God knows all future events, but these events are not an actual infinite series that has been completed. They are a potential infinite series that will continue indefinitely.


Additionally, the objection that God is limited if He cannot know an actual infinite series misunderstands the nature of God's omniscience. God knows all things that are possible and actual, but an actual infinite series is impossible by nature, as it leads to contradictions. Therefore, God cannot know an actual infinite series because such a series does not and cannot exist.



Infinite Series and the Existence of God


The impossibility of an actual infinite regress of causes is one of the strongest arguments for the existence of God as the First Cause. If there were no First Cause, there would be no explanation for the existence of the universe. Everything in the universe is contingent, meaning that it depends on something else for its existence. If there were an infinite regress of causes, nothing would ever come into existence because there would be no first cause to begin the chain of causality.


This line of reasoning aligns with Romans 1:20, which states, "For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse." The very existence of the universe points to the existence of a Creator who is eternal and all-powerful. The impossibility of an infinite regress reinforces this truth by demonstrating that the universe must have had a cause, and that cause must be God.



The Necessity of a First Cause


In conclusion, the concept of an infinite series, particularly an actual infinite regress of causes, is logically impossible. The impossibility of such a series points to the necessity of a First Cause, which is uncaused and self-existent. This First Cause is God, who created the universe and set all things into motion. The existence of God is not only a theological truth but a logical necessity, as the impossibility of an infinite regress of causes leaves no other explanation for the existence of the universe.


The doctrine of creation, as revealed in Scripture, aligns perfectly with the philosophical and logical necessity of a First Cause. As believers, we can be confident that our faith in God as Creator is not only supported by divine revelation but also by sound reasoning and philosophical inquiry.


About the Author

EDWARD D. ANDREWS (AS in Criminal Justice, BS in Religion, MA in Biblical Studies, and MDiv in Theology) is CEO and President of Christian Publishing House. He has authored over 220 books. In addition, Andrews is the Chief Translator of the Updated American Standard Version (UASV).


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