Can We Prove That God Exists?

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Can We Prove That God Exists?

The last proceeding of reason is to recognize that there is an infinity of things which are beyond it. It is but feeble if it does not see so far as to know this. (Blaise Pascal)


No mortal mind can penetrate the secrecy in which the Mighty One dwells and works. Only that which He sees fit to reveal can we comprehend of Him. Reason must acknowledge an authority superior to itself. Heart and intellect must bow to the great I AM. (Ellen White, Ministry of Healing, pg. 438)


Is it possible to prove the central claims of the Christian worldview? Can we prove that God exists, that Scripture is the Word of God, or that Jesus is Son of God?


There is something attractive about having proof, especially for a mathematician, because proof signals certainty. And without proof, there is always room to doubt. Consider, for instance, the Goldbach conjecture. This mathematical hypothesis claims that every even number can be written as the sum of two prime numbers. For example, 10=3+7, 12=5+7, and 14=3+11. With the aid of computers, we’ve verified that this is true for the first few quintillion even numbers (a quintillion is a billion billions)–every single one of them can be expressed as the the sum of two prime numbers.


But mathematicians still don’t accept Goldbach’s claim; it is still considered a “conjecture.” Why? Simply because we haven’t proven it yet. Until we provide an incontestable logical proof, we’re still open to the possibility that one day we might find a (very, very large) even number that Goldbach claim fails for. That is, we cannot have certainty of the claim until we have a proof that demonstrates it.


By way of contrast, there are many statements that mathematicians are able to prove. For instance, mathematicians have proven that every number can be written as the sum of four square numbers: for example, 23=32+32+22+12. We know this is true, not because we have tested every single number (an impossibility), but because we have a proof that shows how this statement logically follows from the axioms of arithmetic. If you agree with the basic rules of arithmetic and the rules of logic, then you must accept the conclusion of such a proof.


In the history of Christianity, many have attempted to take a similar approach to demonstrate the certainty one can have in the Christian faith. For example, around a thousand years ago, the archbishop Anselm offered a simple proof that God exists. It’s called the ontological argument, and goes roughly like this:

  • God is, by definition, the greatest being.
  • It is greater to exist than not to exist.
  • Therefore, God must exist.

Unfortunately, Anselm’s argument didn’t have the effect he had hoped it would. Most philosophers are unpersuaded by it, offering a variety of criticisms. Some still try to defend it, but most agree that there is something suspect with the reasoning, even if it is difficult to pin down where exactly it goes awry. As one comic quipped, “Wouldn’t a God who could find a problem in the ontological argument be even greater?”

The philosopher and mathematician Rene Descartes was attracted to such arguments and echoed them in his Meditations. In this same work, he attempted to establish all of his beliefs–including the belief in God’s existence–as the logical consequence of a single, self-evident axiom: “I think, therefore I am.”

Despite reading the critiques of Descartes’ program in my philosophy courses–such as Nietzsche’s clever challenge of how can one know it is an “I” that is thinking–I was drawn to Descartes’ approach. Might I be able to construct a system, I wondered, in which the great teachings of Scripture about God, salvation, and the nature of reality are built up from a handful of incontestable claims? I set off to do so.


I slowly recognized, though, something curious with this approach. This Descartian reduction is an exercise of human reason and, as such, it depends on the reliability of reason as a means of arriving at truth. In much the same way, every mathematical proof boils down to the reliability of reason as a means of determining truth. But why should I trust my reason? Why should I expect reason to lead to truth?


That might seem like an odd question, especially for a mathematician to ask. At first, it might appear that there are many good reasons to trust reason. After all, reason is logically consistent, it does a really good job at helping us make sense of the world, and so forth. Or, at least, so we reason. But notice the underlying problem here: we’re relying on our reason to establish the validity of reason.


Wanting to find Truth, we look for a guide. We find a man named Reason who promises that he will lead us to Truth. He seems like a trustworthy fellow and appears over time to be reliable, but we want to be certain of his trustworthiness. After all, this is far too important a journey for us to be led astray. So we ask Reason to name someone who can verify his trustworthiness. Behold, the only name he can offer is his own!


Do we still trust him?


Descartes himself recognized this problem. In his Meditations, he considered the possibility that there might be some powerful demon systematically deceiving him. That is, while it would seem to Descartes that his reason was leading him to truth, he realized that a powerful intelligence might be duping him every step along the way. Perhaps what we perceive to be reality is just an illusion. Perhaps what seems like clever reasoning to us is really unintelligible ideas clumsily stringed together. Descartes ultimately rejected this possibility though, believing a good God wouldn’t allow such a thing to happen. Catch that? Descartes ultimately decided to trust his reason because he trusted the goodness of God. Although he followed reason, he believed another Guide was leading him.


Of course, Descartes didn’t have the final word. Several other thinkers have mused over why our reasoning powers are so well developed. Eugene Wigner, the Nobel prize-winning theoretical physicist and mathematician, reflected on the power of human reason in his essay The Unreasonable Effectiveness of Mathematics in the Natural Sciences. As the title suggests, he was especially concerned with learning why mathematics, a purely rational activity, was so good at describing the natural world. Wigner remarked,

The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible. That his recklessness does not lead him into a morass of contradictions is a miracle in itself: certainly it is hard to believe that our reasoning power was brought, by Darwin’s process of natural selection, to the perfection which it seems to possess.


For both Descartes and Wigner, men who devoted their lives to mathematics and similar rational pursuits, when they examined reason, they found it to be pointing to something beyond itself. The 17th century mathematician, physicist, and philosopher Blaise Pascal similarly concluded, “The last proceeding of reason is to recognize that there is an infinity of things which are beyond it. It is but feeble if it does not see so far as to know this.”


You see, for many, their trust in reason as a reliable means of arriving at truth is foundational. That is, it is an axiom in their truth-seeking scheme. And from a purely naturalistic approach, it is difficult to understand why we should hold to such a belief. If we’re merely the result of natural selection, why ought we to expect ourselves to be wired to know truth? Why would survival of the fittest lead to a species interested in the solving the Goldbach conjecture?


Well, perhaps you’re not so interested in the nature of prime numbers. But do you at least believe that it is possible for us to reason to true knowledge about them? If so, why?


Every so often I come across the claim that reason has replaced the need for religious belief. Indeed, a good bit of religion could benefit from a decent dose of common sense. But don’t be fooled into thinking that reason can be our ultimate foundation. It begs for an explanation–a reason to trust reason. It requires a more solid foundation.


Ellen White captures this idea when she reminds us, “Reason must acknowledge an authority superior to itself. Heart and intellect must bow to the great I AM” (Ellen White, Ministry of Healing, pg. 438).


It seems then that Anselm got it quite backwards. The Christian doesn’t need to ground belief in God on the foundation of human reason; rather, it is our confidence in human reason that needs grounding. Scripture offers such a foundation in the opening story of creation, for if we are indeed made in the image of a rational God, even a God who invites us to come and reason, then it makes sense to trust our reasoning capabilities, while acknowledging their limits. Scripture teaches that reason, rightly applied, is a gift from God useful for the pursuit of truth (Isaiah 1:18). It is precisely one’s trust in God that justifies our confidence in reason; you might even say that faith gives birth to reason. How curious then that some have critiqued faith as irrational!


Now this is not the way that many use the word faith. For instance Richard Dawkins, a leader of the new Atheist movement, describes faith in less noble terms:


Faith is the great cop-out, the great excuse to evade the need to think and evaluate evidence. Faith is belief in spite of, even perhaps because of, the lack of evidence.


Is that what faith is? Was that the attitude of the men of faith who establish Oxford University with the motto Dominus illuminatio mea (The Lord is my light) and Harvard and Yale to seek Veritas (Truth), believing that Truth to ultimately trace back to a Man of Galilee? How then have these and similar institutions fueled the rich intellectual history of the Western world, while bearing coats featuring Scripture?


Perhaps Dawkins’ understanding of faith is lacking. Here’s another attempt at understanding the nature of faith:


God never asks us to believe, without giving sufficient evidence upon which to base our faith. His existence, His character, the truthfulness of His word, are all established by testimony that appeals to our reason; and this testimony is abundant. Yet God has never removed the possibility of doubt. Our faith must rest upon evidence, not demonstration. Those who wish to doubt will have opportunity; while those who really desire to know the truth will find plenty of evidence on which to rest their faith. (Ellen White, Steps to Christ, pg. 105)

Faith is evidence-based. Of course, you knew this already. Think of a friend you trust. I suspect that trust isn’t arbitrary. You have reason to trust them. And yet, while faith appeals to reason, faith doesn’t reduce to reasoning. After all, the object of faith is a Person, not a proposition. A deductive proof can walk us, step-by-step, to accept a certain conclusion, but our acceptance of it will only be on an intellectual level. Trust in a Person requires more. Faith takes a step beyond reason, but it is a step towards something that reason itself testifies to–not a step against reason. This “leap of faith” is an activity of the whole self: mind, body, soul. Perhaps that explains why God never presented Himself in the form of a proof: He’s interested in more than just your mental consent. Rather, God presented Himself in the form of a Man who seeks to call us “friend.”

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About the author

Anthony Bosman

Anthony Bosman, PhD, serves as an assistant professor of mathematics at Andrews University. He served as a campus ministry leader while a student at Stanford and Rice University and continues to find his greatest joy in helping students to recognize Christ as "the center and circumference of all truth".