Faith and Reason: An Unprovable Axiom

An Unprovable Axiom

The main purpose of this video is to explain the difference between mathematical proofs and scientific evidence as it relates to matters of faith. In particular, the statement that "God's existence in unprovable" implies, in some sense, that perhaps it should be provable. That implication is looked at in light of the fact that things in science are not proven; they are inferred from evidence. To start out my discussion, I quoted Donald Knuth's statement from his book Things a Computer Scientist Rarely Talks About: "The assumption, that the Bible is God's word, is an unprovable axiom, that I tend to find confirmed, as I look at it."

Equilateral Triangle

As an example of axiomatic method and proof, I cited Euclid's Elements, which has been the epitome of axiomatic method and mathematical proof since it was written over 2000 years ago. The Elements is a set of proofs of fundamental results from mathematics, primarily geometry; these results rely on a set of ten axioms or assumptions. These axioms are called Postulates and Common Notions, and there are five of each. The Postulates are geometric assumptions, while the Common Notions are general statements that could apply to almost anything.

Euclid's Postulates

  1. To draw a straight line from any point to any point.
  2. To produce a finite straight line continuously in a straight line.
  3. To describe a circle with any centre and distance.
  4. That all right angles are equal to one another.
  5. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

Euclid's Common Notions

  1. Things which are equal to the same thing are also equal to one another.
  2. If equals be added to equals, the wholes are equal.
  3. If equals be subtracted from equals, the remainders are equal.
  4. Things which coincide with one another are equal to one another.
  5. The whole is greater than the part.

The very nature of proof is to reason about things that we understand fully, like lines, points, or other artificial creations of mathematics. For natural sciences, like physics, we never prove the laws that govern them because we do not have a full understanding of them. Likewise, we do not fully understand God. So, it is reasonable to assume that we can not prove God's existence.


In the video, I give several examples of scientific discoveries and demonstrate how they are based on evidence and not proof. For gravity, for example, I present several quotes from Isaac Newton who states flatly he is simply making observations for his Theory of Gravity, without any attribution to causes. Centuries later in fact, adjustments were made to his theory of gravity by Lorentz and Einstein, which demonstrated that Newton's observations were not quite correct. This is the proper methodology of the natural sciences; they proceed by observation and refinement, not proof.


Just as it is with natural laws, we should not logically expect a proof of God's existence. A proof implies that we understand God. Why should we expect God is more amenable to proof than the basic laws of nature? However, the lack of a proof of God's existence is often given as evidence for atheism.

Science deals with great uncertainties. In fact, the entire field of statistics has been developed to quantify these uncertainties and infer results from them. Despite this uncertainty, we have no difficulty accepting the results that statistical methods provide. Likewise, we use randomness in many of our most powerful computer science algorithms. When it comes to God, however, we accept neither uncertainty nor randomness, and deem the presence of these to be further evidence against God's existence.

Bell Curve

The intention in this series is to take a rational and scientific approach to questions of faith and develop evidence based on these methods. In doing so, I will avoid appeals to theological arguments because I think the case can be made without them, and I, having been an atheist most of my life, am not in a position to make strong theological arguments. For theology, you should consult the writings of someone more knowledgeable, like His Holiness Pope Bendict XVI.