Occam's Razor

by Francois Tremblay

To understand why Occam’s Razor is a strong-atheistic argument, we must first understand what Occam’s Razor implies, and what its consequences are.

Occam’s Razor is a method to choose between hypotheses which explain the same facts. We can express it simply as: the hypothesis we must choose is the simplest. More rigorously, we can express it as such:

• Posit two hypotheses A and B, both explaining the same set of facts S.
• The set of explanatory entities and processes of hypothesis A is called Ea.
• The set of explanatory entities and processes of hypothesis B is called Eb.
• The intersection of A and B’s explanatory entities and processes is called I.
• If neither Ea-I nor Eb-I equals zero, the hypothesis with the smallest number of superfluous entities and processes is probably the valid one. We do not have a sufficiently large S, or good enough hypotheses, to choose in all confidence. (Insufficient context)

• If Ea-I or Eb-I equals zero, then the corresponding hypothesis is the valid one. (Sufficient context)

  To understand this better, we might want to look at an example of each outcome.

  Suppose that we are in Ancient Greece, and are ignorant of natural law altogether. We are asked to compare:

  S. The apparent variety and adaptation of lifeforms on Earth.
  A. Creation from one or many divine agents.
  B. Gradual adaptation from generation to generation due to natural processes.

  From this, we deduce:

  Ea. One or many divine agents, and their act of creation.
  Eb. Unknown processes acting on successive material forms.
  I. Empty set.

  In this case, what is the cardinality of Ea-I and Eb-I? At first glance, we should say that Eb-I is bigger. It presumes the existence of a great number of material forms, as well as processes acting on them. Ea-I only presumes the existence of a small number of divine agents, and one process of creative activity. Furthermore, inductive arguments would lend considerable support to A. So a person in this situation would choose A.

  However, it is worth noticing that neither Ea-I and Eb-I are equal to zero, so we have an insufficient context. We now know that S is extremely incomplete: for one thing, it does not include any of the modern evidence for evolution, such as the fossil record, DNA, molecular and protein evolution, and so on. Furthermore, A and B are extremely unrefined, which is natural.

  Now suppose that someone comes and tells us that the Earth is flat. We should be quite skeptical of such an assertion! We could then ask him how he can explain the curvature of the Earth, or the round shadow of the Earth on the Moon, or the pictures taken from space. He can then invoke a number of processes that are not known to science, such as some form of special refraction done by air. He will also need to make up more processes to explain the regularity of night and day. We can express this situation as such:

  S. The curvature of the Earth, the round shadow of the Earth on the Moon, the pictures taken from space, the regularity of night and day.
  A. The Earth is round.
  B. The Earth is flat.

  From this, we deduce:

  Ea. The Earth.
  Eb. The Earth, special process or processes of refraction.
  I. The Earth.

  In this case, Ea-I equals zero. We know that A is the valid hypothesis in this case. Eb-I entails one or many processes which are called superfluous.

  It is important to stop here and note that Occam’s Razor does not allow us to conclude that A is “better” than B, but rather that A is valid and that B is invalid, if the premise of the Razor are fulfilled (i.e. that A and B both explain S). This is because there is no evidence for the superfluous entities and explanations, thus they are not shown to exist. We can rephrase this in the following way:

  A1. I alone explains S.
  A2. S is evidence for I and only I.
  B1. “Special process or processes of refraction” do not serve to explain S.
  B2. There is no evidence for “special process or processes of refraction”.

  As such, there is no evidence left to support the existence of “special process or processes of refraction”, and thus we can say that they are beyond rational discussion. What has no evidence whatsoever, is beyond rational discussion. It may be an internally coherent claim, but that is the extent to which we can pronounce it justified. We may conclude the following:

  1. “The Earth is roughly spherical” is true.
  2. “The Earth is flat” is false.

1. “Special process or processes of refraction” are not justified.

   Let us now examine the situation we are placed in, within the atheism-theism debate.

   S. The sum total of all material things, their properties and processes.
   A. Material things change in time by virtue of natural law.
   B. A god created all material things, which change in time by virtue of natural law and divine intervention.

   Of course, theists could attack the relation that A explains S, but science gives us strong reason to trust this relation. Insofar as science is the discipline that studies natural phenomena, and therefore the relation between A and S, and has had tremendous success in proving this relation in innumerable areas of nature, we can make an inductive argument that the relation between A and S will continue.

   Furthermore, we can point out that B does not explain S. For one thing, if a god created all material things, then we should expect things like logic, morality, principles and absolutes to be absent from the universe, from Materialist Apologetics. From the Problem of Evil, we should not expect any evil to exist. From the Argument of Scope, we should observe a universe made at a human scope, which is not what we observe. From the Cosmological Arguments, we should not expect the Big Bang to exist. The number of observed facts that contradict the relation between B and S is endless.

   From all of these, we can make a cumulative case that B is not a valid explanation for S. But for the sake of the argument, we can assume that B is a valid explanation for S, to verify if Occam’s Razor offers us supplemental proof for the falsity of the theistic hypothesis.

   From this, we deduce:

   Ea. All material entities and processes.
   Eb. All material entities and processes, and a god with a creative process or processes.
   I. All material entities and processes.

   In this case, Ea-I equals zero, so we must judge the non-existence of a Creator and controller of the universe, strong-atheism, as the only valid position. Note, however, that I did mention that the relation between A and S is based on induction, and therefore we must qualify our conclusion by saying that strong-atheism is shown to be probably true by Occam’s Razor, not completely true.

   Granted, a believer is free to invoke specific elements of S and try to prove that they cannot be explained by A. But to claim this is the equivalent of saying that the element is explained by B, which is a claim of divine intervention. As I detail in ‘The Impossibility of Divine Intervention’, to claim that divine intervention is possible demands total knowledge of natural law, or in this case to know all about A. Since we do not, such an argument cannot be made. So the “god-of-the-gaps” argument, apart from being an argument from ignorance, is just not a possibility.

   Of course, we would be suspicious of the relation between A and S if we observed a fact deduced from theology. For instance, if we observed that time is not an integral part of the universe, or that matter popped from nothing, then we might hold theism as more credible.

   But given that we do not observe such facts, and that a great number of facts of the universe contradict theism, we have to conclude that we should be far more suspicious of the relation between B and S, than we should be of the relation between A and S.

   Last updated: August 6, 2004