# Occam's Razor

Occam's Razor (or Ockham's Razor) is the philosophical principle which states: entities should not be multiplied beyond necessity. It has been paraphrased in various forms:

"All things being equal, the simplest solution tends to be the best one."
"Out of several equally good explanations, pick the simplest one."

"We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. Therefore, to the same natural effects we must, so far as possible, assign the same causes"

Isaac Newton

"Whenever possible, substitute constructions out of known entities for inferences to unknown entities"

Bertrand Russell

In this context, the word "simplest" means "the explanation that contains the fewest assumptions." Similarly, "equally good" refers to the ability of the explanation to account for the observation and not to the veracity of the explanation. Occam's Razor is one of the key principles of skepticism.

Occam's Razor has perhaps less application to religion than is commonly assumed because religion is often not a predictive explanation. Therefore, any other predictive theory which is even remotely correct is considered better than a non-predictive religious explanation. Occam's Razor does apply in cases where God is needlessly invoked, such as with theistic evolution.

## Expression using logic

A narrow interpretation of Occam's razor may be expressed as logically as:

"A and (B or not B)" is simply A

This was summarised by Ludwig Wittgenstein as:

"If a sign is not necessary then it is meaningless. That is the meaning of Occam's Razor."

## Example

Assume a child contracts a nasty disease which leaves her in terrible pain. She is taken to the doctor and is given medicine. Meanwhile, the parents pray to God for her safe recovery. A few days later she is perfectly healthy again and the parents, in their happiness, proclaim "God saved our child!"

A better explanation for the child's recovery, however, would be that the medicine the doctors gave her did its job. When one compares the two explanations ("God did it" and "The medicine worked") it is clear that the second requires fewer assumptions. God isn't required for the medicine to have worked in the second explanation, therefore it is the one that should be chosen.

## Extending the Razor

Consider any observation which requires a causal explanation; a rainbow, for example. We can devise numerous explanations for this phenomenon:

1. Yahweh creates them as a reminder of his promise to never again flood the entire earth
2. Light dispersion due to refraction as it passes through water droplets
3. Sky pixies sprinkle colored dust in the sky
4. Leprechauns create them to mark pots of gold

Each of these explanations answers the question and they all also prompt additional questions, but only the second answer explains the phenomena in terms which we adequately understand. The additional questions raised by the second explanation (dispersion, refraction, visible spectrum, etc.) are simpler concepts supported by consistent, reliable definitions. Further the way light is defracted is well understood by scientists and supported by experimental evidence. (Incidentally even if Yahweh used scientific defraction to remind us of his promise this leaves unanswered why light was not defracted before the flood and how all the other problems with the story of Noah's ark can be answered.)

Each of the other explanations could be considered equivalent non-answers. The causal subjects are complex constructs which prompt many additional, unanswered questions about the nature of those subjects and how they managed to create the rainbow. The fact that these explanations are non-answers can be made more clear by substituting the subjects into different answer:

• Yahweh creates them to mark pots of gold
• Leprechauns sprinkle colored dust in the sky
• Sky pixies create them as a reminder of their promise to never again flood the entire earth

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.

3.“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.

## God is a parsimonious explanation

Main Article: Divine simplicity

Apologists sometimes argue that God is a simple explanation that is not suitable for elimination by Occam's razor. However, divine simplicity is merely asserted and it is generally regarded by skeptics that proposing an entity that is all powerful, existing at all places, immortal and all knowing is assuming quite a bit! Dawkins called God the "the ultimate 747" because of that entity's shear complexity.

In any case, no possibility is ruled out by this "explanation", since "anything is possible for God" Matthew 19:26 . Therefore, the explanation has little predictive power which is the basis of the explanation's rejection. There is no need to resort to Occam's razor in this case.

## Confusion with reductionism

Occam's Razor is sometimes confused with the related concept of reductionism, which is often accused of oversimplify problems. Occam's Razor has the requirement that explanations can be compared only when "all things being equal" in their predictive power. Therefore, it has no allowance for approximations of theories.