Stop Using the Occam’s Razor Principle

Do you want to know how you can prove the Earth is flat using Occam’s Razor? Do you want to prove God is the reason for everything in the Universe? Do you want to refute Einstein’s theories without knowing anything other than high-school physics?

Well, I’m not going to tell you how to do those things, since they can’t be done unless you misquote Occam’s Razor — something which seems to be inevitable in almost any argument where it is invoked. I will further show that even when it is quoted correctly, the Occam’s Razor is non-operational in practice and should therefore be dropped from any kind of a rational argument. This is likely why it is so often misquoted when applied.

On this basis I will argue for the complete ban on using the so-called Occam’s Razor in any kind of honest argument or debate.

TLDR: Most people misquote and misuse the so-called Occam’s Razor. Even when correctly cited the concept has only limited abstract merit and is completely non-operational. It has approximately zero real-world applications, so please, stop using it as part of your arguments.

To begin, let us examine what was actually stated by William of Occam, to whom the “rule” of preferring simpler explanations or solutions is attributed.

What William of Occam actually said?

William of Occam (a.k.a. Ockham or Ocham) is attributed a variety of different “quotes” pertaining to a problem-solving principle based on parsimony / simplicity. They usually state something close to: simpler solutions are preferable to more complex ones; simpler explanations are preferable to more complex ones.

However, this idea is not unique to William of Occam, and there is actually no direct quote from him that one can produce to support that he even made such claims in his works. The closest one gets to are these two quotes:

“Entia non sunt multiplicanda praeter necessitatem”, translating to “Entities must not be multiplied beyond necessity” and “Frustra fit per plura quod potest fieri per pauciora”, translating to “It is futile to do with more things that which can be done with fewer.” Hardly enlightening stuff, given that the force of evolution drives all organisms towards minimalism and cognitive misery: expending unnecessary energy to achieve a given result tends to get punished by nature through death on the individual level and extinction at the species level.

Keywords to note here are “beyond necessity” and “can be done with fewer”. Note that “necessity” is not defined in the first quote, while in the second it is implicit that we get the same end result. We’ll return to these in the next section.

Other formulations of this principle were provided by many thinkers both long before and after Occam, including the likes of Aristotle, Thomas Aquinas, Newton, Bertrand Russell, and Karl Popper. Aristotle’s formulation, for example is that “We may assume the superiority, other things being equal, of the demonstration which derives from fewer postulates or hypotheses.”. Put more simply:

“other things being equal, simpler explanations are generally better than more complex ones”

Leaving the issue of authorship or originality aside, I argue that this very common-sense idea is often and almost inevitably perverted when used in an actual argument of practical consequences.

Misquoting the principle to prove the Earth is flat

The most often type of misquoting and, following from it, misapplication of the simplicity principle ascribed to Occam is to simply drop the ceteris paribus qualifier, the “other things being equal” part of the principle.

Without it, it becomes simply:

“simpler explanations are generally better than more complex ones”

and is thus ripe for misapplication.

For example, one explanation for the fact that the horizon appears flat to the eye of observes at sea level is that the Earth is a flat surface. It is quite a simple explanation insofar as only a single plane is involved and thus the geometry required to calculate a number of related distances, angles, trajectories, etc. is relatively simple. A bit more complicated explanation is that the Earth is a sphere and that the apparently flat horizon is due to its immense diameter in combination with our vantage point. Yet more complicated is an explanation involving a geoid, as proposed by Gauss. Even more complex is the modern concept of a geoid pear-shaped figure with a triaxial ellipsoid with an ellipsoid of revolution as a reference ellipsoid.

An application of the misquoted Occam’s Razor should suggest that the Gauss geoid concept should be preferred to the modern one, the sphere concept should be preferred to the geoid and the plane concept should be preferred to all others, based on its simplicity. Therefore, an application of this erroneous statement of the Occam’s Razor will lead us to accept the plane hypothesis and therefore to conclude the Earth is flat.

An even more extreme example is God. At least superficially, God is a simple explanation of pretty much everything, so we should prefer the explanation of “God did it” or “God made it to be so” to any other explanation.

Of course, this is pure non-sense.

As the principle in both the Occam formulation and its other formulations explicitly state “all else being equal”. One cannot simply pretend this clause does not exist and apply the rest of it regardless.

Once this clause is in effect, we can see the above exercises as futile. A model of the Earth as a flat plane does not explain all relevant phenomena equally well as a model which posits a Sphere. In fact, it fails on a number of crucially important tests such as navigating an airplane or launching a satellite or the Global Positioning System (GPS). Similarly, a spherical model is inferior to a geoid model which is on its own inferior to the more complex ellipsoid models which allow us to explain a lot more phenomena and to predict physical forces and their effects on bodies moving on Earth or in near-Earth orbit.

So, the more complex model is in fact the preferable model based on its explanatory and predictive qualities, even though it is inferior in terms of its simplicity.

The Occam’s Razor is practically non-operational

Let us say one knows the actual principle and is honest enough in their argument to not misquote it. Can the principle be applied in actual practice?

I argue that even if you are not misquoting the principle, you are likely misapplying it, because it is practically non-operational. I believe the ceteris paribus clause is what makes it so. I can’t think of any practical situation in which two solutions or hypotheses would cover exactly the same phenomena and lead to the same conclusions and predictions about them.

Even for almost identical hypotheses, one hypothesis or the other would refer to more or fewer phenomena, one or the other would cover a situation which the other does not. If that is not the case, then surely one of them will lead to a somewhat different prediction compared to the other. This means that even if we neglect the lack of logical support for the Occam’s Razor (a topic for a separate article), it is rendered non-operational for most if not all practical situations.

This was already hinted on in our discussion of the different models for the shape of the Earth: the proposed explanations did not explain the same phenomena in the same manner, some fail to explain certain phenomena entirely, and predictions based on each of them would differ on multiple occasions. The “all else being equal” requirement is shown to not hold.

Another scenario can be given with regards to planetary motions: comparing Newtonian and Einsteinian laws of motion. Both explain how bodies interact and move relative to each other and both can be used to predict the position or velocity of moving objects on different scales. They even produce the same results under certain conditions.

Since Newtonian theory is unarguably simpler than Einstein’s, if we were to apply Occam’s Razor naively believing the “all else being equal requirement” holds, we should adopt Newton’s theory and throw Einstein work’s away.

However, the ceteris paribus requirement of the Occam’s Razor can easily be shown to be non-operational since Newtonian physics leads to much less accurate measurements and predictions on the planetary scale, among other differences. “All else” is not equal! Therefore, even when theories appear similar on the surface, even when one is in fact a special case of the other, this crucial requirement does not hold.

Avoid using Occam’s Razor in arguments

Given the above, my advice is to generally avoid using the so-called Occam’s principle in any of its variants in arguments. Even if it is taken to be true at face value (despite its lack of logical justification) the Occam’s Razor is non-operational unless you are looking at two hypotheses which explain exactly the same set of phenomena, in exactly the same circumstances, to exactly the same degree of predictive accuracy, which is practically impossible.

If you ever stumble across such a scenario of any practical significance, feel free to contact me and let me know!

Just to be clear, parsimony and simplicity are good things to strive for, both in statistical modeling and in everyday life. However, one should never delude themselves that simplicity is to be the sole or even primary measure of fitness, suitability, etc., or that making things simpler comes at no cost in terms of the resulting outcome — its direction, accuracy, and general quality.