What exactly is Occam's razor?

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Occam's razor is not hard to understand. It says that, other things being equal, simpler explanations (compared to more complex ones) are usually correct. Scientists use it every day to choose between competing theories. The problem is that there is no empirical evidence that the world is simple, and many scientific theories are becoming more and more complex over time. Especially when it comes to different disciplines, Occam's razor does need to be used with caution.

For example, the doctor's common saying mentioned in the article is, "When you hear hoofbeats behind you, think of horses, not zebras." This Occam's reduction principle usually seems to be fine, but there is also a Hickam's dictum that corresponds to it, which simply means: "The patient can have as many diseases as he wants." What does this mean? It means that many patients cannot explain many symptoms by a single disease (reduction). After all, as a cognitive tool/model, Occam's razor cannot be infallible.

If you've ever argued with someone online, you've probably come across Occam's Razor. A favorite argument among keyboard warriors, Occam's Razor is often understood to mean that "the simplest argument is often the most correct." Where does this strange name come from? Is this principle really as magical as people think it is, or is it just a way for people to show off their intelligence and win arguments?

Before we begin, let me briefly tell you the background story. Occam's razor is named after William of Ockham, an English Franciscan monk and theologian who lived in the 13th and 14th centuries. Born in the small town of Ockham in 1285, William of Ockham joined the Franciscan Order at the age of 14, and little is known about his early life. Not surprisingly, his choice of monastic order would have a profound impact on his philosophical views and theological debates.

Ockham was initially educated at the Franciscan monastery in London, where he studied common academic subjects such as logic, natural philosophy, and theology. From 1310 to 1317, he studied theology at Oxford University and began lecturing on the Four Books of Sentences by Bishop Peter of Lombard, a work that was considered a benchmark for theologians at the time.

William of Ockham (1285-1347). © GoHighBrow

Ockham's lectures and commentaries on the Tetrabiblos put him in trouble for the first time in the Catholic Church in terms of philosophy and theology. As a Franciscan friar, Ockham had a theological disagreement with the then-dominant Dominican Order, whose views were embodied in the writings of Saint Thomas Aqunias. The Franciscans and Dominicans disagreed on many issues, one of which was whether Jesus and his followers owned property.

Saint Francis of Assisi believed that Jesus had no private property, and he established the Franciscan Order based on his example, requiring monks to swear to follow poverty for life and rely on others for food, shelter and other necessities of life. He even demolished the new house built specifically for his monastery. Ockham was very motivated and supported these views. In 1324, one of his rivals in Oxford wrote a letter to Pope John XXII to report the matter, and the Pope summoned Ockham to the papal court in Avignon, France, for a hearing.

Pope John XX (1244-1334). © Lapham's Quarterly

Ockham believed that the Catholic Church had accumulated a lot of wealth and power, which was contrary to the teachings of Jesus. He even declared the Pope a heretic and demanded his abdication. For the next four years, Ockham lived in Avignon. The hearing was delayed and the conflict between the Dominicans and the Franciscans became more and more intense. Finally, he fled the city in 1328. Ockham traveled to Italy and Germany and finally settled in Munich, where he lived out the rest of his life and died in 1347.

Occam devoted his life to the study of metaphysics and logic, and created the famous Occam's razor. The school of medieval philosophy that Occam worked in, also known as scholasticism, is very different from our modern concept of philosophy and logic. It is mainly centered on theology and the works of Aristotle. Too much focus on theology may make scholasticism far away from modern philosophy, making students feel at a loss and discrediting the subject.

The truth, however, is more complicated, and Ockham’s work is an excellent case study in how scholastic philosophy helped lay the foundations for modern empiricism and analytic philosophy .

(Empiricism, also known as empiricism, is a theory that states that knowledge comes only or mainly from sensory experience. It is one of several viewpoints in epistemology, other viewpoints include rationalism and skepticism. Analytical philosophy, a school of philosophy, has been popular in the Anglo-American philosophical circles since the early 20th century, challenging and counteracting traditional philosophy. Analytical philosophy focuses on the clarification of language and logic, as well as the analysis of existing knowledge, and is opposed to traditional continental philosophy. Editor's note)

Much of Occam's scholarship dealt with the question of universals, entities that relate to other entities and unite similar entities as general properties. According to this framework, we can take, for example, the property of chairness that owes its existence to a chair, which determines what is and is not a chair in the material world. Philosophical schools of thought have been divided over whether universals are independent of the objects they represent, or are fundamental properties of the objects themselves.

As a nominalist, Occam did not believe that the universe really existed. To him, a chair is just a chair—not part of a universal metaphysical property, but just a concept used to describe a group of related objects. Although a chair shares features with other single chairs, these similarities are only the observer's ideas, not the fundamental properties of the material world.

While all of this may seem like the nitpicking of a few insiders, Occam’s refusal to accept the extra-metaphysical aspects of the old Aristotelian philosophy, including the concept of the universe, led to the development of a simpler, more streamlined worldview that would give rise to empiricism and the scientific method, and directly gave rise to what is now known as Occam’s razor.

Occam's razor is often described as "Entities should not be multiplied beyond necessity." In other words, when comparing two arguments, other things being equal, the simplest argument is most likely to be correct.

Although this principle is often associated with Occam, Occam himself never stated the modern form of his famous "razor" principle in any of his known works. In fact, the basic idea of ​​Occam's razor, the "Principle of Parsimony", first appeared in Aristotle's writings centuries before Occam:

"Heaven created all things for use, and chose the good ones to use, and this is true for all insects."

(Nature does nothing in vain, but always does what is best from among the possibilities, for the substantial being of each kind of animal.)

Theologian and astronomer Liberté Froymont (1587-1653). © Wikipedia

The law of stinginess also appeared in the works of many Greek, Jewish, Muslim, and Christian European philosophers before the 14th century. So why did people associate it with William of Ockham? It is generally believed that the principle was created by later scholars, such as theologian and astronomer Libert Froidmont, who wrote in his 1649 book On Christian Philosophy of the Soul:

"I call this principle Occam's and Nominalists' razor, because with it we shave off all the different entities, leaving only the plural of the name."

Regardless of its origins or specific historical expressions, the basic principle of Occam's razor is timeless: the purpose of a theory is to explain natural phenomena, so the fewer assumptions and twists a theory has, the more likely it is to be tenable, or, as the saying goes when doctors see patients: when you hear the sound of horse hooves, you think of horses, not zebras. (This means that when diagnosing a disease or injury, doctors should try to find the simplest possibility that causes all the symptoms. Editor's note)

As Western philosophy entered the Enlightenment period, old ideas about the universe began to be challenged, and Occam's razor became particularly important. For example, for thousands of years, philosophers believed that the Earth was the center of the universe and that the universe revolved around the Earth. However, this theory was fundamentally flawed because some celestial bodies, such as planets, seemed to periodically stop moving and turn around, a phenomenon known as retrograde motion.

Ptolemy's diagram of the universe. © Wikipedia

In fact, the word “planet” comes from the Greek word “planetai,” meaning “wanderer.” In the 3rd and 2nd centuries BC, in an effort to resolve this apparent contradiction, the Greek philosophers Hipparchus and Ptolemy devised a model of the universe in which the planets not only orbited the Earth but also in smaller orbits called “epicycles,” which combined to explain retrograde motion.

Portuguese cosmographer and cartographer Bartolomeu Velho's model of the geocentric universe, drawn in 1568. © Wikipedia

However, as astronomers discovered increasingly obvious and contradictory celestial phenomena, the Ptolemaic model became a troublesome and complicated "circle within a circle".

In contrast, Nicolaus Copernicus and Galileo Galilei championed a heliocentric model that held the sun, not the earth, at the center of the universe, and better explained retrograde motion. According to this model, the phenomenon was due to the planets orbiting the sun at different speeds, causing some planets to periodically overtake each other, creating the illusion of reversed motion. In the absence of other evidence, the Copernican model had fewer assumptions and twists to explain the same natural phenomenon, and people eventually accepted it.

Copernicus's view of the universe in On the Revolutions of the Celestial Spheres. © Wikipedia

While Occam's razor is a useful remedy when comparing competing theories, it is not the ultimate rule as it is often claimed. After all, the simplest explanation is not always the correct one, especially in science.

For example, Aristotle believed that all objects have a natural tendency to fall toward the center of the universe, a philosophy that neatly explained the phenomenon of gravity, since the Earth was thought to be at the center of the universe. Later, however, Isaac Newton showed that gravity is actually an attractive force exerted by all objects with mass. Later, Albert Einstein revealed that gravity is the result of the mass of an object warping the fabric of space and time. With each example, the explanation of gravity became more complex, while also improving the accuracy of modeling and predicting natural phenomena.

Indeed, the simplicity of a scientific theory has little to do with how true it is; what matters is whether the theory accurately predicts experimental results. This proves the importance of the traditional admonition of Occam’s razor, “all other things being equal”.

In the vast majority of cases, competing theories are not “identical” and there is always a large amount of empirical evidence supporting one side, which makes the application of Occam’s razor meaningless.

However, Occam’s razor does have its applications in science, especially in relation to the principle of falsifiability, which was first proposed by Austrian philosopher Karl Popper in his 1935 book The Logic of Scientific Discovery. Popper saw the principle as a fundamental difference between physical science and other scientific fields, specifically, between Einstein’s theory of relativity and Freud’s psychoanalytic theories.

Philosopher Karl Popper (1902-1994). © Adam Smith Institute

Popper instinctively thought that the former was inherently more scientific than the latter, but could not initially explain exactly why. Later, he realized that the difference was that each theory had the ability to be disproven through experimental evidence. He noticed that psychoanalytic theory was irrefutable, and if an observable behavior contradicted one of Freud's theories, another theory would immediately be proposed to explain the contradiction, which is scientifically called an ad hoc hypothesis . Although it is impossible for every theory to be correct at the same time, there is no mechanism to determine which theory is correct.

By contrast, Einstein's theories were inherently more "dangerous" because they could be disproven by experiment. For example, general relativity predicted that the sun's gravity would deflect the light from distant stars by an amount that was different from that predicted by Newtonian mechanics. So if this deflection could be measured, as physicist Arthur Eddington did in 1919, there would be two possible results: one that supported Einstein's theory, and one that disproved it.

[Scientists are generally skeptical of theories that rely on unproven and unfounded evidence. Therefore, ad hoc hypotheses are often a feature of pseudoscience. Much scientific understanding requires changes to existing theories or assumptions, but this is different from trying to impose explanations. Although ad hoc hypotheses are not recognized by science, their assumptions themselves are not necessarily completely wrong - Einstein once proposed an external assumption called the cosmological constant to general relativity in order to allow the existence of a static universe, which is an ad hoc hypothesis. Although Einstein later considered this assumption to be his "biggest mistake", his assumption can be used to explain dark energy. Editor's note]

All of this tells us that, counterintuitively, a theory that explains everything and is watertight is actually inherently weak and pseudo-scientific. Therefore, a strong theory has a minimal number of assumptions and ad hoc hypotheses and is fundamentally testable and, most importantly, falsifiable.

On a more basic level, many philosophers have argued that the misuse of Occam’s razor can stifle creativity and cause people to think too narrowly. Walter Chatton (1285-1343), a contemporary of William of Occam, even proposed an “anti-razor” principle, also known as the Principle of Plenitude :

“When an affirmative proposition tends to be proved as a thing which actually exists, if two things, however they exist in order of arrangement and duration, are not sufficient to prove the proposition that the other thing is lacking, one must suppose the other thing.”

(In short, if one explanation does not satisfactorily determine the truth of a proposition, and you are convinced that the explanation you have so far is correct, then some other explanation must be available. Editor's note)

Similarly, the German philosopher Immanuel Kant said:

"Don't reduce entities unless necessary."

Surprisingly, the "razor" and the "anti-razor" are not actually contradictory, but play a role in preventing extreme ideas in the process of theory construction. The "razor" opposes the unnecessary increase of complexity, while the "anti-razor" opposes the unnecessary elimination of complexity. In philosophy and science, as in everything, moderation, rationality and careful consideration are the keys to revealing the truth.

Occam's razor is thus a lot like a razor in the physical sense: you can shave closely, but be careful not to shave too close.

By Yehia Amin

Translated by Zhao Hang

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