Occam's razor - what is this principle, in simple terms? What is Occam's Razor? What does "razor" mean?

William of Ockham was one of the most popular philosophers of the 14th century. But modernity knows it only because of the authorship of the principle of simplicity. In one of his books, he suggested cutting off all unnecessary complexity, leaving only the required arguments. This principle is called "Occam's razor" and it sounds something like this: "It is not necessary to multiply entities unnecessarily." In other words, he suggests, where possible, to keep simple explanations without complicating them.

Limits of Occam's Principle

The principle of "Occam's razor" is that reasoning should not be cluttered with unnecessary concepts and terms, if you can do without them. Its wording has changed countless times, but the meaning has remained the same.

Many monographs have been written on how Occam's razor works. This principle has become as significant as the exclusion of the third in logic or in physics.

But is Occam's razor applicable in everyday life? Or can it be used only for scientific purposes? If we talk about the limits of the principle of simplicity, then are such situations possible in science when the economy of thinking does not bring the expected results? And is it always necessary in life to solve problems only as they come?

Of course, such situations are quite real, since both science and our everyday life do not flow smoothly and measuredly. In some cases, it is necessary to make special decisions on which the further course of life or scientific events depends. And there comes a moment when an obsolete theory is replaced by a completely new one. And at this time, you should not solve problems with the help of "Occam's razor". You should not cut off the “excess”, otherwise you will miss something very important specifically for you or humanity as a whole.

So, we can conclude that "Occam's razor" is applicable in the case when no qualitative changes are expected in science and in life.

An example of applying Ockham's formulation

The historian Philoteus Bener, in one of the editions of 1957, reports that Occam's Razor is mainly formulated by the author as follows: "It is not necessary to assert much without necessity." It is worth noting that William of Ockham only voiced the principle of simplicity, known since the time of Aristotle. In logic it is called the "law of sufficient reason".

For an example of a situation to which Occam's principle can be applied, one can cite the answer given by the physicist and mathematician Laplace to Emperor Napoleon. Allegedly, the latter told the scientist that there was not enough room for God in his theories. To which Laplace answered him: "I did not need to consider this hypothesis."

If we reformulate the principle of simplicity and economy into the language of information, then it will look like this: "The most accurate message is a short message."

This rule can be attributed to the current requirements for concretization of concepts. Each of the definitions used must be precise in order to exclude the possibility of creating redundant ones that claim to be all-encompassing.

In logic, the economy of initial assumptions lies in the fact that none of the accepted theses should follow from the others. That is, when proving an axiom, there should not be extra statements that are not directly related to it. Although this savings rule is not mandatory.

Half world.

Only blood will respond with verses:

"I'm not a killer, I'm a poet ...".

When Occam's steel explodes

And the pain will descend from the network of wounds,

Fujiyama will say quietly to me:

"I'm not a killer... I'm a volcano..."

What is Occam's Razor

"Occam's razor" (Law of Sufficient Reason) is a methodological principle named after the English Franciscan monk, nominalist philosopher Ockham ( Ockham, Ockam, Occam; OK. 1285 - 1349), in a simplified form reading: “One should not multiply things unnecessarily”(or "You should not attract new entities unless absolutely necessary"). This principle forms the basis of methodological reductionism, also called the principle of thrift, or the law of economy or the principle of simplicity.

In edition "Ockam. Philosophical Writings. A Selection Edited and Translated by Philotheus Boehner» (New York, 1957) specialist in the history of medieval philosophy Philotheus Bener reports that most often "Occam's razor" given by the author as follows: “Unnecessarily one should not assert much”(lat. Pluralitas non est ponenda sine necessitate).

More specifically, Occam put it this way: "... multiplicity should never be assumed unnecessarily ... [but] everything that can be explained from the difference of matters on a number of grounds - this can be explained equally well or even better with the help of one ground ".

Sometimes the principle is expressed in words “What can be explained in terms of less should not be expressed in terms of more”(lat. Frustra fit per plura quod potest fieri per pauciora). At the same time, the formulation usually given by historians "Entities should not be multiplied unnecessarily"(lat. Entia non sunt multiplicanda sine necessitate) is not found in the works of Occam.

What is called "Occam's Razor", was not formulated by Occam - he just voiced the principle known since the time of Aristotle and in logic called " Law of Sufficient Reason».

Simplified, the meaning of "Occam's razor" is sometimes explained as follows: in any theory (hypothesis, reasoning), the creation of new concepts, terms, definitions, etc. should be avoided. entities, if they can be dispensed with.

Why is the word "razor" in the title? Because it cuts off the excess!

Examples

Among the most famous examples of the application of this principle is the answer that the creator of the first theory of the origin of the solar system, the mathematician and physicist Laplace, gave to Emperor Napoleon. Napoleon allegedly asked (half-jokingly, half-seriously): "Something I don't see in your theory of a place for God." To which Laplace allegedly replied: "Sir, I had no need for this hypothesis."

When the disciples of Plato asked for a definition of man, the greatest philosopher said: "Man is an animal with two legs, devoid of feathers." Hearing this, Diogenes caught a rooster, plucked it, and bringing it to the Academy, announced: “Here is the Platonic man!” After which Plato was forced to add to his definition: "And with wide nails."

Reformulated in the language of information theory, the principle of "Occam's razor" states that the most accurate message is the message of the minimum length.

***

Who is Ockham

OKKAM ( Ockham, Occam) (c. 1285, Ockham, Surrey, England - c. 1349, Munich, Bavaria), English philosopher and theologian, Franciscan monk, ecclesiastical and political writer, the main representative of nominalism of the XIV century, one of the last prominent representatives of scholasticism .

Even while studying at Oxford, he entered the Franciscan order. After graduation, the philosopher remains at Oxford to teach theology and philosophy. He actively supported the head of the Franciscan order from Cesena in his dispute with the pope. In 1323, in connection with the accusation of heresy (for speaking out about the primacy of secular power over the power of the pope), he was summoned by Pope John XXII and imprisoned in Avignon, where he spent 4 years. In 1328, he managed to escape to Germany to the pope's enemy, Emperor Louis IV of Bavaria, to whom, according to legend, he said: "Defend me with a sword, and I will protect you with a pen!" He was excommunicated from the church. Having settled in Munich, Occam remained there until his death.

As a political writer, Occam opposed the pope's claims to secular power, against the absolutism of church and secular power; defended the principle of "evangelical poverty", anticipating in many ways the ideas of the Reformation.

Occam was one of the greatest logicians of the Middle Ages, the most prominent representative nominalism. Thanks to his virtuoso mastery of the art of dialectics, he received from his students the nickname " Doctor I nvincibilis» ( Invincible Teacher).

He owns the idea that the meaning of a term is entirely determined by its function in the statement; in the theory of consequence developed by him, he actually distinguished between material and formal implications, formulated the principle of duality for conjunction and disjunction. Primary cognition, according to Occam, is intuitive, which includes external perceptions and introspection. Concepts that are not reducible to intuitive knowledge and cannot be verified by experience must be removed from science: "essences should not be multiplied unnecessarily." This principle, later called Occam's Razor, played an important role in the struggle against the Middle Ages. realism, the theory of "hidden qualities", unobservable "essences", etc.

"Occam's Razor" can be considered as one of the first clear formulations of the "principle of simplicity", requiring the use of the smallest possible number of independent theoretical assumptions when explaining a certain range of empirical facts. The principle of simplicity runs through the history of the natural sciences. Many eminent naturalists pointed out that he repeatedly played a leading role in their research. In particular, Newton put forward a special methodological requirement "not to overdo it" in the causes when explaining phenomena. At the same time, the concept of simplicity is not unambiguous (simplicity in the sense of ease of manipulation, ease of study; simplicity of the assumptions underlying the theoretical generalization; independence of such assumptions, etc.). It is also not obvious that the desire for a smaller number of premises is itself directly related to an increase in the empirical reliability of a theoretical generalization.

In logic, the desire for "economy of initial assumptions" is expressed in the requirement of independence: none of the accepted axioms should be derived from the rest. This also applies to accepted inference rules. The following usual requirement for proof is also connected in a certain way with the “Occam’s razor”: among its premises there should not be “extra statements”, that is, statements that are not used directly in deriving the thesis being proved. This requirement of “economy of premises” is, of course, not necessary. It also does not seem clear enough and is not included in the very definition of evidence. A proof with "excessive" or overly strong premises is in some sense imperfect, but it remains a proof.

Occam was of the opinion that " the simplest explanations are the best". Based on this principle, he set about solving the problem of universals, but directed his reasoning in a different direction than his predecessors. In the works " The sum of all logic», « natural philosophy», « sum of logic"He argued that only a separate being is real, and universals exist only within the limits of the human mind, reflecting on them. Ockham by no means denied the usefulness of universals, but he did not acknowledge their reality.

Following the scholastic method, Ockham created an ontology of transcendental being, which was close to the ideas of Thomas Aquinas and Duns Scott. According to him, the world consists of single things and entities, and all knowledge is reduced to external and internal experience. Any true knowledge can only be obtained empirically, with the help of the senses. In view of the fact that there are no really existing universals that could be contemplated in consciousness, the mind cannot prove anything, relying only on its own forces. That is why Occam, unlike Anselm of Canterbury, considers unacceptable not only the proofs of the existence of God, but even the very attempts to know God, relying only on reason. Following Duns Scott, Occam proclaims that God is understood not by reason (Thomas Aquinas, Albertus Magnus) and not by illumination (Bonaventure), but only by faith. It is faith and intuitive knowledge that Ockham considers to be the tools of theology, and reason can only help in the search for arguments. Occam's work put an end to attempts to synthesize faith and reason. Reason was supposed to be engaged in the study of nature, and faith was supposed to comprehend God.

Occam's school laid the foundation for modern mechanics and astronomy, and also served as a starting point for the development of modern dynamics. The views held by Ockham were called the "modern way" in comparison with the "old way" of Thomas Aquinas and Duns Scotus. Occam had a significant influence on the subsequent development of logic and philosophy, especially on J. Buridan, Nicholas of Hautecourt and T. Hobbes. It was on the philosophy of Occamai that Martin Luther and other Protestant reformers were raised.

(Based on " Great Soviet Encyclopedia" And " Great Encyclopedia of Cyril and Methodius»)

***

In addition to philosophers, poets and writers sometimes remember Occam's razor, for example, the Strugatsky brothers mention it in their novels. "Beetle in an anthill" And "The Search for a Destiny, or the Twenty-seventh Theorem of Ethics".

In Brown's novel "Point of Deception" given the following interpretation of "Occam's razor" ("the law of economy"): “When there are many explanations for a problem, the simplest is usually the correct one.”.

"Occam's razor" – this name was taken by a Moscow musical group playing in the style of heavy alternative music.

***

Let's live without multiplying the essence without extreme necessity!..

Fans of Umberto Eco, of course, noticed that the protagonist of The Name of the Rose resembles Sherlock Holmes - both in the manner of presentation and, of course, in the principle of deduction. But not everyone knows that he is "written off" from another famous - and, by the way, real - personality who lived in the fourteenth century. This is William of Ockham, medieval philosopher and author of a famous scientific principle. Without it, it is difficult to imagine a strict logical assumption. This principle is known as Occam's Razor.

short biography

The philosopher himself was from the English county of Surrey. More precisely, from a small village called Ockham (or Ockham). Since he took the tonsure, according to custom, as a monk, he was called by his name and the locality where he was born. Therefore, it is more correct to call him William of Ockham. Having entered the Franciscan order, the future philosopher was engaged in theology. Since he supported the current of spirituals, later recognized as heretical, he had many problems with the Vatican. He even had to go to jail. It was only thanks to powerful secular patrons who were enemies of the Pope that he was able to escape a harsher sentence. Strictly speaking, he is not the discoverer of the "Occam's razor" principle. It's just that he very successfully formulated the thesis put forward by Aristotle in his time. This is the principle of sufficient reason.

Essence of the question

Why is this logical postulate so good? First of all, the fact that "Occam's razor" reflects the content of the principle of simplicity. The author was able to formulate this thesis so precisely and briefly, since he was a professional theologian, and thus tried to prove the existence of God. It means that where you can make one assumption, you should not make many of them, if this is not necessary. It can also be understood in such a way that with the help of one explanation it is possible to substantiate a thesis in the same way, or even better, than using a large number of arguments. Therefore, it is often called the principle of economy, frugality or reductionism.

Wording problem

"Occam's Razor" is most often known in a short formulation like: "Entities should not be multiplied unnecessarily." However, the philosopher himself did not write down his thesis in this form. They are not in the works of Ockham himself. In fact, this paraphrase of the principle of the famous Franciscan belongs to English and German commentators on his texts, and only became popular in the seventeenth century. Ockham's formulation sounds more accurate, since the play on Latin words allows us to apply this principle precisely as a "razor blade", that is, to "cut off" a false assumption, and thus reveal the truth.

Occam's Razor in Philosophy

Although the thinker himself tried to use his method in theology, in the era of modern times he found application in the sciences. He became especially popular in philosophy thanks to Leibniz. The latter expanded his understanding, and this thesis began to be interpreted as follows. If we assert that a certain object, process, connection between objects or a law exists, then for this we have facts and logical conclusions from them. This is called foundations. Next, we look at exactly what logically consistent explanations are available for evidence. If they are complex, then you can try to reduce them to simpler ones. Then the "Occam's razor" is applied to see if there is any reason for this. If not, then the simplest statements will be true. If there are such grounds, then this principle is not applicable here. In addition, this logical “blade” itself requires preferring a simpler hypothesis only if it can also very accurately interpret and describe the given phenomenon. More broadly in philosophy, this principle is applied to the rejection of implausible and unconvincing theories.

Occam's razor method in science

As we can see from the above, the Franciscan doctor was not at all against complex explanations, and did not forbid them. He is simply trying to introduce a certain order of consideration and construction of theories so that one can not get confused in false statements. That is why this principle has become the basis of scientific modeling. According to him, having a set of different equivalent models of any phenomenon, one should choose the simplest of them. The principle of "Occam's razor" in this case helps to "cut off" the terms of concepts or constructs that we do not need to explain this phenomenon. If you follow these rules, then the process of building a model becomes easier, and the likelihood of inconsistencies, ambiguities, and abuse is reduced. It is also indispensable when creating complex systems. However, this method is difficult to apply in a situation where the models we have are not equivalent. In addition, the criteria for simplicity themselves often differ. And it is not always clear which model answers them.

In culture

The principle of "Occam's razor" is so popular that it even began to play up in modern literature and cinematography. A fairly well-known historical anecdote is the answer of the astronomer Laplace to Emperor Napoleon. When the ruler asked the scientist where in his theory of the origin of the Universe there would be a place for God, he heard the answer that this hypothesis was too complicated and was rejected by him. On the other hand, in the equally famous series The X-Files, Fox Mulder, in response to his partner Dana Scully's attempts to explain everything, following the principle of economy, calls Occam's razor "the principle of limited imagination." Science fiction writers, from the Strugatsky brothers to Dan Brown, often like to mention this logical principle.

Occam's Razor is a logical technique for dealing with hypotheses.

"Occam's razor" (sometimes "Occam's blade", lat. lex parsimoniae) is a methodological principle that received its name from the English monk-philosopher William Occam (c. 1285-1349). In philosophy, the term "razor" is understood as a tool that helps to discard ("shave", from the English shave away) unlikely, implausible explanations.

The principle sounds like this: “Unnecessary things should not be affirmed” (lat. Pluralitas non est ponenda sine necessitate).

Sometimes the principle is expressed in the words “What can be explained by means of less should not be expressed by means of more” (Latin Frustra fit per plura quod potest fieri per pauciora). At the same time, the wording “essences should not be multiplied unnecessarily” (lat. Entia non sunt multiplicanda sine necessitate), usually given by historians, does not occur in Ockham’s works.

Occam's Razor - the rule for theories that have not yet been confirmed by experience

Do not use multiple explanations if one is sufficient;
- to consider true that which is simpler;
- discard that which is not reducible to intuitive or experiential knowledge;

_________________________________________________

In the modern sense, the principle of Occam's Razor is as follows: if a phenomenon can be explained in two ways, for example, the first - through the involvement of entities (terms, factors, transformations, etc.) A, B and C, and the second - through A, B, C and D, and at the same time both methods give the same result, other things being equal, the first explanation should be considered correct, that is, the essence of D is superfluous, and its involvement is redundant.

At the same time, an important clarification is that Occam's Razor is not an axiom, but a presumption, that is, it does not prohibit more complex explanations in principle, but only recommends the order in which hypotheses are considered, which in most cases is optimal.

Occam was of the opinion that "the simplest explanations are the best." Based on this principle, he set about solving the problem of universals. In the works "The sum of all logic", "Natural Philosophy", he argued that only a separate being is real, and universals exist only within the human mind, reflecting on them. Ockham by no means denied the usefulness of universals, but he did not acknowledge their reality.

In modern science, Occam's razor is usually understood as a general principle stating that if there are several logically consistent explanations of a phenomenon that explain it equally well, then it follows that ceteris paribus, consider the simplest of them to be true. The content of the principle can be reduced to the following: it is not necessary to introduce new laws in order to explain some new phenomenon, if this phenomenon can be fully explained by the old laws.

Attention should be paid to the turns used above “equally well”, “ceteris paribus” and “exhaustively”: Occam’s razor requires preferring a simple explanation only if it explains the phenomenon no less accurately than a complex one, taking into account all currently known moment an array of observations, that is, if there are no objective reasons to prefer a more complex explanation to a simpler one.

Logically, Occam's razor is based on the principle of sufficient reason, introduced by Aristotle, and in its modern form formulated by Leibniz: it is possible to assert the existence of an object, phenomenon, connection, pattern, etc. only if there are grounds, that is, facts or logical conclusions from facts confirming this is a judgment. Considering simple and complex explanations from the point of view of this principle, it is easy to see that if a simple explanation is complete and exhaustive, then there are simply no sufficient grounds for introducing additional components into the reasoning.

On the other hand, if there are such grounds, then the simple explanation is no longer complete and exhaustive (since it does not cover these grounds), that is, the conditions for applying Occam's razor are not met. Albert Einstein formulated the principle of Occam's Razor in this way: "Everything should be simplified as long as possible, but no more."

Also called the principle of thrift, or the law of economy.

However, what is called "Occam's Razor" was not formulated by Occam, he only formulated a principle known since the time of Aristotle and in logic called "principle of sufficient reason". "Occam's Razor" is only the name of the principle, and not its attribution (indication of authorship).

Principle of Scientific Proof: The shortest representation is the most true.

Historical digression

In "Ockam. Philosophical Writings. A Selection Edited and Translated by Philotheus Boehner" (New York, 1957), a specialist in the history of medieval philosophy, Philotheus Boehner, reports that most often "Occam's Razor" is given by the author in the following formulation: "Unnecessarily one should not assert much" (lat. Pluralitas non est ponenda sine necessitate ). More specifically, Occam put it this way:

Sometimes the principle is expressed in the words "That which can be explained by means of less, should not be expressed by means of more" (lat. Frustra fit per plura quod potest fieri per pauciora ). At the same time, the formulation usually given by historians “essences should not be multiplied unnecessarily” (lat. Entia non sunt multiplicanda sine necessitate ) is not found in the works of Occam.

In modern science, Occam's razor is usually understood as a more general principle, stating that if there are several logically consistent definitions or explanations of a phenomenon, then the simplest of them should be considered correct.

The content of the principle can be simplified as follows: it is not necessary to introduce new laws to explain some new phenomenon if this phenomenon can be explained by old laws. Now this principle is a powerful tool of scientific critical thought. Occam himself formulated this principle as a confirmation of the existence of God. They, in his opinion, can definitely explain everything without introducing anything new.

Examples

Among the most famous examples of the application of this principle is the answer that the creator of the first theory of the origin of the solar system, the mathematician and physicist Laplace, gave to Emperor Napoleon. Napoleon supposedly asked (half-jokingly, half-seriously): "Something I do not see in your theory of a place for God," to which Laplace allegedly replied: "Sir, I had no need for this hypothesis."
When Plato's students asked for a definition of man, the philosopher said: "Man is an animal with two legs, devoid of feathers." Hearing this, Diogenes of Sinop caught a rooster, plucked it and, bringing it to the Academy, announced: “Here is the Platonic man!” After which Plato was forced to add to his definition: "And with flat nails."
Reformulated in the language of information theory, the principle of "Occam's Razor" states that the most accurate message is the message of the minimum length.
Albert Einstein reformulated the principle of "Occam's Razor" as follows: "Everything should be simplified as long as possible, but no more."

Literature

Robert T. Carroll"Occam's Razor" // Encyclopedia of Delusions: a collection of incredible facts, amazing discoveries and dangerous beliefs = The Skeptic's Dictionary: A Collection of Strange Beliefs, Amusing Deceptions, and Dangerous Delusions. - M .: "Dialectics", 2005. - C 78-82 ISBN 5-8459-0830-2