Occam's razor

The Latin maxim Entia non sunt multiplicanda praeter necessitatem , which is so well-known and popular among modern scholars, was first called William Hamilton , professor of logic and metaphysics of the University of Edinburgh, William Hamilton , in the book Conversations on Philosophy and literature ”published in 1852 ^[2] .

The term was a kind of Englishization of the Latin Novaculum Nominalium - the "blade of nominalism." In turn, the Latin term was a literal translation from the French witty expression of the philosopher Etienne Condillac - “ Rasoir des Nominaux ”, thus christening this Latin expression in the work “Sources of Human Consciousness”, published in 1746 ^[2] . Upon further investigation, it turns out that maxim refers to nominalism in the proper sense of the word rather conditionally.

The then young Gottfried Leibniz , who interpreted the works of his teacher in his own way in his famous dissertation published in 1670, first associated with nominalism (but not with Ockham!) Because of its popularity, Leibniz’s dissertation has been reprinted more than once, along with a new look at nominalism, imperceptibly spreading its new “axiom” ^[2] .

However, not one of the significant medieval authors (not only nominalists) formulated an axiom in this form. Literally, in this very order of words, in print it appeared for the first time only in 1654 in the book of the German scientist Johann Klauberg “Logic. Old and new ”(Logica vetus et nova, Groningen, 1654); even earlier, in 1639, close to the Klauberg version, the axiom was formulated by the learned monk , a professor of philosophy at St. Francisan College of Rome. Isidora, originally from Irish, is “a little-known man of great talent and very independent views” ^[2] . In the comments on the new edition of Duns Scott 's Opus Oxoniense, this scholar wrote that the expression “ non sunt multiplicanda entia sine necessitate ” is “a common axiom often found among scholastics .” And this is the earliest expression of the Latin maxim, later known as Occam's Razor.

Just half a century after the first mention, in the universal Encyclopedia Britannica , the term Occam's Razor was already noted as a full synonym for the Law of parsimony, the formulation of which was attributed to Occam's encyclopedia ^[3] . However, already in 1918, an article entitled The Myth of Occam's Razor was published in the popular scientific journal Mind , published in Canada by York University and dedicated to questions of philosophy. The author, after at least three years of research, came to the conclusion that the expression known as “Occam's razor” does not belong to Occam. As, however, is the assertion of the "Law of Economy", which was already indicated by Aristotle in his Physics , but "completely and completely" described by "the greatest of medieval thinkers," Occam's teacher, Duns Scott ^[2] .

A typical case of the "Stigler's Law" , which states that not a single scientific discovery is named after its discoverer ^[4] .

In later encyclopedias, dictionaries, and philosophical publications, instead of the originally given maxim “ Entia non sunt multiplicanda praeter necessitatem ” (“You should not multiply entities without necessity”), which is not related to Ockham, two other formulas are really found in his works. So, in the modern thorough edition of Ockham in English - “Ockham. Philosophical Writings. A Selection Edited and Translated by Philotheus Boehner ”(New York, 1957), Philotheus Boehner, a connoisseur of medieval philosophy, pointed out that the“ Occam's razor ”is often implied by the author in an implicit form, but is clearer and most often expressed in the formulas:“ Pluralitas non est ponenda sine neccesitate ”(“ Many should not be affirmed unnecessarily ”) and“ Frustra fit per plura quod potest fieri per pauciora ”(“ It is unnecessary to explain through much that is possible through less ”), found in different places of his reasoning. In one of these places, for example, Ockham says:

... multiplicity should never be assumed unnecessarily ... [but] everything that can be explained from the difference in matter for a number of reasons - it can be explained equally well or even better with the help of one basis.

Maxims of Occam in its imaginary and real forms may seem similar to indistinguishability, but only at the sight of a person who is far from the heated debate of theologians and philosophers. So, back in 1915, in the same Mind magazine, with the inherent solidity of the magazine, it was proved that the Occam’s Razor, taken according to Hamilton, simply could not be Occam’s saying, since it contradicted his whole philosophy ^[2] .

Occam himself, of course, did not suspect any "Occam's razor". And he did not consider himself a nominalist, since nominalism was officially recognized as heresy back in 1092. Acquainted with the writings of Aristotle, medieval thinkers spent a lot of ink to assimilate his legacy, aligning it as much as possible with the religion of Revelation . One of the controversial, “hot”, questions of that time was the question of “universals,” whether they have their own essence . The answer to this question led to a host of new questions, such as, for example, “Did Jesus have an angel?” Or “Who was more complex, an angel or an archangel?” - which, roughly speaking, became the main content of the flames in the Late Middle Ages and in Proto-renaissance discussions.

Ockham, as follows from his cautious maxims, developed Aristotle's individual intuitions, criticizing, like him, the “excessive” “world of ideas”, insisting on the existence of universals only in thought, but not in reality, and relying on the “ The law of economy. " His predecessors, except for Duns Scott (1265-1308), the famous commentators of Aristotle - Robert Grossetest (1175-1253) and Maimonides (1138-1204).

However, it should be remembered that the "Law of Economy", - this is an "effective tool against Platonism" ^[5] , - according to Ockham, is applicable only in the field of logic , which he tried to separate by all forces of his mind from ontology : after all, recognizing simplicity a priori is more perfect than complexity ( “The simpler the better”) you can quickly quickly come to the exclusion of the double nature of Christ, then the trinity of God, and then of God himself. What was the most terrible dream for a Franciscan monk. But it happened - in fact, due to the logic so beloved by Ockham. A few hundred years after his death.

In the original, the “principle of saving” is generated, it seems, in an unshakable conviction that perfection itself should be simple. This seems to be the metaphysical foundation on which we stand, just like the Middle Ages and antiquity. As then, many of our disputes are not about this principle, but about what is considered necessary and sufficient. ^[6]

Original text

The original principle seems to have been invoked within the context of a belief in the notion that perfection is simplicity itself. This seems to be a metaphysical bias which we share with the medievals and the ancient Greeks. For, like them, most of our disputes are not about this principle but about what counts as necessary.

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

Attention should be paid to the above-mentioned turns of “equally good”, “ceteris paribus” and “exhaustive”: Occam’s razor requires a simple explanation only if it explains the phenomenon no less accurately than complex, given all the current moment an array of observations, that is, if there are no objective reasons to prefer a more complex explanation to a simple one.

Logically, Occam’s razor is based on the principle of sufficient reason , introduced by Aristotle, and in a modern form formulated by Leibniz : to confirm the existence of an object, phenomenon, connection, pattern, etc., is possible only if there are grounds, that is, facts or logical conclusions from facts confirming this is a judgment. Considering a simple and complex explanation from the point of view of this principle, it is easy to see that if a simple explanation is complete and comprehensive, then there are simply no sufficient grounds for introducing additional components into the discussion. On the other hand, if there are such reasons, then a simple explanation is no longer complete and exhaustive (since it does not cover these reasons), that is, the conditions for using Occam's razor are not fulfilled.

In philosophy, the term “razor” refers to a tool that helps to discard (shave) improbable, implausible explanations. And since the shaving tool is a razor, razor, the same name has been transferred to the truth-establishing tool.

Examples of other "razors": Popper's falsifiability principle , Hanlon razor, Hitchens razor .

One of the problems of the original formulation of the principle is that it is applicable only to models with the same descriptive ability (that is, it involves the choice of the simplest of the models that equally well explain observational facts). A more general razor shape can be obtained from Bayesian model comparisons . This method allows you to choose a model that is optimal in terms of both its complexity and its power (descriptive power). As a rule, this problem is absolutely not solved exactly, but such approximations as the Akaike information criterion , Bayesian information criterion , variational Bayesian methods , false discover rate and Laplace's method are used .

In the scientific disciplines of machine learning and artificial intelligence, the Occam principle is used in the Occam learning approach, or more generally in the Free energy principle .

• Among the most famous examples of the application of this principle is the answer given to the emperor Napoleon by the creator of the first theory of the appearance of the solar system, the mathematician and physicist Laplace . Napoleon asked why the word “God”, constantly repeated by Lagrange , did not appear in his composition at all, to which Laplace replied: “This is because I did not need this hypothesis” ^[7] .
• One of the modern examples that is used in science and philosophy sounds something like this: “If an event has two or more different solutions leading to one answer, then the simplest solution will be true, which requires fewer unknowns (variables).”
• When the students asked Plato to give a definition of man, the philosopher said: "Man is an animal on two legs, devoid of feathers." Hearing this, Diogenes caught a rooster, plucked it and, having brought it to the Academy, announced: “Here is a Platonic man!” After which Plato added to his definition: “And with flat nails” ^[8] .
• Reformulated in the language of information theory , Occam's razor principle states that the most accurate message is a message of minimum length .
• In this sense, Albert Einstein formulated the principle of Occam's razor: “Everything should be simplified as long as possible, but no more.”

• Hanlon Razor
• Common sense
• Scientific skepticism
• KISS Principle
• Reductionism
• Duck test
• Falsifiability
• Eliminative materialism

in Russian

• Occam's Razor // Carroll R. T. Encyclopedia of Misconceptions: A Collection of Unbelievable Facts, Amazing Discoveries and Dangerous Beliefs = The Skeptic's Dictionary: A Collection of Strange Beliefs, Amusing Deceptions, and Dangerous Delusions. - M .: "Dialectics" , 2005. - S. 78-82. - ISBN 5-8459-0830-2 .

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