Ockham's razor

Ockham's razor is a principle attributed to the fourteenth century English logician and Franciscan friar William of Ockham. Originally a tent pole of the reductionist philosophy of nominalism, today, it is more often interpreted as a heuristic guideline that advises economy, parsimony, or simplicity in theories. Ockham's razor states that the explanation of any phenomenon should make as few assumptions as possible, eliminating those that make no difference in the observable predictions of the explanatory hypothesis or theory. The principle is often expressed in Latin as the "lex parsimoniae" (law of succinctness): "entia non sunt multiplicanda praeter necessitatem," which translates to, "entities should not be multiplied beyond necessity."

Contents

History

The origins of what has come to be known as Ockham's razor are traceable to the works of earlier philosophers such as John Duns Scotus (1265–1308), Thomas Aquinas (c. 1225–1274), and even Aristotle (384–322 B.C.E.) (Charlesworth 1956). The term "Ockham's razor" first appeared in 1852 in the works of Sir William Rowan Hamilton (1805–1865), long after Ockham's death around 1349. Ockham did not invent the idea of parsimony in reason, so the association of the razor with him may be due to the frequency and effectiveness with which he used it (Ariew 1976). And though he stated the principle in various ways, the most popular version was written not by himself but by John Ponce of Cork in 1639 (Thorburn 1918).

Justifications and applications

Ockham's razor has always been associated with the aesthetic concept of simplicity. Prior to the twentieth century, it was believed that nature itself was simple and that simpler theories about nature were thus more likely to be true. Thomas Aquinas made this argument in the thirteenth century, writing, "If a thing can be done adequately by means of one, it is superfluous to do it by means of several; for we observe that nature does not employ two instruments where one suffices" (Pegis 1945). Beginning in the twentieth century, however, epistemological justifications based on induction, pragmatism, and probability theory have become more popular among philosophers. See Roger Ariew's 1976 dissertation, "Ockham's Razor: A Historical and Philosophical Analysis of Ockham's Principle of Parsimony."

The razor's strict form, which prohibits irrelevant assumptions in a given theory, is justified by the fact that all assumptions introduce possibilities for error. If an assumption does not improve the accuracy of a theory, its only effect is to make the theory more error-prone, and since error is undesirable in any theory, unnecessary assumptions should be avoided.

However, Ockham's razor is not equivalent to the idea that "perfection is simplicity." Albert Einstein probably had this in mind when he wrote in 1933 that "The supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience." This is often paraphrased as, "Theories should be as simple as possible, but no simpler." It often happens that the best explanation is much more complicated than the simplest possible explanation because it requires fewer assumptions. In the light of this, the popular rephrasing of the razor—that "The simplest explanation is the best one"—can lead to a gross oversimplification when the word simple is taken at face value.

Regarding this matter, Ockham stated, "No plurality should be assumed unless it can be proved (a) by reason, or (b) by experience, or (c) by some infallible authority." The last clause "refers to the Bible, the Saints and certain pronouncements of the Church" (Hoffmann 1997). Thus in the original spirit of Ockham's razor, the existence of God and matters of the Church become the essential pluralities of an argument. Although the historical use of Ockham's razor focuses solely on its value of simplicity, it should be noted that the point of Ockham's razor originally focused not on just the need to avoid unnecessary assumption, but rather to distinguish which assumptions and variables can be permitted in making an argument. William of Ockham utilized the razor to ground his philosophy and logic in his faith; however, the use of Ockham's razor has been taken out of the context of its original theological implications.

Science and Ockham's razor

Ockham's razor has become a basic tool for those who follow the scientific method. The primary activity of science —formulating theories and selecting the most promising ones—is impossible without a way of choosing from among the theories which fit the evidence equally well, the number of which can be arbitrarily large. When it is proposed as a principle of science, Ockham's razor is construed as a decision procedure for choosing among competing systems of hypotheses. In this context, a system of hypotheses, together with its supporting definitions and its logical consequences, is commonly described as a theory. To evaluate the utility of a radular (razor-like) tool in this setting, it is necessary to establish both the ground rules of scientific procedure and the operational definition of a particular brand of razor with a significant degree of formal precision.

There are two senses in which Ockham's razor can be seen at work in the history of science. One is ontological reduction by elimination and the other is by intertheoretic competition.

The following are ontological examples of reduction by elimination: The impetus of Aristotelian Physics, the angelic motors of medieval celestial mechanics, the four humors of ancient and medieval medicine, demonic possession as an explanation of mental illness, Phlogiston from premodern chemistry, and vital spirits of premodern Biology.

In the cases of intertheoretical competition, there are three examples from the history of science where the simpler of two competing theories, each of which explains all the observed phenomena, has been chosen over its ontologically bloated competitor: the Copernican heliocentric model of celestial mechanics over the Ptolemaic geocentric model, the mechanical theory of heat over the Caloric theory, and the Einsteinian theory of electromagnetism over the luminiferous aether theory.

In the first example, the Copernican model is said to have been chosen over the Ptolemaic due to its greater simplicity. The Ptolemaic model, in order to explain the apparent retrograde motion of Mercury relative to Venus, posited the existence of epicycles within the orbit of Mercury. The Copernican model (as expanded by Kepler) was able to account for this motion by displacing the Earth from the center of the solar system and replacing it with the sun as the orbital focus of planetary motions while simultaneously replacing the circular orbits of the Ptolemaic model with elliptical ones. In addition, the Copernican model excluded any mention of the crystalline spheres that the planets were thought to be embedded in according the Ptolemaic model. In a single stroke the Copernican model reduced by a factor of two the ontology of Astronomy.

According to the Caloric theory of heat, heat is a weightless substance that can travel from one object to another. This theory arose from the study of cannon boring and the invention of the steam engine. It was while studying cannon boring that Count Rumford made observations that conflicted with the Caloric theory and he formulated his mechanical theory to replace it. The Mechanical theory eliminated the Caloric theory and was ontologically simpler than its predecessor.

During the 19th century Physicists believed that light required a medium of transmission much as sound waves do. It was hypothesized that a universal aether was such a medium and much effort was expended to detect it. In one of the most famous negative experiments in the history of science, the Michelson-Morley experiment failed to find any evidence of its existence. Then when Einstein constructed his theory of special relativity without any reference to the Universal aether, this subsequently became the accepted view, thus providing another example of a theory chosen in part for its greater ontological simplicity.

Religion

In the philosophy of religion, Ockham's razor is sometimes applied to the existence of God; if the concept of God does not help to explain the universe, it is argued, God is irrelevant and should be cut away (Schmitt 2005). Thus, it is argued that the idea of the existence of God is an unnecessary plurality that creates more ambiguity. However, in the original spirit with which William of Ockham utilized the razor, the existence of God and matters of the Church are the essential pluralities of an argument in order to create the simplest, thereby the most effective, argument.

The history of theistic thought illustrates the point that certain arguments assume the plurality of the existence of God. The cosmological argument, for example, states that the universe must be the result of a "first cause" and that that first cause must be God. Similarly, the teleological argument credits the appearance of design and order in the universe to supernatural intelligence. Many people believe in miracles or have what they call religious experiences, and some theists consider creationism to be more believable than naturalistic explanations for the diversity and history of life on earth.

Philosophy

Probably the first person to make use of the principle was Ockham himself. He writes "The source of many errors in philosophy is the claim that a distinct signified thing always corresponds to a distinct word in such a way that there are as many distinct entities being signified as there are distinct names or words doing the signifying." (Summula Philosophiae Naturalis III, chap. 7, see also Summa Totus Logicae Bk I, C.51). We are apt to suppose that a word like "paternity" signifies some "distinct entity," because we suppose that each distinct word signifies a distinct entity. This leads to all sorts of absurdities, such as "a column is to the right by to-the-rightness," "God is creating by creation, is good by goodness, is just by justice, is powerful by power," "an accident inheres by inherence," "a subject is subjected by subjection," "a suitable thing is suitable by suitability," "a chimera is nothing by nothingness," "a blind thing is blind by blindness," and " a body is mobile by mobility." We should say instead that a man is a father because he has a son (Summa C.51). He further utilizes the razor in creating his argument against the problem of the universals, his metaphysics, epistemology, and logic.

Another application of the principle is to be found in the work of George Berkeley (1685–1753). Berkeley was an idealist who believed that all of reality could be explained in terms of the mind alone. He famously invoked Ockham's razor against Idealism's metaphysical competitor, materialism, claiming that matter was not required by his metaphysic and was thus could be eliminated. Idealism has few adherents today and Berkeley's arguments find few sympathetic ears.

Dale Jacquette (1994) claims that Ockham's razor is the rationale behind eliminativism and reductionism in the philosophy of mind. Eliminativism is the thesis that the ontology of folk psychology, including such entities as "pain," "joy," "desire," "fear," etc., are eliminable in favor of an ontology of a completed neuroscience.

Variations

The use of Ockham's Razor requires a context that defines which variables are necessary and which are not. Its original use by William of Ockham utilized a theological framework within which he used the razor in order to formulate his philosophy. Nonetheless, the use of Ockham's razor has been applied commonly to stress the value of simplicity in an argument.

The principle is most often expressed as "Entia non sunt multiplicanda praeter necessitatem," or "Entities should not be multiplied beyond necessity," but this sentence was written by later authors and is not found in Ockham's surviving writings. This also applies to "non est ponenda pluritas sine necessitate," which translates literally into English as "pluralities ought not be posited without necessity." It has inspired numerous expressions including "parsimony of postulates," the "principle of simplicity," the "KISS principle" (Keep It Simple, Stupid), and in some medical schools "When you hear hoofbeats, think horses, not zebras."

Other common restatements are, "Entities are not to be multiplied without necessity," and, "The simplest answer is usually the correct answer."

Or, as Einstein put it "As simple as possible, but no simpler"

Leonardo da Vinci (1452–1519) lived after Ockham's time and has a variant of Ockham's razor. His variant short-circuits the need for sophistication by equating it to simplicity. "Simplicity is the ultimate sophistication."

Ockham's razor is now usually stated as follows: "Of two equivalent theories or explanations, all other things being equal, the simpler one is to be preferred."

As this is ambiguous, Isaac Newton's version may be better: "We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances."

In the spirit of Ockham's razor itself, the rule is sometimes stated as: "The simplest explanation is usually the best."

Another common statement of it is : "The simplest explanation that covers all the facts."

This is an over-simplification, or at least a little misleading.

The earliest versions of the razor clearly imply that if a more complex theory is necessary then it need not be invalid. Perhaps a better way to state it is: "A correct theory of phenomena is only as complex as is necessary—and no more so—to explain said phenomena."

Anti-razors

Ockham's razor has met some opposition from people who have considered it too extreme or rash. Walter of Chatton, a contemporary of William of Ockham (1287–1347), took exception to Ockham's razor and Ockham's use of it. In response he devised his own anti-razor: "If three things are not enough to verify an affirmative proposition about things, a fourth must be added, and so on." Although there have been a number of philosophers who have formulated similar anti-razors since Chatton's time, Chatton's anti-razor has not known anything like the success of Ockham's razor.

Anti-razors have also been created by Gottfried Wilhelm Leibniz (1646–1716), Immanuel Kant (1724–1804), and Karl Menger (1902-1985). Leibniz's version took the form of a principle of plenitude, as Arthur Lovejoy has called it, the idea being that God created the world with the most possible creatures. Kant felt a need to moderate the effects of Ockham's razor and thus created his own counter-razor: "The variety of beings should not rashly be diminished." Karl Menger did not find mathematicians to be generous enough with regard to variables so he formulated his Law Against Miserliness which took one of two forms: "Entities must not be reduced to the point of inadequacy," and, "It is vain to do with fewer what requires more." (Maurer 1984) A less serious, but (some might say) even more extremist anti-razor is Pataphysics, the science of imaginary solutions invented by Alfred Jarry (1873–1907). Perhaps the ultimate in anti-reductionism, Pataphysics seeks no less than to view each event in the universe as completely unique, subject to no laws but its own.

References

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  • Jacquette, Dale (1994). Philosophy of Mind. Engleswoods Cliffs, New Jersey: Prentice Hall. ISBN 0130309338, 34–36.
  • Jaynes, Edwin Thompson 1994 . Model Comparison and Robustness. Probability Theory: The Logic of Science.
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All links retrieved February 11, 2015.

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