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Encyclopedia > Occam's razor

Occam's razor (sometimes spelled Ockham's razor) is a principle attributed to the 14th-century English logician and Franciscan friar William of Ockham. The principle 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 parsimony" or "law of succinctness"): "entia non sunt multiplicanda praeter necessitatem", or "entities should not be multiplied beyond necessity". Image File history File links Question_book-3. ... Occams Razor is the third episode of the first season of House, which premiered on the FOX network on November 30, 2004. ... This 14th-century statue from south India depicts the gods Shiva (on the left) and Uma (on the right). ... A logician is a philosopher, mathematician, or other whose topic of scholarly study is logic. ... The Order of Friars Minor and other Franciscan movements are disciples of Saint Francis of Assisi. ... A friar is a member of a religious mendicant order of men. ... William of Ockham (also Occam or any of several other spellings, IPA: ) (c. ... For other uses, see Phenomena (disambiguation). ... Look up Hypothesis in Wiktionary, the free dictionary. ... The word theory has a number of distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion. ... Look up parsimony in Wiktionary, the free dictionary. ...


This is often paraphrased as "All other things being equal, the simplest solution is the best." In other words, when multiple competing theories are equal in other respects, the principle recommends selecting the theory that introduces the fewest assumptions and postulates the fewest entities. It is in this sense that Occam's razor is usually understood.


Originally a tenet of the reductionist philosophy of nominalism, it is more often taken today as a heuristic maxim (rule of thumb) that advises economy, parsimony, or simplicity, often or especially in scientific theories. Descartes held that non-human animals could be reductively explained as automata — De homines 1622. ... In philosophy, nominalism is the theory that abstract terms, general terms, or universals do not represent objective real existents, but are merely names, words, or vocal utterances (flatus vocis). ... For other uses, see Heuristic (disambiguation). ... According to Immanuel Kant, a maxim is a subjective principle or rule, that the will of an individual uses in making a decision. ... The word theory has a number of distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion. ...

Contents

History

'From Duns Scotus' Ordinatio - 'Pluralitas non est ponenda sine necessitate - plurality is not to be posited without necessity'

William Ockham (c. 1285–1349) is remembered as an influential nominalist, but his popular fame as a great logician rests chiefly on the maxim attributed to him and known as Occam's razor Entia non sunt multiplicanda praeter necessitatem or "Entities should not be multiplied unnecessarily." The term razor refers to the act of shaving away unnecessary assumptions to get to the simplest explanation. No doubt this represents correctly the general tendency of his philosophy, but it has not so far been found in any of his writings. His nearest pronouncement seems to be Numquam ponenda est pluralitas sine necessitate [Plurality is never to be posited without necessity], which occurs in his theological work on the Sentences of Peter Lombard (Quaestiones et decisiones in quattuor libros Sententiarum Petri Lombardi (ed. Lugd., 1495), i, dist. 27, qu. 2, K). In his Summa Totius Logicae, i. 12, Ockham cites the principle of economy, Frustra fit per plura quod potest fieri per pauciora [It is futile to do with more things that which can be done with fewer].

Thorburn, 1918, pp. 352-3; Kneale and Kneale, 1962, p. 243.

(Latin translations shown in square brackets in excerpt above are interpolations by WP editor.)


The origins of what has come to be known as Occam's razor are traceable to the works of earlier philosophers such as Maimonides (1138-1204), John Duns Scotus (1265–1308), Thomas Aquinas (c. 1225–1274), Alhacen), and even Aristotle (384–322 BC) (Charlesworth 1956). The term "Ockham's razor" first appeared in 1852 in the works of Sir William Rowan Hamilton (1805–1865), centuries after Ockham's death. Ockham did not invent this "razor," so its association with him may be due to the frequency and effectiveness with which he used it (Ariew 1976). Though Ockham 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). Commonly used image indicating one artists conception of Maimonidess appearance Maimonides (March 30, 1135 or 1138–December 13, 1204) was a Jewish rabbi, physician, and philosopher in Spain, Morocco and Egypt during the Middle Ages. ... John Duns Scotus (c. ... Aquinas redirects here. ... (Arabic: أبو علي الحسن بن الحسن بن الهيثم, Latinized: Alhacen or (deprecated) Alhazen) (965 – 1039), was an Arab[1] Muslim polymath[2][3] who made significant contributions to the principles of optics, as well as to anatomy, astronomy, engineering, mathematics, medicine, ophthalmology, philosophy, physics, psychology, visual perception, and to science in general with his introduction of the... For other uses, see Aristotle (disambiguation). ... William Rowan Hamilton Sir William Rowan Hamilton (August 4, 1805 – September 2, 1865) was an Irish mathematician, physicist, and astronomer who made important contributions to the development of optics, dynamics, and algebra. ...


The version of the Razor most often found in Ockham's work is Numquam ponenda est pluralitas sine necessitate [Plurality ought never be posited without necessity.]


Justifications

Aesthetic and practical considerations

Prior to the 20th century, it was a commonly-held belief that nature itself was simple and that simpler theories about nature were thus more likely to be true; this notion was deeply rooted in the aesthetic value simplicity holds for human thought and the justifications presented for it often drew from theology. Thomas Aquinas made this argument in the 13th 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."[1] Theology finds its scholars pursuing the understanding of and providing reasoned discourse of religion, spirituality and God or the gods. ... Aquinas redirects here. ... (12th century - 13th century - 14th century - other centuries) As a means of recording the passage of time, the 13th century was that century which lasted from 1201 to 1300. ...


The common form of the razor, used to distinguish between equally explanatory theories, can be supported by appeals to the practical value of simplicity. Theories exist to give accurate explanations of phenomena, and simplicity is a valuable aspect of an explanation because it makes the explanation easier to understand and work with. Thus, if two theories are equally accurate and neither appears more probable than the other, the simple one is to be preferred over the complicated one, because simplicity is practical. In computer science, for instance, tractability itself can be affected, such as with sorting algorithms. Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... As a branch of the theory of computation in computer science, computational complexity theory describes the scalability of algorithms, and the inherent difficulty in providing scalable algorithms for specific computational problems. ... In computer science and mathematics, a sorting algorithm is an algorithm that puts elements of a list in a certain order. ...


Beginning in the 20th century, epistemological justifications based on induction, logic, pragmatism, and probability theory have become more popular among philosophers. Theory of knowledge redirects here: for other uses, see theory of knowledge (disambiguation) According to Plato, knowledge is a subset of that which is both true and believed Epistemology or theory of knowledge is the branch of philosophy that studies the nature, methods, limitations, and validity of knowledge and belief. ... Aristotle appears first to establish the mental behaviour of induction as a category of reasoning. ... Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ... Pragmatism is a philosophic school that originated in the late nineteenth century with Charles Sanders Peirce, who first stated the pragmatic maxim. ... Probability theory is the branch of mathematics concerned with analysis of random phenomena. ...


Empirical justification

One way a theory or a principle could be justified is empirically; that is to say, if simpler theories were to have a better record of turning out to be correct than more complex ones, that would corroborate Occam's razor. However, Occam's razor is not a theory in the classic sense of being a model that explains physical observations, relying on induction; rather, it is a heuristic maxim for choosing among such theories and underlies induction. Justifying such a guideline against some hypothetical alternative thus fails on account of invoking circular logic. In logic, begging the question describes a type of logical fallacy, petitio principii, in which the conclusion of an argument is implicitly or explicitly assumed in one of the premises. ...


To wit: There are many different ways of making inductive inferences from past data concerning the success of different theories throughout the history of science, and inferring that "simpler theories are, other things being equal, generally better than more complex ones" is just one way of many- which only seems more plausible to us because we are already assuming the razor to be true (see e.g. Swinburne 1997 and Williams, Gareth T, 2008). This, however, does not exclude legitimate attempts at a deductive justification of the razor (and indeed these are inherent to many of its modern derivatives). Failing even that, the razor may be accepted a priori on pragmatist grounds. Pragmatism is a philosophic school that originated in the late nineteenth century with Charles Sanders Peirce, who first stated the pragmatic maxim. ...


Karl Popper

Karl Popper argues that a preference for simple theories need not appeal to practical or aesthetic considerations. Our preference for simplicity may be justified by his falsifiability criterion: We prefer simpler theories to more complex ones "because their empirical content is greater; and because they are better testable" (Popper 1992). In other words, a simple theory applies to more cases than a more complex one, and is thus more easily falsifiable. Sir Karl Raimund Popper (July 28, 1902 â€“ September 17, 1994) was an Austrian and British[1] philosopher and a professor at the London School of Economics. ... Falsifiability (or refutability or testability) is the logical possibility that an assertion can be shown false by an observation or a physical experiment. ...


Elliott Sober

The philosopher of science Elliott Sober once argued along the same lines as Popper, tying simplicity with "informativeness": The simplest theory is the more informative one, in the sense that less information is required in order to answer one's questions (Sober 1975). He has since rejected this account of simplicity, purportedly because it fails to provide an epistemic justification for simplicity. He now expresses views to the effect that simplicity considerations (and considerations of parsimony in particular) do not count unless they reflect something more fundamental. Philosophers, he suggests, may have made the error of hypostatizing simplicity (i.e. endowed it with a sui generis existence), when it has meaning only when embedded in a specific context (Sober 1992). If we fail to justify simplicity considerations on the basis of the context in which we make use of them, we may have no non-circular justification: "just as the question 'why be rational?' may have no non-circular answer, the same may be true of the question 'why should simplicity be considered in evaluating the plausibility of hypotheses?'" (Sober 2001) Elliott Sober -- Hans Reichenbach Professor and William F. Vilas Research Professor in the Department of Philosophy at University of Wisconsin. ... Theory of knowledge redirects here: for other uses, see theory of knowledge (disambiguation) According to Plato, knowledge is a subset of that which is both true and believed Epistemology or theory of knowledge is the branch of philosophy that studies the nature, methods, limitations, and validity of knowledge and belief. ... Sui generis is a (post) Latin expression, literally meaning a scholar like what pradeep is or unique in its characteristics. ...


Jerrold Katz

Jerrold Katz has outlined a deductive justification of Occam's razor: "If a hypothesis, H, explains the same evidence as a hypothesis G, but does so by postulating more entities than G, then, other things being equal, the evidence has to bear greater weight in the case of H than in the case of G, and hence the amount of support it gives H is proportionately less than it gives G" (Katz 1998). Jerrold J. Katz (1932-2002) was an American philosopher and linguist. ...


Richard Swinburne

Richard Swinburne argues for simplicity on logical grounds: "...other things being equal -- the simplest hypothesis proposed as an explanation of phenomena is more likely to be the true one than is any other available hypothesis, that its predictions are more likely to be true than those of any other available hypothesis, and that it is an ultimate a priori epistemic principle that simplicity is evidence for truth" (Swinburne 1997). Richard G. Swinburne (born December 26, 1934) is an eminent British professor and philosopher primarily interested in the philosophy of religion and philosophy of science. ...


He maintains that we have an innate bias towards simplicity and that simplicity considerations are part and parcel of common sense. Since our choice of theory cannot be determined by data (see Underdetermination and Quine-Duhem thesis), we must rely on some criterion to determine which theory to use. Since it is absurd to have no logical method by which to settle on one hypothesis amongst an infinite number of equally data-compliant hypotheses, we should choose the simplest theory: "...either science is irrational [in the way it judges theories and predictions probable] or the principle of simplicity is a fundamental synthetic a priori truth" (Swinburne 1997). This article needs to be cleaned up to conform to a higher standard of quality. ... Confirmation holism, also called epistemological holism is the claim that a scientific theory cannot be tested in isolation; a test of one theory always depends on other theories and hypotheses. ...


Applications

Science and the scientific method

The aforementioned problem of underdetermination poses a serious obstacle to applications of the scientific method. Formulating theories and selecting the most promising ones is impossible without a way of choosing among an arbitrarily large number of theories, all of which fit with the evidence equally well. If any one principle could single-handedly reduce all these infinite possibilities to find the one best theory, at first glance one might deduce that the whole of scientific method simply follows from it, and thus that it alone would be sufficient to power the whole process of hypothesis formulation and rejection scientists undertake. This article needs to be cleaned up to conform to a higher standard of quality. ... Scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. ...


However, while the necessity of some method or another to determine a working hypothesis in spite of the problem of underdetermination is by and large undisputed, the progression of actual science and actual scientific consensus is far removed from some simple formula which accepts "the evidence" and outputs "the best theory". Axioms may be taken for granted that are not at all true; theories might exist that are better supported by the evidence but will be overlooked because scientists were collecting data from the wrong places or asking the wrong questions to begin with (this was emphasized by Thomas Kuhn, who outright rejected induction as the main driving force of scientific progress altogether in favor of paradigm shifts). Resorting to the importance of Occam's Razor within the limits of inductive arguments still leaves open problems of formulation; "the simplest explanation tends to be the best" is hardly a formally precise statement and it may be difficult to use it, as is, to rigorously compare two competing hypotheses. This leaves open the possibility of rigorous modern formulations, and indeed such formulations have been derived which- while being outside the scope of Occam's original razor- are true to its spirit and yield useful results (see below, "probability theory"). As a matter of fact, the razor's first known appearance, in Maimonides "The Guide for the Perplexed" was indeed done in the context of choosing between two competing scientific (cosmological) theories. Thomas Samuel Kuhn (July 18, 1922 – June 17, 1996) was an American intellectual who wrote extensively on the history of science and developed several important notions in the philosophy of science. ... Paradigm shift is the term first used by Thomas Kuhn in his 1962 book The Structure of Scientific Revolutions to describe a change in basic assumptions within the ruling theory of science. ...


In physics, for example, one measurement of the simplicity of a theory is the number of free parameters. A theory with adjustable free parameters is considered to be less desirable than one with fewer free parameters, and a desirable goal of physics is to provide a theory with the minimum number of parameters required to explain the observations.


Occam'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" often paraphrased as "Theories should be as simple as possible, but no simpler." Or even put more simply "make it simple, not simpler". It often happens that the best explanation is much more complicated than the simplest possible explanation because its postulations amount to less of an improbability. Thus the popular rephrasing of the razor - that "the simplest explanation is the best one" - fails to capture the gist of the reason behind it, in that it conflates a rigorous notion of simplicity and ease of human comprehension. The two are obviously correlated, but hardly equivalent. “Einstein” redirects here. ...


There are two senses in which Occam'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. This article is about ontology in philosophy. ...


In the former case the following are 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 theory from premodern chemistry, and vital spirits of premodern biology. For other uses, see Aristotle (disambiguation). ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects. ... Demonic possession, in supernatural belief systems, is a form of spiritual possession whereby certain malevolent extra-dimensional entities, demons, gain control over a mortal persons body, which is then used for an evil or destructive purpose. ... Phlogiston theory was a 17th century attempt to explain oxidation processes, such as fire and rust. ... For the song by Girls Aloud see Biology (song) Biology studies the variety of life (clockwise from top-left) E. coli, tree fern, gazelle, Goliath beetle Biology (from Greek: βίος, bio, life; and λόγος, logos, speech lit. ...


In the latter case 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. Copernicus redirects here. ... Heliocentric Solar System Heliocentrism (lower panel) in comparison to the geocentric model (upper panel) In astronomy, heliocentrism is the theory that the sun is at the center of the Universe and/or the Solar System. ... This article is about the geographer, mathematician and astronomer Ptolemy. ... The geocentric model (in Greek: geo = earth and centron = centre) of the universe is a paradigm which places the Earth at its center. ... The caloric theory is an obsolete scientific theory that heat consists of a fluid called caloric that flows from hotter to colder bodies. ... The luminiferous aether: it was hypothesised that the Earth moves through a medium of aether that carries light In the late 19th century luminiferous aether (light-bearing aether) was the term used to describe a medium for the propagation of light. ...

  • 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 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 Aether this subsequently became the accepted view, thus providing another example of a theory chosen in part for its greater ontological simplicity.

This article is about the planet. ... (*min temperature refers to cloud tops only) Atmospheric characteristics Atmospheric pressure 9. ... In the Ptolemaic system of astronomy, the epicycle (literally: on the cycle in Greek) was a geometric model to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. ... Kepler redirects here. ... // The term steam engine may also refer to an entire railroad steam locomotive. ... For other persons named Benjamin Thompson, see Benjamin Thompson (disambiguation). ... The Michelson-Morley experiment, one of the most important and famous experiments in the history of physics, was performed in 1887 by Albert Michelson and Edward Morley at what is now Case Western Reserve University, and is considered by some to be the first strong evidence against the theory of...

Biology

Biologists or philosophers of biology use Occam's razor in either of two contexts both in evolutionary biology: the units of selection controversy and Systematics. George C. Williams in his book Adaptation and Natural Selection (1966) argues that the best way to explain altruism among animals is based on low level (i.e. individual) selection as opposed to high level group selection. Altruism is defined as behavior that is beneficial to the group but not to the individual, and group selection is thought by some to be the evolutionary mechanism that selects for altruistic traits. Others posit individual selection as the mechanism which explains altruism solely in terms of the behaviors of individual organisms acting in their own self interest without regard to the group. The basis for Williams's contention is that of the two, individual selection is the more parsimonious theory. In doing so he is invoking a variant of Occam's razor known as Lloyd Morgan's Canon: "In no case is an animal activity to be interpreted in terms of higher psychological processes, if it can be fairly interpreted in terms of processes which stand lower in the scale of psychological evolution and development" (Morgan 1903). This article is about evolution in biology. ... Biological systematics is the study of the diversity of life on the planet earth, both past and present, and the relationships among living things through time. ... George Williams Professor George Christopher Williams (b. ... Cover of the 1996 edition. ... For the ethical doctrine, see Altruism (ethics). ... Coined by 19th-century British psychologist C. Lloyd Morgan, Morgans Canon (more usually called Lloyd Morgans Canon, or occasionally Morgans Canon of Interpretation) remains a fundamental precept of comparative (animal) psychology. ...


However, more recent work by biologists, such as Richard Dawkins's The Selfish Gene, has revealed that Williams's view is not the simplest and most basic. Dawkins argues the way evolution works is that the genes that are propagated in most copies will end up determining the development of that particular species, i.e., natural selection turns out to select specific genes, and this is really the fundamental underlying principle, that automatically gives individual and group selection as emergent features of evolution. Clinton Richard Dawkins, FRS (born March 26, 1941) is a British ethologist, evolutionary biologist and popular science writer who holds the Charles Simonyi Chair for the Public Understanding of Science at the University of Oxford. ... Original book cover from the painting The Expectant Valley by zoologist Desmond Morris The Selfish Gene is a very popular and somewhat controversial book on evolutionary theory by Richard Dawkins, published in 1976. ... ...


Zoology provides an example. Musk oxen, when threatened by wolves, will form a circle with the males on the outside and the females and young on the inside. This as an example of a behavior by the males that seems to be altruistic. The behavior is disadvantageous to them individually but beneficial to the group as a whole and was thus seen by some to support the group selection theory. Zoology (from Greek: ζῴον, zoion, animal; and λόγος, logos, knowledge) is the biological discipline which involves the study of animals. ... Binomial name Ovibos moschatus (Zimmermann, 1780) The Musk ox (Ovibos moschatus) is a bovine noted for its thick coat and for the strong odor of the male. ... Wolf Wolf Man Mount Wolf Wolf Prizes Wolf Spider Wolf 424 Wolf 359 Wolf Point Wolf-herring Frank Wolf Friedrich Wolf Friedrich August Wolf Hugo Wolf Johannes Wolf Julius Wolf Max Franz Joseph Cornelius Wolf Maximilian Wolf Rudolf Wolf Thomas Wolf As Name Wolf Breidenbach Wolf Hirshorn Other The call... Altruism refers to both a practice or habit (in the view of many, a virtue) as well as an ethical doctrine. ...


However, a much better explanation immediately offers itself once one considers that natural selection works on genes. If the male musk ox runs off, leaving his offspring to the wolves, his genes will not be propagated. If however he takes up the fight his genes will live on in his offspring. And thus the "stay-and-fight" gene prevails. This is an example of kin selection. An underlying general principle thus offers a much simpler explanation, without retreating to special principles as group selection. In evolutionary biology, kin selection refers to changes in gene frequency across generations that are driven at least in part by interactions between related individuals, and this forms much of the conceptual basis of the theory of social evolution. ...


Systematics is the branch of biology that attempts to establish genealogical relationships among organisms. It is also concerned with their classification. There are three primary camps in systematics; cladists, pheneticists, and evolutionary taxonomists. The cladists hold that genealogy alone should determine classification and pheneticists contend that similarity over propinquity of descent is the determining criterion while evolutionary taxonomists claim that both genealogy and similarity count in classification. Biological systematics is the study of the diversity of life on the planet earth, both past and present, and the relationships among living things through time. ... For the song by Girls Aloud see Biology (song) Biology studies the variety of life (clockwise from top-left) E. coli, tree fern, gazelle, Goliath beetle Biology (from Greek: βίος, bio, life; and λόγος, logos, speech lit. ... Genealogy (from Greek: γενεα, genea, family; and λόγος, logos, knowledge) is the study and tracing of family pedigrees. ...


It is among the cladists that Occam's razor is to be found, although their term for it is cladistic parsimony. Cladistic parsimony (or maximum parsimony) is a method of phylogenetic inference in the construction of cladograms. Cladograms are branching, tree-like structures used to represent lines of descent based on one or more evolutionary change(s). Cladistic parsimony is used to support the hypothesis(es) that require the fewest evolutionary changes. For some types of tree, it will consistently produce the wrong results regardless of how much data is collected (this is called long branch attraction). For a full treatment of cladistic parsimony see Elliott Sober's Reconstructing the Past: Parsimony, Evolution, and Inference (1988). For a discussion of both uses of Occam's razor in Biology see Elliott Sober's article Let's Razor Ockham's Razor (1990). Maximum parsimony, often simply referred to as parsimony, is a non-parametric statistical method commonly used in computational phylogenetics for estimating phylogenies. ... It has been suggested that Clade be merged into this article or section. ... Long branch attraction (LBA) is a phenomenon in phylogenetic analyses (most commonly those employing maximum parsimony) when rapidly evolving lineages are inferred to be closely related, regardless of their true evolutionary relationships. ...


Other methods for inferring evolutionary relationships use parsimony in a more traditional way. Likelihood methods for phylogeny use parsimony as they do for all likelihood tests, with hypotheses requiring few differing parameters (i.e., numbers of different rates of character change or different frequencies of character state transitions) being treated as null hypotheses relative to hypotheses requiring many differing parameters. Thus, complex hypotheses must predict data much better than do simple hypotheses before researchers reject the simple hypotheses. Recent advances employ information theory, a close cousin of likelihood, which uses Occam's Razor in the same way. In statistics, a likelihood function is a conditional probability function considered a function of its second argument with its first argument held fixed, thus: and also any other function proportional to such a function. ... Not to be confused with information technology, information science, or informatics. ...


Francis Crick has commented on potential limitations of Occam's razor in biology. He advances the argument that because biological systems are the products of (an on-going) natural selection, the mechanisms are not necessarily optimal in an obvious sense. He cautions: "While Ockham's razor is a useful tool in the physical sciences, it can be a very dangerous implement in biology. It is thus very rash to use simplicity and elegance as a guide in biological research." [2] Francis Harry Compton Crick OM FRS (8 June 1916 – 28 July 2004), (Ph. ...


Medicine

When discussing Occam's razor in contemporary medicine, doctors and philosophers of medicine speak of diagnostic parsimony. Diagnostic parsimony advocates that when diagnosing a given injury, ailment, illness, or disease a doctor should strive to look for the fewest possible causes that will account for all the symptoms. While diagnostic parsimony might often be beneficial, credence should also be given to the counter-argument modernly known as Hickam's dictum, which succinctly states that "patients can have as many diseases as they damn well please". It is often statistically more likely that a patient has several common diseases, rather than having a single rarer disease which explains their myriad symptoms. Also, independently of statistical likelihood, some patients do in fact turn out to have multiple diseases, which by common sense nullifies the approach of insisting to explain any given collection of symptoms with one disease. These misgivings emerge from simple probability theory, which is already taken into account in many modern variations of the razor; and from the fact that the loss function is much greater in medicine than in most of general science, namely loss of a person's health and potentially life, and thus it is better to test and pursue all reasonable theories even if there is some theory that appears the most likely. For the chemical substances known as medicines, see medication. ... This article is being considered for deletion in accordance with Wikipedias deletion policy. ... In statistics, decision theory and economics, a loss function is a function that maps an event (technically an element of a sample space) onto a real number representing the economic cost or regret associated with the event. ...


Diagnostic parsimony and the counter-balance it finds in Hickam's dictum have very important implications in medical practice. Any set of symptoms could be indicative of a range of possible diseases and disease combinations; though at no point is a diagnosis rejected or accepted just on the basis of one disease appearing more likely than another, the continuous flow of hypothesis formulation, testing and modification benefits greatly from estimates regarding which diseases (or sets of diseases) are relatively more likely to be responsible for a set of symptoms, given the patient's environment, habits, medical history and so on. For example, if a hypothetical patient's immediately apparent symptoms include fatigue and cirrhosis and they test negative for Hepatitis C, their doctor might formulate a working hypothesis that the cirrhosis was caused by their drinking problem, and then seek symptoms and perform tests to formulate and rule out hypotheses as to what has been causing the fatigue; but if the doctor were to further discover that the patient's breath inexplicably smells of garlic and they are suffering from pulmonary edema, they might decide to test for the relatively rare condition of Selenium poisoning. Exhaustion redirects here. ... Cirrhosis is a consequence of chronic liver disease characterized by replacement of liver tissue by fibrotic scar tissue as well as regenerative nodules, leading to progressive loss of liver function. ... This page is for the disease. ... Alcoholism is the consumption of, or preoccupation with, alcoholic beverages to the extent that this behavior interferes with the drinkers normal personal, family, social, or work life, and may lead to physical or mental harm. ... Pulmonary edema is swelling and/or fluid accumulation in the lungs. ... For other uses, see Selenium (disambiguation). ...


Prior to effective anti-retroviral therapy for HIV it was frequently stated that the most obvious implication of Occam's razor, that of cutting down the number of postulated diseases to a minimum, does not apply to patients with AIDS - as they frequently did have multiple infectious processes going on at the same time. While the probability of multiple diseases being higher certainly reduces the degree to which this kind of analysis is useful, it does not go all the way to invalidating it altogether - even in such a patient, it would make more sense to first test a theory postulating three diseases to be the cause of the symptoms than a theory postulating seven. Species Human immunodeficiency virus 1 Human immunodeficiency virus 2 Human immunodeficiency virus (HIV) is a retrovirus that causes acquired immunodeficiency syndrome (AIDS, a condition in humans in which the immune system begins to fail, leading to life-threatening opportunistic infections). ... For other uses, see AIDS (disambiguation). ...


Religion

In the philosophy of religion, Occam'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). It is argued to imply that, in the absence of compelling reasons to believe in God, disbelief should be preferred. Such arguments are based on the assertion that belief in God requires more and more complex assumptions to explain the universe than non-belief. Philosophy of religion is the rational study of the meaning and justification ( or rebuttal) of fundamental religious claims, particularly about the nature and existence of God (or gods, or the divine). ... Arguments for and against the existence of God have been proposed by philosophers, theologians, and others. ...


The history of theistic thought has produced many arguments attempting to show that this is not the case- that the difficulties encountered by a theory without God are equal to or greater than those encountered by a theory postulating one. 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 creationists consider divine design to be more believable than naturalistic explanations for the diversity and history of life on earth. The cosmological argument is a metaphysical argument for the existence of God, or a first mover of the cosmos. ... A teleological argument, or argument from design, is an argument for the existence of God or a creator based on perceived evidence of order, purpose, design and/or direction in nature. ... For other uses, see Miracle (disambiguation). ... In religious experience, or sacred experience, the believer comes in contact with transcendental reality. ... Creationism is generally the belief that the universe was created by a deity, or alternatively by one or more powerful and intelligent beings. ...


The majority of the scientific community generally does not accept these arguments, and prefers to rely on explanations that deal with the same phenomena within the confines of existing scientific models. Among leading scientists defined as members of the National Academy of Sciences, 72.2% expressed disbelief and 93% expressed disbelief or doubt in the existence of a personal god in a survey conducted in 1998[3] (an ongoing survey being conducted by Elaine Ecklund of Rice University since 2004 indicates that this figure drops to as low as 38% when non-eminent scientists and social scientists are included and the definition of "God" is expanded to allow a non-personal god as per Pantheism or Deism).[4]The typical scientific view challenges the validity of the teleological argument by the effects of emergence, leading to the creation-evolution controversy; likewise, religious experiences have naturalistic explanations in the psychology of religion. Other theistic arguments, such as the argument from miracles, are sometimes pejoratively said to be arguing for a mere God of the gaps - whether or not God actually works miracles, any explanation that "God did it" must fit the facts and make accurate predictions better than more parsimonious guesses like "something did it", or else Occam's razor still cuts God out. Lovett Hall William Marsh Rice University (commonly called Rice University and opened in 1912 as The William Marsh Rice Institute for the Advancement of Letters, Science and Art) is a private, comprehensive research university located in Houston, Texas, USA, near the Museum District and adjacent to the Texas Medical Center. ... Pantheism (Greek: πάν ( pan ) = all and θεός ( theos ) = God) literally means God is All and All is God. It is the view that everything is of an all-encompassing immanent abstract God; or that the universe, or nature, and God are equivalent. ... For other uses, see Ceremonial Deism. ... A termite cathedral mound produced by a termite colony: a classic example of emergence in nature. ... The creation-evolution controversy (also termed the creation vs. ... Psychology of religion is psychologys theory of religious experiences and beliefs. ... The Argument from Miracles is an argument for the existence of God relying on eyewitness testimony of impossible (or extremely improbable events) to establish the active intervention of a supernatural supreme being (or supernatural agents acting on behalf of that being). ... The God of the gaps refers to a view of God deriving from a theistic position in which anything that can be explained by human knowledge is not in the domain of God, so the role of God is therefore confined to the gaps in scientific explanations of nature. ...


Rather than argue for the necessity of God, some theists consider their belief to be based on grounds independent of, or prior to, reason, making Occam's razor irrelevant. This was the stance of Søren Kierkegaard, who viewed belief in God as a leap of faith which sometimes directly opposed reason (McDonald 2005); this is also the same basic view of Clarkian Presuppositional apologetics, with the exception that Clark never thought the leap of faith was contrary to reason. (See also: Fideism). In a different vein, Alvin Plantinga and others have argued for reformed epistemology, the view that God's existence can properly be assumed as part of a Christian's epistemological structure. (See also: Basic beliefs). Yet another school of thought, Van Tillian Presuppositional apologetics, claims that God's existence is the transcendentally necessary prior condition to the intelligibility of all human experience and thought. In other words, proponents of this view hold that there is no other viable option to ultimately explain any fact of human experience or knowledge, let alone a simpler one. Søren Aabye Kierkegaard (IPA: , but usually Anglicized as ;  ) 5 May 1813 – 11 November 1855) was a prolific 19th century Danish philosopher and theologian. ... This article or section does not cite its references or sources. ... Gordon Haddon Clark (August 31, 1902-April 9, 1985) was an American philosopher and Calvinist theologian. ... Presuppositional apologetics is a school of Christian apologetics, a field of Christian theology that aims to (1) present a rational basis for the Christian faith, (2) defend the faith against objections, and (3) expose the perceived flaws of other worldviews. ... In Christian theology, fideism is any of several belief systems which hold, on various grounds, that reason is irrelevant to religious faith. ... Alvin Carl Plantinga (born 15 November 1932 in Ann Arbor, Michigan, USA) is a contemporary American philosopher known for his work in epistemology, metaphysics, the philosophy of religion and modest support of intelligent design. ... Reformed epistemology is the title given to a broad body of epistemological viewpoints relating to Gods existence that have been offered by a group of Protestant Christian philosophers that includes Alvin Plantinga, William Alston, and Nicholas Wolterstorff among others. ... Theory of knowledge redirects here: for other uses, see theory of knowledge (disambiguation) According to Plato, knowledge is a subset of that which is both true and believed Epistemology or theory of knowledge is the branch of philosophy that studies the nature, methods, limitations, and validity of knowledge and belief. ... In foundationalism, basic beliefs are beliefs which do not depend on other beliefs for their validity, and which form the basis for other beliefs. ... Cornelius Van Til Cornelius Van Til (May 4, 1895 - April 17, 1987), born in Grootegast, the Netherlands, was a Christian philosopher, Reformed theologian, and presuppositional apologist. ... Presuppositional apologetics is a school of Christian apologetics, a field of Christian theology that aims to (1) present a rational basis for the Christian faith, (2) defend the faith against objections, and (3) expose the perceived flaws of other worldviews. ... In philosophy, transcendental/transcendence, has three different but related primary meanings, all of them derived from the words literal meaning (from Latin), of climbing or going beyond: one that originated in Ancient philosophy, one in Medieval philosophy and one in modern philosophy. ...


Considering that the razor is often wielded as an argument against theism, it is somewhat ironic that Ockham himself was a theist. He considered some Christian sources to be valid sources of factual data, equal to both logic and sense perception. He wrote, "No plurality should be assumed unless it can be proved (a) by reason, or (b) by experience, or (c) by some infallible authority"; referring in the last clause "to the Bible, the Saints and certain pronouncements of the Church" (Hoffmann 1997). In Ockham's view, an explanation which does not harmonize with reason, experience or the aforementioned sources cannot be considered valid.


Philosophy of mind

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", " a body is mobile by mobility". We should say instead that a man is a father because he has a son (Summa C.51).


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 Occam's razor against Idealism's metaphysical competitor, materialism, claiming that matter was not required by his metaphysic and was thus eliminable. For the second husband of Henrietta Howard, Countess of Suffolk, see George Berkeley (MP). ...


In the 20th century Philosophy of Mind, Occam's razor found a champion in J. J. C. Smart, who in his article "Sensations and Brain Processes" (1959) claimed Occam's razor as the basis for his preference of the mind-brain identity theory over mind body dualism. Dualists claim that there are two kinds of substances in the universe: physical (including the body) and mental, which is nonphysical. In contrast identity theorists claim that everything is physical, including consciousness, and that there is nothing nonphysical. The basis for the materialist claim is that of the two competing theories, dualism and mind-brain identity, the identity theory is the simpler since it commits to fewer entities. Smart was criticized for his use of the razor and ultimately retracted his advocacy of it in this context. John Jameison Carswell Smart, or Jack Smart, (born 1920, M.A. (Glasgow, 1946), B.Phil (Oxford, 1948)) is a Scottish-Australian philosopher. ...


Paul Churchland (1984) cites Occam's razor as the first line of attack against dualism, but admits that by itself it is inconclusive. The deciding factor for Churchland is the greater explanatory prowess of a materialist position in the Philosophy of Mind as informed by findings in neurobiology. Paul Churchland (born 1942 in Vancouver, British Columbia, Canada) is a philosopher noted for his studies in neurophilosophy and the philosophy of mind. ...


Dale Jacquette (1994) claims that Occam'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.


Probability Theory and Statistics

One intuitive justification of Occam's Razor's admonition against unnecessary hypotheses is a direct result of basic probability theory. By definition, all assumptions introduce possibilities for error; If an assumption does not improve the accuracy of a theory, its only effect is to increase the probability that the overall theory is wrong. Probability theory is the branch of mathematics concerned with analysis of random phenomena. ...


There are various papers in scholarly journals deriving formal versions of Occam's razor from probability theory and applying it in statistical inference, and also of various criteria for penalizing complexity in statistical inference. Recent papers have suggested a connection between Occam's razor and Kolmogorov complexity. It has been suggested that this article or section be merged with inferential statistics. ... In computer science, the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin complexity, stochastic complexity, algorithmic entropy, or program-size complexity) of an object such as a piece of text is a measure of the computational resources needed to specify the object. ...


One of the problems with the original formulation of the principle is that it only applies to models with the same explanatory power (i.e. prefer the simplest of equally good models). A more general form of Occam's razor can be derived from Bayesian model comparison and Bayes factors, which can be used to compare models that don't fit the data equally well. These methods can sometimes optimally balance the complexity and power of a model. Generally the exact Ockham factor is intractable but approximations such as Akaike Information Criterion, Bayesian Information Criterion, Variational Bayes and Laplace Approximation are used. Many artificial intelligence researchers are now employing such techniques. The posterior probability of a model given data, P(H|D), is given by Bayes theorem: P(H|D) = P(D|H)P(H)/P(D) The key data_dependent term P(D|H) is a likelihood, and is sometimes called the evidence for model H; evaluating it correctly is the... In statistics, the use of Bayes factors is a Bayesian alternative to classical hypothesis testing. ... Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. ... Akaikes information criterion, developed by Hirotsugu Akaike under the name of an information criterion (AIC) in 1971 and proposed in Akaike (1974), is a measure of the goodness of fit of an estimated statistical model. ... In statistics, the Schwarz criterion (also Schwarz information criterion (SIC) or Bayesian information criterion (BIC)) is an information criterion in statistics. ... In Bayesian network theory, the joint conditional posterior $P(h|v)$ is often intractable but the joint posterior $P(h,v)$ is tractable. ... AI redirects here. ...


William H. Jefferys and James O. Berger (1991) generalise and quantify the original formulation's "assumptions" concept as the degree to which a proposition is unnecessarily accommodating to possible observable data. The model they propose balances the precision of a theory's predictions against their sharpness - theories which sharply made their correct predictions are preferred over theories which would have accommodated a wide range of other possible results. This, again, reflects the mathematical relationship between key concepts in Bayesian inference (namely marginal probability, conditional probability and posterior probability). Bayesian inference is statistical inference in which evidence or observations are used to update or to newly infer the probability that a hypothesis may be true. ... This article defines some terms which characterize probability distributions of two or more variables. ... This article defines some terms which characterize probability distributions of two or more variables. ... The posterior probability can be calculated by Bayes theorem from the prior probability and the likelihood function. ...


The statistical view leads to a more rigorous formulation of the razor than previous philosophical discussions. In particular, it shows that 'simplicity' must first be defined in some way before the razor may be used, and that this definition will always be subjective. For example, in the Kolmogorov-Chaitin Minimum description length approach, the subject must pick a Turing machine whose operations describe the basic operations believed to represent 'simplicity' by the subject. However one could always choose a Turing machine with a simple operation that happened to construct one's entire theory and would hence score highly under the razor. This has led to two opposing views of the objectivity of Occam's razor. The minimum description length principle is a formalization of Occams Razor in which the best hypothesis for a given set of data is the one that leads to the largest compression of the data. ... For the test of artificial intelligence, see Turing test. ...


Subjective Razor

The Turing machine can be thought of as embodying a Bayesian prior belief over the space of rival theories. Hence Occam's razor is not an objective comparison method, and merely reflects the subject's prior beliefs. One's choice of exactly which razor to use is culturally relative. A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ... Cultural relativism is the principle that an individual humans beliefs and activities make sense in terms of his or her own culture. ...


Objective Razor

The minimum instruction set of a Universal Turing machine requires approximately the same length description across different formulations, and is small compared to the Kolmogorov complexity of most practical theories. For instance John Tromp's minimal universal interpreters, based on the Lambda Calculus and Combinatory logic are 210 and 272 bits respectively. Marcus Hutter has used this consistency to define a "natural" Turing machine[5] of small size as the proper basis for excluding arbitrarily complex instruction sets in the formulation of razors. In computer science, the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin complexity, stochastic complexity, algorithmic entropy, or program-size complexity) of an object such as a piece of text is a measure of the computational resources needed to specify the object. ... The lambda calculus is a formal system designed to investigate function definition, function application, and recursion. ... Not to be confused with combinational logic, a topic in digital electronics. ... Marcus Hutter (born 1967) was born and educated in Munich, where he studied physics and computer science. ...


One possible conclusion from mixing these concepts - Kolmogorov complexity and Occam's Razor - is that an ideal data compressor would also be a scientific explanation/formulation generator. Some attempts have been made to re-derive known laws from considerations of simplicity or compressibility.[6][7]


Variations

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". The English language is a West Germanic language that originates in England. ... The term KISS is an acronym of the phrase Keep It Simple, Stupid, and the KISS principle states that design simplicity should be a key goal and unnecessary complexity avoided. ... Zebra is a slang medical term for an obscure and unlikely diagnosis from ordinary symptoms. ...


Other common restatements are:

Entities are not to be multiplied without necessity.

and

The simplest answer is usually the correct answer.

A restatement of Occam's razor, in more formal terms, is provided by information theory in the form of minimum message length (MML). Tests of Occam's razor on decision tree models which initially appeared critical have been shown to actually work fine when re-visited using MML. Other criticisms of Occam's razor and MML (e.g., a binary cut-point segmentation problem) have again been rectified when - crucially - an inefficient coding scheme is made more efficient. Not to be confused with information technology, information science, or informatics. ... Minimum message length (MML) is a formal information theory restatement of Occams Razor: even when models are not equal in goodness of fit accuracy to the observed data, the one generating the shortest overall message is more likely to be correct (where the message consists of a statement of... Minimum message length (MML) is a formal information theory restatement of Occams Razor: even when models are not equal in goodness of fit accuracy to the observed data, the one generating the shortest overall message is more likely to be correct (where the message consists of a statement of... In operations research, specifically in decision analysis, a decision tree is a decision support tool that uses a graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. ... Minimum message length (MML) is a formal information theory restatement of Occams Razor: even when models are not equal in goodness of fit accuracy to the observed data, the one generating the shortest overall message is more likely to be correct (where the message consists of a statement of... Minimum message length (MML) is a formal information theory restatement of Occams Razor: even when models are not equal in goodness of fit accuracy to the observed data, the one generating the shortest overall message is more likely to be correct (where the message consists of a statement of...


"When deciding between two models which make equivalent predictions, choose the simpler one," makes the point that a simpler model that doesn't make equivalent predictions is not among the models that this criterion applies to in the first place. [2]


Leonardo da Vinci (1452–1519) lived after Ockham's time and has a variant of Occam's razor. His variant short-circuits the need for sophistication by equating it to simplicity. “Da Vinci” redirects here. ...

Simplicity is the ultimate sophistication.

Occam'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. Wikiquote has a collection of quotations related to: Simplicity Simplicity is the property, condition, or quality of being simple or un-combined. ...

As this is ambiguous, Isaac Newton's version may be better: Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ...

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 Occam'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. See above, "In science".


Many people are familiar with Occam's Razor phrased as such:

If it walks like a duck and quacks like a duck, it's a duck

Controversial aspects of the Razor

Occam's razor is not an embargo against the positing of any kind of entity, or a recommendation of the simplest theory come what may[8] (Note that simplest theory is something like "only I exist" or "nothing exists"). Simpler theories are preferable other things being equal. The other things in question are the evidential support for the theory[9] Therefore, according to the principle, a simpler but less correct theory should not be preferred over a more complex but more correct one. Solipsism (Latin: solus, alone + ipse, self) is the philosophical idea that My mind is the only thing that I know exists. Solipsism is an epistemological or metaphysical position that knowledge of anything outside the mind is unjustified. ...


For instance, classical physics is simpler than subsequent theories, but should not be preferred over them because it is demonstrably wrong in certain respects. It is the first requirement of a theory that it works, that its predictions are correct and it has not been falsified. Occam's razor is used to adjudicate between theories that have already passed these tests, and which are moreover equally well-supported by the evidence.[10] Classical physics is physics based on principles developed before the rise of quantum theory, usually including the special theory of relativity and general theory of relativity. ...


Another contentious aspect of the Razor is that a theory can become more complex in terms of its structure (or syntax), while its ontology (or semantics) becomes simpler, or vice versa.[11] The theory of relativity is often given as an example. For other uses, see Syntax (disambiguation). ... This article is about ontology in philosophy. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... Two-dimensional analogy of space-time curvature described in General Relativity. ...


Galileo Galilei lampooned the misuse of Occam's Razor in his Dialogue. The principle is represented in the dialogue by Simplicio. The telling point that Galileo presented ironically was that if you really wanted to start from a small number of entities, you could always consider the letters of the alphabet as the fundamental entities, since you could certainly construct the whole of human knowledge out of them (a view that Abraham Abulafia presented much more expansively). Galileo redirects here. ... Frontispiece and title page of the Dialogue The Dialogue Concerning the Two Chief World Systems (Dialogo sopra i due massimi sistemi del mondo) was a 1632 book by Galileo, comparing the Copernican system, and the traditional Ptolemaic system. ... “Abulafia” redirects here. ...


Anti-razors

Occam's razor has met some opposition from people who have considered it too extreme or rash. Walter of Chatton was a contemporary of William of Ockham (1287–1347) who took exception to Occam'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, no one anti-razor has perpetuated in as much notoriety as Occam's razor. Walter Chatton was a 14th century Philosopher who regularly sparred philosophically with William Ockham, famous for his Ockhams Razor. ...


Anti-razors have also been created by Gottfried Wilhelm Leibniz (1646–1716), Immanuel Kant (1724–1804), and Karl Menger. Leibniz's version took the form of a principle of plenitude, as Arthur Lovejoy has called it, the idea being that God created the most varied and populous of possible worlds. Kant felt a need to moderate the effects of Occam's Razor and thus created his own counter-razor: "The variety of beings should not rashly be diminished."[12] Gottfried Leibniz Gottfried Wilhelm von Leibniz (July 1, 1646 in Leipzig - November 14, 1716 in Hannover) was a German philosopher, scientist, mathematician, diplomat, librarian, and lawyer of Sorb descent. ... Kant redirects here. ... Karl Menger Karl Menger (Vienna, Austria, January 13, 1902 – Highland Park, Illinois, USA, October 5, 1985) was a mathematician of great scope and depth. ... The plenitude principle or principle of plenitude asserts that everything that can happen will happen. ... Arthur Onken Lovejoy (Berlin, October 10, 1873 - Baltimore, December 30, 1962) was an influential intellectual historian, and the founder of the history of ideas. ...


Karl Menger found mathematicians to be too parsimonious 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". See "Ockham's Razor and Chatton's Anti-Razor" (1984) by Armand Maurer. 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. Variations on this theme were subsequently explored by the Argentinian writer Jorge Luis Borges in his story/mock-essay Tlön, Uqbar, Orbis Tertius. There is also Crabtree's Bludgeon, which takes a cynical view that 'No set of mutually inconsistent observations can exist for which some human intellect cannot conceive a coherent explanation, however complicated.' Pataphysics, a term coined by the French writer Alfred Jarry, is a philosophy dedicated to studying what lies beyond the realm of metaphysics. ... Alfred Jarry Alfred Jarry (September 8, 1873 – November 1, 1907) was a French writer born in Laval, Mayenne, France, not far from the border of Brittany; he was of Breton descent on his mothers side. ... Borges redirects here. ... Tlön, Uqbar, Orbis Tertius is a short story by the 20th century Argentine writer Jorge Luis Borges. ... (NB: This article is under construction: still researching origins) Crabtrees Bludgeon is a foil to Occams Razor, and may be expressed so: Its origin is obscure, but appears to be associated with R. V. Jones and may appear in the Crabtree Orations, a set of satirical academic commentaries...


Humorous parallels of Occam's Razor have been postulated - and may contain an element of truth. Notable among these is the premise stated by eminent pathologist, Ed Uthman, MD, who gave us Uthman's Razor: "Of two equally plausible explanations, the more cynical one is correct."


Golden Mean

Some other thinkers believe that the best position in this dispute is to avoid oversimplification, standing in a reasonable middle term, or Golden Mean. This is illustrated by the famous phrase attributed to Einstein (though actually of unknown origin): "Everything should be made as simple as possible, but not simpler." In philosophy, especially that of Aristotle, the golden mean is the desirable middle between two extremes, one of excess and the other of deficiency. ... Einstein redirects here. ...


An argument supporting the mean is contained in the anti-razor. That is, if three factors do not suffice, a fourth must be included. At that point, should an answer be found, the postulate will be as simple as it can be and still be effective. Take as an example of oversimplification, the razor analogous phrase, "When you hear hoofbeats, think horses, not zebras". While satisfying as an axiom promoting simplicity, it fails to consider the locus of the observer. In the African Veldt, or even in a zoo or circus tent, the hoofbeats might be more likely to be those of zebras than horses. This counter argument, even when not regarded so literally, but rather in its axiomatic form, provides the anti-razor that seeks the mean. "When you hear hoofbeats, think horses, not zebras, unless, of course, you're in Africa."


Occam's Razor in Popular Culture

  • In the movie Contact (1997) based on Carl Sagan's novel the character played by Jodie Foster experiences an uncertain combination of space and time travel while using a device constructed by men following plans supposedly sent to earth by aliens. Despite all efforts, none of it was registered by the several cameras and recorders placed for this purpose. Latter, when confronted by the scientific community, the scientist's spokesman uses the Occam's Razor principle in an attempt to discredit her by making her agree that this unlikely alien-driven experience would be easier to explain as a simple hallucination.

And the Guardian reports about a lawsuit in which J.K Rowlings, authoress of the Harry Potter books gives testimony against a book publisher: "And she was scathing that Vander Ark had missed her reference to Occamy in Fantastic Beasts and Where to Find Them. It was a reference to Occam's razor, the principle that nothing should be presumed to exist if not absolutely necessary." Reference: . [13] Spiral Architect is a Norwegian technical metal band. ... A Sceptics Universe (released 2000) is the first and as of 2006 only full length studio album released by Spiral Architect, a Norwegian technical metal band. ...


Notes

  1. ^ Pegis 1945
  2. ^ Crick 1988, p.146.
  3. ^ Larson and Witham, 1998 "Leading Scientists Still Reject God"
  4. ^ Ref to survey at Livescience article from Physorg.com
  5. ^ Algorithmic Information Theory
  6. ^ [http://arxiv.org/pdf/math-ph/0009007 'Occam’s Razor as a formal basis for a physical theory' by Andrei N. Soklakov]
  7. ^ 'Why Occam's Razor' by Russell Standish
  8. ^ ["But Ockham's razor does not say that the more simple a hypothesis, the better." http://www.skepdic.com/occam.html Skeptic's Dictionary]
  9. ^ "when you have two competing theories which make exactly the same predictions, the one that is simpler is the better."Usenet Phyics FAQs
  10. ^ "Today, we think of the principle of parsimony as a heuristic device. We don't assume that the simpler theory is correct and the more complex one false. We know from experience that more often than not the theory that requires more complicated machinations is wrong. Until proved otherwise, the more complex theory competing with a simpler explanation should be put on the back burner, but not thrown thrown onto the trash heap of history until proven false. (The Skeptic's dictionary)
  11. ^ "While these two facets of simplicity are frequently conflated, it is important to treat them as distinct. One reason for doing so is that considerations of parsimony and of elegance typically pull in different directions. Postulating extra entities may allow a theory to be formulated more simply, while reducing the ontology of a theory may only be possible at the price of making it syntactically more complex." Stanford Encyclopedia of Philosophy
  12. ^ Original Latin: Entium varietates non temere esse minuendas. Kant, Immanuel (1950): The Critique of Pure Reason, transl. Kemp Smith, London. Available here: [1]
  13. ^ http://books.guardian.co.uk/news/articles/0,,2273675,00.html]

References

Image File history File links This is a lossless scalable vector image. ... Paul Churchland (born 1942 in Vancouver, British Columbia, Canada) is a philosopher noted for his studies in neurophilosophy and the philosophy of mind. ... MIT Press Books The MIT Press is a university publisher affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts. ... Francis Harry Compton Crick OM FRS (8 June 1916 – 28 July 2004), (Ph. ... Basic Books is a book publisher founded in 1952. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 267th day of the year (268th in leap years) in the Gregorian calendar. ... John Wiley & Sons, Inc. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... is the 104th day of the year (105th in leap years) in the Gregorian calendar. ... Pearson can mean Pearson PLC the media conglomerate. ... Edwin Thompson Jaynes (July 5, 1922 – April 30, 1998) was Wayman Crow Distinguished Professor of Physics at Washington University in St. ... Oxford University Press (OUP) is a highly-respected publishing house and a department of the University of Oxford in England. ... David J.C. MacKay (born April 22, 1967) is the professor of natural philosophy in the department of Physics at the University of Cambridge. ... The headquarters of the Cambridge University Press, in Trumpington Street, Cambridge. ... The Stanford Encyclopedia of Philosophy (hereafter SEP) is a free online encyclopedia of philosophy run and maintained by Stanford University. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... is the 104th day of the year (105th in leap years) in the Gregorian calendar. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... is the 105th day of the year (106th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 42nd day of the year in the Gregorian calendar. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... is the 105th day of the year (106th in leap years) in the Gregorian calendar. ... Oxford University Press (OUP) is a highly-respected publishing house and a department of the University of Oxford in England. ... The headquarters of the Cambridge University Press, in Trumpington Street, Cambridge. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... is the 105th day of the year (106th in leap years) in the Gregorian calendar. ... Marquette University Press is a university press. ... The Princeton University Press is a publishing house, a division of Princeton University, that is highly respected in academic publishing. ...

See also

This article or section is in need of attention from an expert on the subject. ... Bayesian inference is statistical inference in which evidence or observations are used to update or to newly infer the probability that a hypothesis may be true. ... Buridans ass is the common name for the paradox which states that an entirely rational ass, placed exactly in the middle between two stacks of hay of equal size and quality, will starve since it cannot make any rational decision to start eating one rather than the other. ... Ceteris paribus is a Latin phrase, literally translated as with other things [being] the same, and usually rendered in English as all other things being equal. ... It has been suggested that Clade be merged into this article or section. ... Curve fitting is finding a curve which matches a series of data points and possibly other constraints. ... Source coding redirects here. ... Eliminativists argue that our modern belief in the existence of mental phenomena is analogous to our ancient belief in obsolete theories such as the geocentric model of the universe. ... Falsifiability (or refutability or testability) is the logical possibility that an assertion can be shown false by an observation or a physical experiment. ... Hanlons razor is an adage which reads: Also worded as: // According to Joseph Bigler,[1] the quotation first came from a certain Robert J. Hanlon as a submission for a book compilation of various jokes related to Murphys law published in 1980 entitled Murphys Law Book Two... The term KISS is an acronym of the phrase Keep It Simple, Stupid, and the KISS principle states that design simplicity should be a key goal and unnecessary complexity avoided. ... In computer science, the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin complexity, stochastic complexity, algorithmic entropy, or program-size complexity) of an object such as a piece of text is a measure of the computational resources needed to specify the object. ... Minimum message length (MML) is a formal information theory restatement of Occams Razor: even when models are not equal in goodness of fit accuracy to the observed data, the one generating the shortest overall message is more likely to be correct (where the message consists of a statement of... Coined by 19th-century British psychologist C. Lloyd Morgan, Morgans Canon (more usually called Lloyd Morgans Canon, or occasionally Morgans Canon of Interpretation) remains a fundamental precept of comparative (animal) psychology. ... Occam is a parallel programming language that builds on Communicating Sequential Processes (CSP) and shares many of their features. ... Noisy (roughly linear) data is fit to both linear and polynomial functions. ... Look up parsimony in Wiktionary, the free dictionary. ... Philosophy of science is the study of assumptions, foundations, and implications of science, especially in the natural sciences and social sciences. ... The poverty of the stimulus (POTS) argument is an argument in favour of linguistic nativism, which is the claim that humans are born with a specific adaptation for language that both funds and limits their competence to acquire specific types of natural languages over the course of their cognitive development... In user interface design, programming language design, and ergonomics, the principle (or rule or law) of least astonishment (or surprise) states that, when two elements of an interface conflict or are ambiguous, the behaviour should be that which will least surprise the human user or programmer at the time the... In epistemology and in its broadest sense, rationalism is any view appealing to reason as a source of knowledge or justification (Lacey 286). ... In statistics, there is no clear, unambiguous way to define a Bayesian prior by the method of imaginary reference sets. ... Scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. ... The term scientific reductionism has been used to describe various reductionist ideas about science. ... Wikiquote has a collection of quotations related to: Simplicity Simplicity is the property, condition, or quality of being simple or un-combined. ... Turtles all the way down. ... Metaphysical naturalism is any worldview in which nature is all there is and all things supernatural (which stipulatively includes as well as spirits and souls, non-natural values, and universals as they are commonly conceived) do not exist. ...

External links

The Skeptics Dictionary is a web site with a collection of cross-referenced skeptical essays by Robert Todd Carroll, PhD. It primarily exposes claims that its editors consider pseudoscientific (sometimes in a pseudoskeptical fashion though). ... The New England Skeptical Society is an organization which produces a podcast featuring debunking of myths and conspiracy theories, as well as discussion of scientific developments in laymens terms, and interviews with authors and other famous skeptics. ... David J.C. MacKay (born April 22, 1967) is the professor of natural philosophy in the department of Physics at the University of Cambridge. ... The posterior probability of a model given data, P(H|D), is given by Bayes theorem: P(H|D) = P(D|H)P(H)/P(D) The key data_dependent term P(D|H) is a likelihood, and is sometimes called the evidence for model H; evaluating it correctly is the... Minimum message length (MML) is a formal information theory restatement of Occams Razor: even when models are not equal in goodness of fit accuracy to the observed data, the one generating the shortest overall message is more likely to be correct (where the message consists of a statement of... Minimum message length (MML) is a formal information theory restatement of Occams Razor: even when models are not equal in goodness of fit accuracy to the observed data, the one generating the shortest overall message is more likely to be correct (where the message consists of a statement of... Year 2005 (MMV) was a common year starting on Saturday (link displays full calendar) of the Gregorian calendar. ... is the 296th day of the year (297th in leap years) in the Gregorian calendar. ... PlanetMath is a free, collaborative, online mathematics encyclopedia. ... ABC Radio National is an Australia-wide radio network with many various programs, involving news and current affairs, arts, music, society, science, drama, comedy. ... A podcast is a series of digital-media files which are distributed over the Internet using syndication feeds for playback on portable media players and computers. ... Image File history File links Question_book-3. ...


  Results from FactBites:
 
Occam's razor (0 words)
What is known as Occam's razor was a common principle in medieval philosophy and was not originated by William, but because of his frequent usage of the principle, his name has become indelibly attached to it.
For example, atheists often apply Occam's razor in arguing against the existence of God on the grounds that God is an unnecessary hypothesis.
On the other hand, if Occam's razor means that when confronted with two explanations, an implausible one and a probable one, a rational person should select the probable one, then the principle seems unnecessary because so obvious.
  More results at FactBites »

 
 

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