Occam's razor....look it up.
Occam's razor (or
Ockham's razor[1]),
entia non sunt multiplicanda praeter necessitatem, is the principle that "entities must not be multiplied beyond necessity" and the conclusion, thereof, that the simplest explanation or strategy tends to be the best one. The principle is attributed to 14th-century English
logician and
Franciscan friar,
William of Ockham. Occam's razor may be alternatively phrased as
pluralitas non est ponenda sine necessitate ("plurality should not be posited without necessity").
[2]
Occam'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 (translating to the
law of parsimony,
law of economy or
law of succinctness). When competing hypotheses are equal in other respects, the principle recommends selection of the hypothesis that introduces the fewest assumptions and postulates the fewest entities while still sufficiently answering the question. It is in this sense that Occam's razor is usually understood. To quote
Isaac Newton, "we are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. Therefore, to the same natural effects we must, so far as possible, assign the same causes."
[3]
In science, Occam’s razor is used as a
heuristic (rule of thumb) to guide scientists in the development of theoretical models rather than as an arbiter between published models.
[4][5] In the scientific method, Occam's razor is not considered an irrefutable principle of
logic, and certainly not a scientific result.
[6][7][8][9]
Contents
[hide]
[edit] History
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 maxim 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 must never 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.
[10]
Part of a page from Duns Scotus' book
Ordinatio:
Pluralitas non est ponenda sine necessitate, i.e. "Plurality is not to be posited without necessity"
The origins of what has come to be known as Occam's razor are traceable to the works of earlier philosophers such as
Alhazen (965–1039),
[11] Maimonides (1138–1204),
John Duns Scotus (1265–130
,
Thomas Aquinas (c. 1225–1274), and even
Aristotle (384–322 BC) (Charlesworth 1956). The term "Ockham's razor" first appeared in 1852 in the works of
Sir William Hamilton, 9th Baronet (1788–1856), 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 191
.
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".
[edit] Justifications
[edit] Aesthetic and practical considerations
Prior to the 20th century, it was a commonly-held belief that nature itself was simple and that simpler hypotheses 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."
[12]
The common form of the razor, used to distinguish between equally explanatory hypotheses, can be supported by appeals to the practical value of simplicity. Hypotheses 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 hypotheses 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.
Beginning in the 20th century,
epistemological justifications based on
induction,
logic,
pragmatism, and
probability theory have become more popular among philosophers.
[edit] 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.
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, 200
. 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.
[edit] 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.
[edit] 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)
[edit] 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).
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).
[edit] Applications
[edit] Science and the scientific method
In science, Occam’s razor is used as a
heuristic (rule of thumb) to guide scientists in the development of theoretical models rather than as an arbiter between published models.
[4][5] In
physics,
parsimony was an important
heuristic in the formulation of
special relativity by
Albert Einstein[13][14], the development and application of the
principle of least action by
Pierre Louis Maupertuis and
Leonhard Euler,
[15] and the development of
quantum mechanics by
Louis de Broglie,
Richard Feynman, and
Julian Schwinger.
[5][16][17] In
chemistry, Occam’s razor is often an important
heuristic when developing a model of a
reaction mechanism.
[18][19] However, while it is useful as a heuristic in developing models of reaction mechanisms, it has been shown to fail as a criterion for selecting among published models.
[5]
In the scientific method, parsimony is an
epistemological,
metaphysical or
heuristic preference, not an irrefutable principle of
logic, and certainly not a scientific result.
[6][7][8][9] As a logical principle, Occam's razor would demand that scientists accept the simplest possible theoretical explanation for existing data. However, science has shown repeatedly that future data often supports more complex theories than existing data. Science tends to prefer the simplest explanation that is consistent with the data available at a given time, but history shows that these simplest explanations often yield to complexities as new data become available.
[4][7] Science is open to the possibility that future experiments might support more complex theories than demanded by current data and is more interested in designing experiments to discriminate between competing theories than favoring one theory over another based merely on philosophical principles.
[6][7][8][9]
When scientists use the idea of parsimony, it only has meaning in a very specific context of inquiry. A number of background assumptions are required for parsimony to connect with plausibility in a particular research problem. The reasonableness of parsimony in one research context may have nothing to do with its reasonableness in another. It is a mistake to think that there is a single global principle that spans diverse subject matter.
[9]
As a methodological principle, the demand for simplicity suggested by Occam’s razor cannot be generally sustained. Occam’s razor cannot help toward a rational decision between competing explanations of the same empirical facts. One problem in formulating an explicit general principle is that complexity and simplicity are perspective notions whose meaning depends on the context of application and the user’s prior understanding. In the absence of an objective criterion for simplicity and complexity, Occam’s razor itself does not support an objective
epistemology.
[8]
The problem of deciding between competing explanations for empirical facts cannot be solved by formal tools. Simplicity principles can be useful heuristics in formulating hypotheses, but they do not make a contribution to the selection of theories. A theory that is compatible with one person’s world view will be considered simple, clear, logical, and evident, whereas what is contrary to that world view will quickly be rejected as an overly complex explanation with senseless additional hypotheses. Occam’s razor, in this way, becomes a “mirror of prejudice.”
[8]
It has been suggested that Occam’s razor is a widely accepted example of extraevidential consideration, even though it is entirely a metaphysical assumption. There is little empirical evidence that the world is actually simple or that simple accounts are more likely than complex ones to be true.
[20]
Most of the time, Occam’s razor is a conservative tool, cutting out crazy, complicated constructions and assuring that hypotheses are grounded in the science of the day, thus yielding ‘normal’ science: models of explanation and prediction. There are, however, notable exceptions where Occam’s razor turns a conservative scientist into a reluctant revolutionary. For example,
Max Planck interpolated between the
Wien and
Jeans radiation laws used an Occam’s razor logic to formulate the quantum hypothesis, and even resisting that hypothesis as it became more obvious that it was correct.
[5]
However, on many occasions Occam's razor has stifled or delayed scientific progress.
[8] For example, appeals to simplicity were used to deny the phenomena of meteorites, ball lightning, continental drift, and reverse transcriptase. It originally rejected
DNA as the carrier of genetic information in favor of proteins, since proteins provided the simpler explanation. Theories that reach far beyond the available data are rare, but
general relativity provides one example.
In hindsight, one can argue that it is simpler to consider
DNA as the carrier of genetic information, because it uses a smaller number of building blocks (four nitrogenous bases). However, during the time that proteins were the favored genetic medium, it seemed like a more complex hypothesis to confer genetic information in DNA rather than proteins.
One can also argue (also in hindsight) for atomic building blocks for matter, because it provides a simpler explanation for the observed reversibility of both mixing and chemical reactions as simple separation and re-arrangements of the atomic building blocks. However, at the time, the
atomic theory was considered more complex because it inferred the existence of invisible particles which had not been directly detected.
Ernst Mach and the logical positivists rejected the
atomic theory of
John Dalton, until the reality of atoms was more evident in
Brownian motion, as explained by
Albert Einstein.
[21]
In the same way, hindsight argues that postulating the
aether is more complex than transmission of light through a
vacuum. However, at the time, all known waves propagated through a physical medium, and it seemed simpler to postulate the existence of a medium rather than theorize about wave propagation without a medium. Likewise, Newton's idea of light particles seemed simpler than Young's idea of waves, so many favored it; however in this case, as it turned out, neither the wave- nor the particle-explanation alone suffices, since light behaves like waves as well as as like particles (
wave–particle duality).
Three axioms presupposed by the scientific method are realism (the existence of objective reality), the existence of observable natural laws, and the constancy of observable natural law. Rather than depend on provability of these axioms, science depends on the fact that they have not been objectively falsified. Occam’s razor and
parsimony support, but do not prove these general axioms of science. The general principle of science is that theories (or models) of natural law must be consistent with repeatable experimental observations. This ultimate arbiter (selection criterion) rests upon the axioms mentioned above.
[7]
There are many examples where Occam’s razor would have picked the wrong theory given the available data. Simplicity principles are useful philosophical preferences for choosing a more likely theory from among several possibilities that are each consistent with available data. However, anyone invoking Occam’s razor to support a model should be aware that additional data may well falsify the model currently favored by Occam’s razor. One accurate observation of a white crow falsifies the theory that “all crows are black”. Likewise, a single instance of Occam’s razor picking a wrong theory falsifies the razor as a general principle
[7]. Note however that this only applies if the razor is meant to pick the correct theory for all time; if this is not the case, and it is only applied to pick the simplest theory which fits all the currently known data and it is understood that, should new data arise, the razor will have to be reapplied, then the principle keeps its validity.
If multiple models of natural law make exactly the same testable predictions, they are equivalent and there is no need for parsimony to choose one that is preferred. For example, Newtonian, Hamiltonian, and Lagrangian classical mechanics are equivalent. Physicists have no interest in using Occam’s razor to say the other two are wrong. Likewise, there is no demand for simplicity principles arbitrate between wave and matrix formulations of quantum mechanics. Science often does not demand arbitration or selection criteria between models which make the same testable predictions.
[7]
[edit] 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).
However, more recent biological analyses, 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.
Zoology provides an example.
Muskoxen, 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.
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.
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.
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 (198
. For a discussion of both uses of Occam's razor in Biology see Elliott Sober's article
Let's Razor Ockham's Razor (1990).
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.
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."
[22]
[edit] 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. This philosophy is one of several demonstrated in the popular medical
adage "
when you hear hoofbeats, think horses, not zebras". 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 [
sic]". 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. Because misdiagnosis can result in the loss of a person's health and potentially life, it is thus considered better to test and pursue all reasonable theories even if there is some theory that appears the most likely.
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.
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.
[edit] Religion
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dispute is resolved. (November 2009) 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. For example, in his documentary
"The Root of All Evil?",
Richard Dawkins points out that none of the
miraculous cures in
Lourdes, France, require the existence of a God to explain them; the "cures" are always for diseases that may have become better by themselves.
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.
Most scientists generally do not accept these arguments, and prefer 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, in the
United States, 72.2% expressed disbelief and 93% expressed disbelief or doubt in the existence of a personal god in a survey conducted in 1998
[23] (an ongoing survey being conducted by Elaine Ecklund of
Rice University since 2004 indicates that this figure drops to as low as 38% when social scientists are included and the definition of "God" is expanded to allow a non-personal god as per
Pantheism or
Deism).
[24] 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.
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.
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. It must be noted, however, that in Ockham's time, the Church had tremendous influence on people and their ideas, and the Ockham's razor may be applied to today's subjects.
[edit] 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.
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.
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.
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.
[edit] Probability theory and statistics
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(May 2009) 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.
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.
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.
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).
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.
[edit] 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.
[edit] 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.
Marcus Hutter has used this consistency to define a "natural" Turing machine
[25] of small size as the proper basis for excluding arbitrarily complex instruction sets in the formulation of razors. Describing the program for the universal program as the "hypothesis", and the representation of the evidence as program data, it has been formally proven under
ZF that "the sum of the log universal probability of the model plus the log of the probability of the data given the model should be minimized."
[26]
One possible conclusion from mixing the concepts of 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.
[27][28]
According to
Jürgen Schmidhuber, the appropriate mathematical theory of Occam's razor already exists, namely,
Ray Solomonoff's theory of optimal inductive inference
[29] and its extensions
[30].
[edit] Variations
This article or section may contain
previously unpublished synthesis of published material that conveys ideas not attributable to the original sources. See the
talk page for details.
(June 200 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).
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.
"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.
[31]
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.
Simplicity is the ultimate sophistication.
Another related quote is attributed to
Albert Einstein
Make everything as simple as possible, but not simpler.
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.
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 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 is usually the best.
This is an over-simplification, or at least a little misleading. See above, "
In science".
[edit] 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
[32] (Note that simplest theory is something like "
only I exist" or "nothing exists").
The other things in question are the evidential support for the theory
[33] Therefore, according to the principle, a simpler but less correct theory should not be preferred over a more complex but more correct one.
It is this fact which gives the lie to the common misinterpretation of Occam's Razor that "the simplest" one is usually the correct one.
For instance,
classical physics is simpler than more recent theories; nonetheless it should not be preferred over them, because it is demonstrably wrong in certain respects.
Occam's razor is used to adjudicate between theories that have already passed 'theoretical scrutiny' tests, and which are equally well-supported by the evidence.
[34]
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.
[35] The
theory of relativity is often given as an example of the proliferation of complex words to describe a simple concept.
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.
[edit] 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 has 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, although this could be the case of the Late Renaissance Italian motto of unknown attribution
Se non è vero, è ben trovato ("Even if it is not true, it is well conceived") when referred to a particularly artful explanation.
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."
[36] Einstein supposedly remarked, "Everything should be made as simple as possible, but not simpler."
[37]
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.'
While not technically contradicting the razor's notion that (other things being equal) "the simplest explanation is always the best", the reverse corollary — that the
best explanation is not always the
simplest — is well expressed by the
Sir Arthur Conan Doyle character,
Sherlock Holmes, in
The Sign of the Four, especially in the following famous quote:
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth."
