Occam's Razor

This article discusses the logical precept of Occam's Razor. For other (band-related) meanings, see Ockham's Razor (bands).

Table of contents

1 Numerous ways of expression 2 History of Occam's Razor 3 Science and Occam's Razor 4 Medicine/philosophy of medicine and Occam's Razor 5 Astronomy/philosophy of astronomy and Occam's Razor 6 Biology/philosophy of biology and Occam's Razor 7 Computer science and Occam's Razor 8 Chemistry/philosophy of chemistry and Occam's Razor 9 History/philosophy of history and Occam's Razor 10 Neuroscience/Philosophy of Neuroscience and Occam's Razor 11 Psychology/philosophy of psychology and Occam's Razor 12 Statistics and Occam's Razor 13 Religion/philosophy of religion and Occam's Razor 14 Philosophy of mind and Occam's Razor 15 Justifications for Occam's Razor 16 Chatton's Anti-razor and Occam's Razor 17 See also 18 References 19 External links

Numerous ways of expression

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 Occam's surviving writings. William wrote, in Latin, Pluralitas non est ponenda sine neccesitate, which translates literally into English as "Plurality should not be posited without necessity".

Dave Beckett of the University of Kent at Canterbury writes: "The medieval rule of parsimony, or principle of economy, frequently used by Ockham came to be known as Ockham's razor." [1]

Occam's Razor has also been referred to as "parsimony of postulates" and the "principle of simplicity" and "K.I.S.S." (keep it simple, stupid). Another proverb expressing the idea that is often heard in medical schools is, "When you hear hoofbeats, think horses, not zebras." Like many maxims, it has deficiencies; African doctors are not well advised to follow it.

A re-statement of Occam's Razor, in more formal terms, is provided by information theory in the form of minimum message length.

Another variant of this law is Thargola's Sword from Nightfall, (originally a short story by Isaac Asimov and later expanded to a novel in conjunction with Robert Silverberg): "We must drive a sword through any hypothesis that is not strictly necessary".

Occam's Razor is nowadays usually stated as follows:

"Of two equivalent theories or explanations, all other things being equal, the simpler one is to be preferred."

"We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances."

History of Occam's Razor

William of Ockham(1287-1347) is usually given credit for formulating the razor that bears his name which is typically phrased "entities are not to be multiplied beyond necessity." In Latin, the language used by William, it would be "entia non sunt multiplicanda preaeter necessitatem" but this phrase does not appear in any of his extant writings. It is not until 1639 that this phrasing was coined by John Ponce of Cork. There are a variety of similar phrases such as "frustra fit per plura quod potest fieri per pauciora", non est ponenda pluritas sine necessitate", and "si duae res sufficient ad ejus veritatem, superfluum est ponere aliam (tertiam) rem" that do. These translate as "in vain we do by many which can be done by means of fewer", "pluralities ought not be supposed without necessity", and "if two things are sufficient for the purpose of truth, it is superfluous to suppose another" respectively. The origins of what has come to be known as Occam's razor is traceable to the works of earlier philosophers such as John Duns Scotus (1265-1308) and even as early as Aristotle (384-322 B.C.)(Charlesworth, 1956). Even the name 'Occam's Razor' was unknown to William. This phrase does not appear until the 19th century in the works of Sir William Hamilton(1805-1865). It is perhaps how often and effectively he used it that accounts for its association with Ockham. See Roger Ariew's dissertation of 1976, Ockham's Razor: A Historical and Philosophical Analysis of Ockham's Principle of Parsimony and W. M. Thornburn's The Myth of Occam's Razor.

Science and Occam's Razor

Occam's Razor has become a basic perspective for those who follow the scientific method. It is important to note that it is a heuristic argument that does not necessarily give correct answers; it is a loose guide to choosing the scientific hypothesis which (currently) contains the least number of unproven assumptions. Often, several hypotheses are equally "simple" and Occam's Razor does not express any preference in such cases.

For example, after a storm you notice that a tree has fallen. Based on the evidence of "a storm" and "a fallen tree" a reasonable hypothesis would be that "the storm blew down the tree" -- a hypothesis that requires only one assumption -- that it was, in fact, a strong wind that knocked over the tree, rather than a meteor or an elephant. The hypothesis that "the tree was knocked over by marauding 200 meter tall space aliens" requires several additional assumptions (concerning the very existence of aliens, their ability and desire to travel interstellar distances and the alien biology that allows them to be 200 meters tall in terrestrial gravity) and is therefore less preferable.

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." It often happens that the best explanation is much more complicated than the simplest possible explanation because it requires fewer assumptions. Some people have oversimplified Occam's Razor as "The simplest explanation is the best (or true) one".

There are two senses in which Occam's razor can been seen at work in the history of science. One is ontological reduction by elimination and the other is by intertheoretic competion. 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 from premodern chemistry, and vital spirits of premodern Biology. It is anticipated by Paul and Patricia Churchland that the ontology of Folk Psychology awaits a similar fate that it will be eliminated in favor of a neurobiological ontology.

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. 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 crystaline spheres that the planets were thought to be imbedded 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 thus ontologically simpler than its predecessor. During the 19th cenrtury 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. Einstein capitalized on this finding and constructed his theory without any reference to the Aether, thus providing another example of a theory chosen in part for its greater ontological simplicity.

Medicine/philosophy of medicine and Occam's Razor

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.

Astronomy/philosophy of astronomy and Occam's Razor

How is Occam's Razor used in contemporary Astronomy/Cosmology?

Biology/philosophy of biology and Occam's Razor

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 contension 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 Cannon.

Williams provides an example from zoology. Musk oxen when threatened by wolves will form a circle with the males on the outside and the females and young on the inside. Biologists often cite this as an example of altruistic behavior by the males that is disadvantageous to them individually but beneficial to the group as a whole and thus supportive of the group selection theory. Williams, however, offers an alternative interpretation based on individual selection. When treatened by a larger or more dangerous animal, an individual Musk oxen will either fight of flee. The males being larger than the females and young perceive wolves as less dangerous and are willing to fight while the females and young flee to the interior of the circle. From this perspective there is no need for group selection. Each individual is acting in it's own self interest.

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 criteria 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 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 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 Occam's Razor(1990).

Computer science and Occam's Razor

Artificial Intelligence has recently moved to a heavily probabilistic, Bayesian research program, see Statistics section below.

Chemistry/philosophy of chemistry and Occam's Razor

For contemporary uses of Occam's razor in Chemistry see Ockham's Razor and Chemistry by Roald Hoffmann, Vladimir I. Minkin, and Barry K. Carpenter at: http://www.hyle.org/journal/issues/3/hoffman.htm

History/philosophy of history and Occam's Razor

When reconstructing the past we are to admit no more causes of an event or events than are necessary or supported by the evidence.

Neuroscience/Philosophy of Neuroscience and Occam's Razor

See eliminative materialism

Psychology/philosophy of psychology and Occam's Razor

See Morgan's Canon and references.

Statistics and Occam's Razor

There are various papers in scholarly journals deriving 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 inference and Bayesian model comparison, which can be used to compare models that don't fit the data equally well (see e.g. Jaynes, 1994; Duda, Hart & Stork, 2000; MacKay, 2003). These methods can sometimes optimally balance the complexity and power of a model.

Religion/philosophy of religion and Occam's Razor

In the philosophy of religion Occam's Razor is sometimes used to challenge arguments for the existence of God. None of these applications has been considered definitive because the competing assumptions are not (and perhaps cannot be) precisely defined. Also, it should be added that the principle is only a guide to the best theory based on current knowledge, not the "truth."

William may have been inspired by earlier thinkers. For example, Book V of Aristotle's Physics has the statement "Nature operates in the shortest way possible."

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 held much more expansively.)

Adding another layer of irony, many modern scientists and mathematicians seriously propose that the basic "entities" of reality may be "bits of information", i.e. the digits of binary code, in which case the entities of William of Occam might be seen as foreshadowing the logic of George Boole and modern computing.

Perhaps due to the abstruse nature of medieval logic and the obscure goals of William of Occam as a theologian and logician, discussion and application of Ockham's Razor is frequently full of ironies.

It is argued that Ockham was an intellectual forefather of the Scientific Method because he argued for a degree of intellectual freedom in a time of dogmatic belief. He can also, however, be seen as an apologist for Divine Omnipotence, since he was concerned to demonstrate that creation was contingent and the Creator free to change the rules at will. Thus, if God is free to make an infinity of worlds with completely different rules from those which prevail in our world, then we are free to imagine such worlds and their logical and practical consequences (within the bounds set by the Church's infallible Dogma).

Perhaps the best formulation of Occam's Razor is the one which states that, of equally good explanations for a phenomenon, the best one is the simplest explanation which accounts for all the facts.

Occam's Razor could also be said to apply to the elimination of the soul as a superfluous entity.

Creationists sometimes employ Occam's razor in defense of their theory of Cosmogenesis and Geogenesis claiming that theirs is the simpler theory as compared with the scientific account. Unfortunately for creationists their theory does not adequately explain all the observed phenomena.

Philosophy of mind and Occam's Razor

Perhaps the earliest application of Occam's Razor in the philosophy of mind is to be found in the work of George Berkeley(1685-1753). Berkeley was an idealist believing 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. Idealism has few adherents today and Berkeley's arguments find few sympathetic ears.

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 the mental which is nonphysical.In contrast identity theorist 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 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 rational 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.

Justifications for Occam's Razor

Occam's Razor is known by several different names including the Principle of Parsimony, The Principle of Simplicity, and The Principle of Economy. The reason for these alternate names can be explained by the association of simplicity and parsimony with Occam's Razor. Prior to the 20th century it was believed that the metaphysical justification for Occam's Razor was simplicity. It was thought that nature was in some sense simple. From the beginning of the 20th century on this view fell out of favor as scientists presented an ever increasingly complex world view. In response, philosophers turned away from metaphysical justifications for Occam's Razor to epistemological ones including inductive, pragmatic, likelihood and probabilistic justifications which is where things stand today. For a summary of epistemological justifications for Occam's Razor see Roger Ariew's dissertation of 1976 "Ockham's Razor: A Historical and Philosophical Analysis of Ockham's Principle of Parsimony.

Chatton's Anti-razor and Occam's Razor

Walter of Chatton was a contemporary of William of Ockham (1287-1347) who took exception to Ockham's razor and Ockham's use of it. So in response he devised his own anti-razor:'if three things are not enough to verify an affirmative proposition about things, a fourth must be added, and so on'. Although there have been a number of philosophers who have formulated similar anti-razors since Chatton's time, Chatton's anti-razor has not known anything like the success of Occam's razor. Among those who have coined their own anti-razors are Gottfried Wilhelm Leibniz (1646-1716), Immanuel Kant (1724-1804), and Karl Menger (20th century). Leibniz's version took the form of a principle of plentitude as Arthur Lovejoy has called it. The idea behind the principle was that God created the world with the most possible creatures. Kant felt a need to moderate the effects of Ockham's razor and thus created his own counter razor;'the variety of beings should not rashly be deminished'. Karl Menger found mathematicians to be too parsimonious with regard to variables so he formulated his Law Against Miserliness which took either 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.

See also

• Falsifiability
• philosophy of science
• Hanlon's razor
• Rationalism
• Bayesian inference
• Bayesian model comparison
• Kolmogorov complexity
• scientific reductionism
• Morgan's Canon
• simplicity
• cladistics
• curve fitting problem
• eliminative materialism
• Buridan's Ass

• Ariew, R.(1976) Ockham's Razor: A Historical and Philosophical Analysis of Ockham's Principle of Parsimony. Philosophy. Champane-Urbana, University of Illinois.
• Charlesworth, M. J. (1956). "Aristotle's Razor." Philosophical Studies (Ireland) 6: 105-112.
• Churchland, P. (1984) Matter and Consciousness. Cambridge, Massachusetts, The MIT Press.
• Epstein, R. (1984). The Principle of Parsimony and Some Applications in Psychology. Journal of Mind Behavior 5:119-130
• Jacquette, D. (1994). Ockham's Razor. Philosophy of Mind. Engleswoods Cliffs, N.J., Prentice Hall:34-36.
• Maurer, A. (1984). Ockham's Razor and Chatton's Anti-Razor. Medieval Studies 46:463-475.
• Menger, Karl. A Counterpart
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