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", roughly translated as "entities must not be multiplied beyond necessity".

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 an heuristic maxim (rule of thumb) that advises economy, parsimony, or simplicity, often or especially in scientific theories.

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."

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.

Beginning in the 20th century, epistemological justifications based on induction, logic, pragmatism, and probability theory have become more popular among philosophers.

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[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, 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.

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.

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.

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 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 (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). 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.