Occam's razor

Attributed to William of Ockham, a 14th-century English philosopher and theologian, it is frequently cited as Entia non sunt multiplicanda praeter necessitatem, which translates as "Entities must not be multiplied beyond necessity",[1][2] although Occam never used these exact words.

[8] Ockham stated the principle in various ways, but the most popular version, "Entities are not to be multiplied without necessity" (Non sunt multiplicanda entia sine necessitate) was formulated by the Irish Franciscan philosopher John Punch in his 1639 commentary on the works of Duns Scotus.

[9] The origins of what has come to be known as Occam's razor are traceable to the works of earlier philosophers such as John Duns Scotus (1265–1308), Robert Grosseteste (1175–1253), Maimonides (Moses ben-Maimon, 1138–1204), and even Aristotle (384–322 BC).

[10][11] Aristotle writes in his Posterior Analytics, "We may assume the superiority ceteris paribus [other things being equal] of the demonstration which derives from fewer postulates or hypotheses."

While it has been claimed that Occam's razor is not found in any of William's writings,[15] one can cite statements such as 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.

Nevertheless, the precise words sometimes attributed to William of Ockham, Entia non sunt multiplicanda praeter necessitatem (Entities must not be multiplied beyond necessity),[16] are absent in his extant works;[17] this particular phrasing comes from John Punch,[18] who described the principle as a "common axiom" (axioma vulgare) of the Scholastics.

12, William of 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.

[29] Ernst Mach formulated the stronger version of Occam's razor into physics, which he called the Principle of Economy stating: "Scientists must use the simplest means of arriving at their results and exclude everything not perceived by the senses.

"[27] The idea of parsimony or simplicity in deciding between theories, though not the intent of the original expression of Occam's razor, has been assimilated into common culture as the widespread layman's formulation that "the simplest explanation is usually the correct one.

This endless supply of elaborate competing explanations, called saving hypotheses, cannot be technically ruled out – except by using Occam's razor.

The probabilistic (Bayesian) basis for Occam's razor is elaborated by David J. C. MacKay in chapter 28 of his book Information Theory, Inference, and Learning Algorithms,[36] where he emphasizes that a prior bias in favor of simpler models is not required.

William H. Jefferys and James O. Berger (1991) generalize and quantify the original formulation's "assumptions" concept as the degree to which a proposition is unnecessarily accommodating to possible observable data.

[37] They state, "A hypothesis with fewer adjustable parameters will automatically have an enhanced posterior probability, due to the fact that the predictions it makes are sharp.

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).

However, this criticism is also potentially true for any type of phylogenetic inference, unless the model used to estimate the tree reflects the way that evolution actually happened.

In biogeography, parsimony is used to infer ancient vicariant events or migrations of species or populations by observing the geographic distribution and relationships of existing organisms.

"[64] Thomas Aquinas, in the Summa Theologica, uses a formulation of Occam's razor to construct an objection to the idea that God exists, which he refutes directly with a counterargument:[65] Further, it is superfluous to suppose that what can be accounted for by a few principles has been produced by many.

So also whatever is done voluntarily must also be traced back to some higher cause other than human reason or will, since these can change or fail; for all things that are changeable and capable of defect must be traced back to an immovable and self-necessary first principle, as was shown in the body of the Article.Rather than argue for the necessity of a god, some theists base their belief upon grounds independent of, or prior to, reason, making Occam's razor irrelevant.

In his article "Sensations and Brain Processes" (1959), J. J. C. Smart invoked Occam's razor with the aim to justify his preference of the mind-brain identity theory over spirit-body dualism.

Later utilitarian writers have tended to abandon this idea, in large part due to the impracticality of determining each alleged criminal's relative sensitivity to specific punishments.

[70] Marcus Hutter's universal artificial intelligence builds upon Solomonoff's mathematical formalization of the razor to calculate the expected value of an action.

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.

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 of small size as the proper basis for excluding arbitrarily complex instruction sets in the formulation of razors.

[71][72] 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.

[81] The no free lunch (NFL) theorems for inductive inference prove that Occam's razor must rely on ultimately arbitrary assumptions concerning the prior probability distribution found in our world.

[b] Furthermore, it may be used to prioritize empirical testing between two equally plausible but unequally testable hypotheses; thereby minimizing costs and wastes while increasing chances of falsification of the simpler-to-test hypothesis.

[citation needed] 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.

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.

Physicist R. V. Jones contrived Crabtree's Bludgeon, which states that "[n]o set of mutually inconsistent observations can exist for which some human intellect cannot conceive a coherent explanation, however complicated.