Ockham’s Razor

Occam’s razor, Ockham’s razor, Ocham’s razor (Latin: novacula Occami), or law of parsimony (Latin: lex parsimoniae) is the problem-solving principle that “entities should not be multiplied without necessity”,^[1][2] or more simply, the simplest explanation is usually the right one. The idea is attributed to English Franciscan friar William of Ockham (c. 1287–1347), a scholastic philosopher and theologian who used a preference for simplicity to defend the idea of divine miracles. This philosophical razor advocates that when presented with competing hypotheses about the same prediction, one should select the solution with the fewest assumptions,^[3] and that this is not meant to be a way of choosing between hypotheses that make different predictions.

Similarly, in science, Occam’s razor is used as an abductive heuristic in the development of theoretical models rather than as a rigorous arbiter between candidate models.^[4][5] In the scientific method, Occam’s razor is not considered an irrefutable principle of logic or a scientific result; the preference for simplicity in the scientific method is based on the falsifiability criterion. For each accepted explanation of a phenomenon, there may be an extremely large, perhaps even incomprehensible, number of possible and more complex alternatives. Since failing explanations can always be burdened with ad hoc hypotheses to prevent them from being falsified, simpler theories are preferable to more complex ones because they are more testable.

History

The phrase Occam’s razor did not appear until a few centuries after William of Ockham’s death in 1347. Libert Froidmont, in his On Christian Philosophy of the Soul, takes credit for the phrase, speaking of “novacula occami“.^[9] Ockham did not invent this principle, but the “razor”—and its association with him—may be due to the frequency and effectiveness with which he used it.^[10] 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.^[11]

Formulations before William of Ockham

Part of a page from John Duns Scotus’s book Commentaria oxoniensia ad IV libros magistri Sententiarus, showing the words: “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 John Duns Scotus (1265–1308), Robert Grosseteste (1175–1253), Maimonides (Moses ben-Maimon, 1138–1204), and even Aristotle (384–322 BC).^[12][13] 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.” Ptolemy (c. AD 90 – c. AD 168) stated, “We consider it a good principle to explain the phenomena by the simplest hypothesis possible.”^[14]

Phrases such as “It is vain to do with more what can be done with fewer” and “A plurality is not to be posited without necessity” were commonplace in 13th-century scholastic writing.^[14] Robert Grosseteste, in Commentary on [Aristotle’s] the Posterior Analytics Books (Commentarius in Posteriorum Analyticorum Libros) (c. 1217–1220), declares: “That is better and more valuable which requires fewer, other circumstances being equal… For if one thing were demonstrated from many and another thing from fewer equally known premises, clearly that is better which is from fewer because it makes us know quickly, just as a universal demonstration is better than particular because it produces knowledge from fewer premises. Similarly in natural science, in moral science, and in metaphysics the best is that which needs no premises and the better that which needs the fewer, other circumstances being equal.”^[15]

The Summa Theologica of Thomas Aquinas (1225–1274) states that “it is superfluous to suppose that what can be accounted for by a few principles has been produced by many.” Aquinas uses this principle to construct an objection to God’s existence, an objection that he in turn answers and refutes generally (cf. quinque viae), and specifically, through an argument based on causality.^[16] Hence, Aquinas acknowledges the principle that today is known as Occam’s razor, but prefers causal explanations to other simple explanations (cf. also Correlation does not imply causation).

William of Ockham

William of Ockham (circa 1287–1347) was an English Franciscan friar and theologian, an influential medieval philosopher and a nominalist. His popular fame as a great logician rests chiefly on the maxim attributed to him and known as Occam’s razor. The term razor refers to distinguishing between two hypotheses either by “shaving away” unnecessary assumptions or cutting apart two similar conclusions.

While it has been claimed that Occam’s razor is not found in any of William’s writings,^[17] one can cite statements such as Numquam ponenda est pluralitas sine necessitate William of Ockham – Wikiquote (“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).

Nevertheless, the precise words sometimes attributed to William of Ockham, Entia non-sunt multiplicanda praeter necessitatem (Entities must not be multiplied beyond necessity),^[18] are absent in his extant works;^[19] this particular phrasing comes from John Punch,^[20] who described the principle as a “common axiom” (axioma vulgare) of the Scholastics.^[11] William of Ockham’s contribution seems to restrict the operation of this principle in matters pertaining to miracles and God’s power; so, in the Eucharist, a plurality of miracles is possible^{[further explanation needed]}, simply because it pleases God.^[14]

This principle is sometimes phrased as Pluralitas non-est ponenda sine necessitate (“Plurality should not be posited without necessity”).^[21] In his Summa Totius Logicae, i. 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. 352–53; Kneale and Kneale, 1962, p. 243.)

Later formulations

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, as far as possible, assign the same causes.”^[22][23]

Bertrand Russell offers a particular version of Occam’s razor: “Whenever possible, substitute constructions out of known entities for inferences to unknown entities.”^[24]

Around 1960, Ray Solomonoff founded the theory of universal inductive inference, the theory of prediction based on observations – for example, predicting the next symbol based upon a given series of symbols. The only assumption is that the environment follows some unknown but computable probability distribution. This theory is a mathematical formalization of Occam’s razor.^[25][26][27]

Another technical approach to Occam’s razor is ontological parsimony.^[28] Parsimony means spareness and is also referred to as the Rule of Simplicity. This is considered a strong version of Occam’s razor.^[29][30] A variation used in medicine is called the “Zebra”: a physician should reject an exotic medical diagnosis when a more commonplace explanation is more likely, derived from Theodore Woodward’s dictum “When you hear hoofbeats, think of horses not zebras”.^[31]

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.”^[32]

This principle goes back at least as far as Aristotle, who wrote “Nature operates in the shortest way possible.”^[29] 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.”