Editing Occam's razor (section)

== 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 1649 ''Philosophia Christiana de Anima'' (''On Christian Philosophy of the Soul''), gives him credit for the phrase, speaking of "''novacula occami''".<ref name="Sober 2015 4">{{Cite book |title=Ockham's Razors: A User's Manual |last=Sober |first=Elliott |publisher=Cambridge University Press |year=2015 |isbn=978-1107692534 |pages=4|author-link=Elliott Sober}}</ref> Ockham did not invent this principle, but its fame—and its association with him—may be due to the frequency and effectiveness with which he used it.<ref>Roger Ariew, Ockham's Razor: A Historical and Philosophical Analysis of Ockham's Principle of Parsimony, 1976</ref> Ockham stated the principle in various ways, but the most popular version, "Entities are not to be multiplied without necessity" ({{lang|la|Non sunt multiplicanda entia sine necessitate}}) was formulated by the Irish [[Franciscan]] philosopher [[John Punch (theologian)|John Punch]] in his 1639 commentary on the works of [[Duns Scotus]].<ref name="commentary">Johannes Poncius's commentary on John Duns Scotus's ''Opus Oxoniense,'' book III, dist. 34, q. 1. in John Duns Scotus ''Opera Omnia'', vol.15, Ed. Luke Wadding, Louvain (1639), reprinted Paris: Vives, (1894) p.483a</ref>

=== Formulations before William of Ockham ===
[[File:Pluralitas.jpg|thumb|Part of a page from [[John Duns Scotus]]'s book ''Commentaria oxoniensia ad IV libros magistri Sententiarus'', showing the words: "{{lang|la|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&nbsp;BC).<ref>Aristotle, ''Physics'' 189a15, ''On the Heavens'' 271a33. See also Franklin, ''op cit''. note 44 to chap. 9.</ref><ref>{{Cite journal |last=Charlesworth |first=M. J. |year=1956 |title=Aristotle's Razor |journal=Philosophical Studies |volume=6 |pages=105–112 | doi=10.5840/philstudies1956606}}</ref> Aristotle writes in his ''[[Posterior Analytics]]'', "We may assume the superiority {{lang|la|ceteris paribus}} [other things being equal] of the demonstration which derives from fewer postulates or hypotheses." [[Ptolemy]] ({{nowrap|{{Circa |AD 90|168}}}}) stated, "We consider it a good principle to explain the phenomena by the simplest hypothesis possible."<ref name="Franklin">{{Cite book |title=The Science of Conjecture: Evidence and Probability before Pascal |last=Franklin |first=James |publisher=The Johns Hopkins University Press |year=2001 |author-link=James Franklin (philosopher)}} Chap 9. p.&nbsp;241.</ref>

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 [[Scholasticism|scholastic]] writing.<ref name="Franklin" /> Robert Grosseteste, in ''Commentary on'' [Aristotle's] ''the Posterior Analytics Books'' (''Commentarius in Posteriorum Analyticorum Libros'') ({{Circa|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."<ref>[[Alistair Cameron Crombie]], ''Robert Grosseteste and the Origins of Experimental Science 1100–1700'' (1953) pp. 85–86</ref>

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]].<ref>{{Cite web |url=http://www.newadvent.org/summa/1002.htm#article3 |title=SUMMA THEOLOGICA: The existence of God (Prima Pars, Q. 2) |publisher=Newadvent.org |url-status=live |archive-url=https://web.archive.org/web/20130428053715/http://www.newadvent.org/summa/1002.htm#article3 |archive-date=28 April 2013 |access-date=26 March 2013}}</ref> 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 ===
[[File:William of Ockham - Logica 1341.jpg|thumb|[[Manuscript]] illustration of 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,<ref>{{Cite web |url=http://boingboing.net/2013/02/11/what-ockham-really-said.html |title=What Ockham really said |last=Vallee |first=Jacques |date=11 February 2013 |publisher=Boing Boing |url-status=live |archive-url=https://web.archive.org/web/20130331171919/http://boingboing.net/2013/02/11/what-ockham-really-said.html |archive-date=31 March 2013 |access-date=26 March 2013}}</ref> one can cite statements such as {{Lang|la|Numquam ponenda est pluralitas sine necessitate}} ("Plurality must never be posited without necessity"), which occurs in his theological work on the [[The Four Books of Sentences|''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, {{lang|la|Entia non sunt multiplicanda praeter necessitatem}} (Entities must not be multiplied beyond necessity),<ref>{{Cite book |title=The linguistics Student's Handbook |last=Bauer |first=Laurie |publisher=Edinburgh University Press |year=2007 |location=Edinburgh}} p. 155.</ref> are absent in his extant works;<ref>{{Cite book |title=A Dictionary of Philosophy |last=Flew |first=Antony |publisher=Pan Books |year=1979 |location=London |author-link=Antony Flew}} p. 253.</ref> this particular phrasing comes from [[John Punch (theologian)|John Punch]],<ref>[[Alistair Cameron Crombie|Crombie, Alistair Cameron]] (1959), ''Medieval and Early Modern Philosophy'', Cambridge, MA: Harvard, Vol. 2, p. 30.</ref> who described the principle as a "common axiom" (''axioma vulgare'') of the Scholastics.<ref name="commentary" /> William of Ockham himself seems to restrict the operation of this principle in matters pertaining to miracles and God's power, considering a plurality of miracles possible in the [[Eucharist]]{{Explain | date = February 2021 | reason = Currently impossible to figure out what this means (exceptions including Christians). Probably should just drop it as the first clause may be enough, or should just footnote it. }} simply because it pleases God.<ref name="Franklin" />

This principle is sometimes phrased as {{lang|la|Pluralitas non est ponenda sine necessitate}} ("Plurality should not be posited without necessity").<ref name="Britannica">{{Cite encyclopedia |url=https://www.britannica.com/EBchecked/topic/424706/Ockhams-razor |title=Ockham's razor |year=2010 |publisher=Encyclopædia Britannica Online |url-status=live |archive-url=https://web.archive.org/web/20100823154602/https://www.britannica.com/EBchecked/topic/424706/Ockhams-razor |archive-date=23 August 2010 |access-date=12 June 2010 |encyclopedia=Encyclopædia Britannica}}</ref> In his ''Summa Totius Logicae'', i. 12, William of Ockham cites the principle of economy, {{lang|la|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.&nbsp;352–53; [[William Kneale (logician)|Kneale]] and Kneale, 1962, p.&nbsp;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."<ref name="Hawking">{{Cite book |url=https://books.google.com/books?id=0eRZr_HK0LgC&pg=PA731 |title=On the Shoulders of Giants |last=Hawking |first=Stephen |publisher=Running Press |year=2003 |isbn=978-0-7624-1698-1 |page=731 |author-link=Stephen Hawking |access-date=24 February 2016 }}{{Dead link|date=August 2023 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref>Primary source: {{harvtxt|Newton|2011|p=387}} wrote the following two "philosophizing rules" at the beginning of part&nbsp;3 of the [[Philosophiæ Naturalis Principia Mathematica|Principia]] 1726 edition.
: Regula I. Causas rerum naturalium non-plures admitti debere, quam quæ & veræ sint & earum phænomenis explicandis sufficient.
: Regula II. Ideoque effectuum naturalium ejusdem generis eædem assignandæ sunt causæ, quatenus fieri potest.</ref>
In the sentence [[hypotheses non fingo]], Newton affirms the success of this approach.

[[Bertrand Russell]] offers a particular version of Occam's razor: "Whenever possible, substitute constructions out of known entities for inferences to unknown entities."<ref>{{Cite book |url=http://plato.stanford.edu/entries/logical-construction/ |title=Logical Constructions |publisher=Metaphysics Research Lab, Stanford University |year=2016 |access-date=29 March 2011 |archive-date=26 January 2021 |archive-url=https://web.archive.org/web/20210126031419/https://plato.stanford.edu/entries/logical-construction/ |url-status=live }}</ref>

Around 1960, [[Ray Solomonoff]] founded the [[Solomonoff's theory of inductive inference|theory of universal inductive inference]], the theory of prediction based on observations{{Snd}}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.<ref name="ReferenceA">Induction: From Kolmogorov and Solomonoff to De Finetti and Back to Kolmogorov JJ McCall – Metroeconomica, 2004 – Wiley Online Library.</ref><ref name="ReferenceB">{{Cite journal |last=Soklakov |first=A. N. |year=2002 |title=Occam's Razor as a formal basis for a physical theory |journal=Foundations of Physics Letters |volume=15 |issue=2 |pages=107–135 |arxiv=math-ph/0009007 |bibcode=2000math.ph...9007S |doi=10.1023/A:1020994407185|s2cid=14940740 }}</ref><ref>{{Cite journal |last1=Rathmanner |first1=Samuel |last2=Hutter |first2=Marcus |author-link2=Marcus Hutter |year=2011 |title=A philosophical treatise of universal induction |journal=Entropy |volume=13 |issue=6 |pages=1076–1136 |arxiv=1105.5721 |bibcode=2011Entrp..13.1076R |doi=10.3390/e13061076|s2cid=2499910 |doi-access=free }}</ref>

Another technical approach to Occam's razor is [[Ontological commitment#Ontological parsimony|ontological parsimony]].<ref name="Baker">{{Cite encyclopedia |url=http://plato.stanford.edu/archives/sum2011/entries/simplicity/#OntPar |title=Simplicity |last=Baker |first=Alan |date=25 February 2010 |editor-last=Zalta |editor-first=Edward N. |encyclopedia=The Stanford Encyclopedia of Philosophy (Summer 2011 Edition) |access-date=6 April 2013 |archive-date=24 February 2021 |archive-url=https://web.archive.org/web/20210224044741/https://plato.stanford.edu/archives/sum2011/entries/simplicity/#OntPar |url-status=live }}</ref> Parsimony means spareness and is also referred to as the Rule of Simplicity. This is considered a strong version of Occam's razor.<ref name="math.ucr.edu">{{Cite web |url=http://math.ucr.edu/home/baez/physics/General/occam.html |title=What is Occam's Razor? |website=math.ucr.edu |url-status=live |archive-url=https://web.archive.org/web/20170706234202/http://math.ucr.edu/home/baez/physics/General/occam.html |archive-date=6 July 2017}}</ref><ref>{{Cite book |url=https://books.google.com/books?id=shdlDQAAQBAJ&pg=PT30 |title=Everywhere The Soles of Your Feet Shall Tread |last=Stormy Dawn |date=17 July 2017 |publisher=Archway |isbn=9781480838024 |access-date=22 May 2017 |archive-date=28 October 2023 |archive-url=https://web.archive.org/web/20231028141247/https://books.google.com/books?id=shdlDQAAQBAJ&pg=PT30#v=onepage&q&f=false |url-status=live }}</ref> A variation used in medicine is called the "[[Zebra (medicine)|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".<ref>{{Cite book |title=Zebra Cards: An Aid to Obscure Diagnoses |last=Sotos |first=John G. |publisher=Mt. Vernon Book Systems |year=2006 |isbn=978-0-9818193-0-3 |location=Mt. Vernon, VA |orig-year=1991}}</ref>

[[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."<ref>{{Cite journal |last=Becher |first=Erich |year=1905 |title=The Philosophical Views of Ernst Mach |journal=The Philosophical Review |volume=14 |issue=5 |pages=535–562 |doi=10.2307/2177489 |jstor=2177489}}</ref>

This principle goes back at least as far as Aristotle, who wrote "Nature operates in the shortest way possible."<ref name="math.ucr.edu" /> 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."<ref name="math.ucr.edu" />