Editing Occam's razor (section)

=== 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" />