Editing Occam's razor (section)

=== Science and the scientific method ===
[[File:Heliocentric.jpg|thumb|250px|right|[[Andreas Cellarius]]'s illustration of the Copernican system, from the ''[[Harmonia Macrocosmica]]'' (1660). Future positions of the sun, moon and other solar system bodies can be calculated using a [[Geocentrism|geocentric]] model (the earth is at the centre) or using a [[Heliocentrism#Modern science|heliocentric model]] (the sun is at the centre). Both work, but the geocentric model requires a much more complex system of calculations than the heliocentric model. This was pointed out in a preface to [[Copernicus]]'s first edition of ''[[De revolutionibus orbium coelestium]]''.]]
In [[science]], Occam's razor is used as a [[heuristic]] to guide scientists in developing theoretical models rather than as an arbiter between published models.<ref name="fn_(100)" /><ref name="fn_(101)" /> In [[physics]], parsimony was an important heuristic in the development and application of the [[principle of least action]] by [[Pierre Louis Maupertuis]] and [[Leonhard Euler]],<ref name="fn_(104)">{{Cite book |title=Mémoires de l'Académie Royale |last=de Maupertuis |first=P. L. M. |year=1744 |page=423 |language=fr}}</ref> in [[Albert Einstein]]'s formulation of [[special relativity]],<ref name="fn_(102)">{{Cite journal |last=Einstein |first=Albert |author-link=Albert Einstein |year=1905 |title=Does the Inertia of a Body Depend Upon Its Energy Content? |url=https://zenodo.org/record/1424057 |journal=Annalen der Physik |language=de |issue=18 |pages=639–41 |doi=10.1002/andp.19053231314 |bibcode=1905AnP...323..639E |volume=323 |doi-access=free |access-date=21 October 2019 |archive-date=21 October 2019 |archive-url=https://web.archive.org/web/20191021050723/https://zenodo.org/record/1424057 |url-status=live }}</ref><ref name="fn_(103)">L. Nash, The Nature of the Natural Sciences, Boston: Little, Brown (1963).</ref> and in the development of [[quantum mechanics]] by [[Max Planck]], [[Werner Heisenberg]] and [[Louis de Broglie]].<ref name="fn_(101)" /><ref name="fn_(105)">{{Cite book |title=Annales de Physique |last=de Broglie |first=L. |year=1925 |pages=22–128 |language=fr |issue=3/10}}</ref>

In [[chemistry]], Occam's razor is often an important heuristic when developing a model of a [[reaction mechanism]].<ref name="fn_(107)">RA Jackson, Mechanism: An Introduction to the Study of Organic Reactions, Clarendon, Oxford, 1972.</ref><ref name="fn_(108)">Carpenter, B. K. (1984). ''Determination of Organic Reaction Mechanism'', New York: Wiley-Interscience.</ref> Although it is useful as a heuristic in developing models of reaction mechanisms, it has been shown to fail as a criterion for selecting among some selected published models.<ref name="fn_(101)" /> In this context, Einstein himself expressed caution when he formulated Einstein's [[Constraint counting|Constraint]]: "It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience."<ref>{{Cite journal |last=Einstein |first=Albert |date=1934 |title=On the Method of Theoretical Physics |url=https://www.jstor.org/stable/184387 |journal=Philosophy of Science |volume=1 |issue=2 |pages=165 [163–169] |doi=10.1086/286316 |jstor=184387 |s2cid=44787169 |access-date=22 January 2023 |archive-date=22 January 2023 |archive-url=https://web.archive.org/web/20230122233537/https://www.jstor.org/stable/184387 |url-status=live }}</ref><ref>{{Cite book |last=Mettenheim |first=Christoph von |url=https://books.google.com/books?id=hLSR2or-bGAC |title=Popper Versus Einstein: On the Philosophical Foundations of Physics |date=1998 |publisher=Mohr Siebeck |isbn=978-3-16-146910-7 |page=34 |language=en |access-date=22 January 2023 |archive-date=22 January 2023 |archive-url=https://web.archive.org/web/20230122233538/https://books.google.com/books?id=hLSR2or-bGAC |url-status=live }}</ref><ref>{{Cite book |last1=Geis |first1=Gilbert |url=https://books.google.com/books?id=xdbQMywnrdwC&dq=%22the+supreme+goal+of+all+theory+is+to+make+the+irreducible+basic+elements+as+simple+and+as+few+as+possible+without+having+to+surrender+the+adequate+representation+of+a+single+datum+of%22&pg=PA39 |title=Crimes of the Century: From Leopold and Loeb to O.J. Simpson |last2=Geis |first2=Professor Emeritus of Criminology Law and & Society Gilbert |last3=Bienen |first3=Leigh B. |date=1998 |publisher=UPNE |isbn=978-1-55553-360-1 |page=39 |language=en |access-date=10 February 2023 |archive-date=5 April 2023 |archive-url=https://web.archive.org/web/20230405182025/https://books.google.com/books?id=xdbQMywnrdwC&dq=%22the+supreme+goal+of+all+theory+is+to+make+the+irreducible+basic+elements+as+simple+and+as+few+as+possible+without+having+to+surrender+the+adequate+representation+of+a+single+datum+of%22&pg=PA39 |url-status=live }}</ref> An often-quoted version of this constraint (which cannot be verified as posited by Einstein himself)<ref>{{Cite web |url=http://quoteinvestigator.com/2011/05/13/einstein-simple/ |title=Everything Should Be Made as Simple as Possible, But Not Simpler |date=13 May 2011 |url-status=live |archive-url=https://web.archive.org/web/20120529075018/http://quoteinvestigator.com/2011/05/13/einstein-simple/ |archive-date=29 May 2012}}</ref> reduces this to "Everything should be kept as simple as possible, but not simpler."

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 hypothesis|''ad hoc'' hypotheses]] to prevent them from being falsified, simpler theories are preferable to more complex ones because they tend to be more [[test method|testable]].<ref name="fn_(109)">{{Cite book |last=Alan Baker |title=Stanford Encyclopedia of Philosophy |publisher=Stanford University |year=2010 |location=California |chapter=Simplicity |chapter-url=http://plato.stanford.edu/entries/simplicity/ |orig-year=2004 |access-date=22 January 2005 |archive-date=26 March 2014 |archive-url=https://web.archive.org/web/20140326180129/http://plato.stanford.edu/entries/simplicity/ |url-status=live }}</ref><ref name="fn_(110)">{{Cite journal |last1=Courtney |first1=A. |last2=Courtney |first2=M. |year=2008 |title=Comments Regarding 'On the Nature of Science' |journal=Physics in Canada |volume=64 |issue=3 |pages=7–8 |arxiv=0812.4932 |bibcode=2008arXiv0812.4932C}}</ref><ref name="fn_(114)">{{Cite book |last=Sober |first=Elliott |title=Explanation and Its Limits |publisher=Cambridge University Press |year=1994 |editor-last=Knowles |editor-first=Dudley |pages=73–93 |chapter=Let's Razor Occam's Razor}}</ref> As a logical principle, Occam's razor would demand that scientists accept the simplest possible theoretical explanation for existing data. However, science has shown repeatedly that future data often support more complex theories than do existing data. Science prefers the simplest explanation that is consistent with the data available at a given time, but the simplest explanation may be ruled out as new data become available.<ref name="fn_(100)" /><ref name="fn_(110)" /> That is, science is open to the possibility that future experiments might support more complex theories than demanded by current data and is more interested in designing experiments to discriminate between competing theories than favoring one theory over another based merely on philosophical principles.<ref name="fn_(109)" /><ref name="fn_(110)" /><ref name="fn_(114)" />

When scientists use the idea of parsimony, it has meaning only in a very specific context of inquiry. Several background assumptions are required for parsimony to connect with plausibility in a particular research problem.{{Clarify | date = February 2021 | reason = This sentence is so vague/abstract that it seems to add very little to the discussion. For example, try dropping it, there doesn't seem to be much lost.}} The reasonableness of parsimony in one research context may have nothing to do with its reasonableness in another. It is a mistake to think that there is a single global principle that spans diverse subject matter.<ref name="fn_(114)" />

It has been suggested that Occam's razor is a widely accepted example of extraevidential consideration, even though it is entirely a metaphysical assumption. Most of the time, however, Occam's razor is a conservative tool, cutting out "crazy, complicated constructions" and assuring "that hypotheses are grounded in the science of the day", thus yielding "normal" science: models of explanation and prediction.<ref name="fn_(101)" /> There are, however, notable exceptions where Occam's razor turns a conservative scientist into a reluctant revolutionary. For example, [[Max Planck]] interpolated between the [[Wien approximation|Wien]] and [[Rayleigh–Jeans law|Jeans]] radiation laws and used Occam's razor logic to formulate the quantum hypothesis, even resisting that hypothesis as it became more obvious that it was correct.<ref name="fn_(101)" />

Appeals to simplicity were used to argue against the phenomena of meteorites, [[ball lightning]], [[continental drift]], and [[reverse transcriptase]].<ref>{{Cite journal |last1=Rabinowitz |first1=Matthew |last2=Myers |first2=Lance |last3=Banjevic |first3=Milena |last4=Chan |first4=Albert |last5=Sweetkind-Singer |first5=Joshua |last6=Haberer |first6=Jessica |last7=McCann |first7=Kelly |last8=Wolkowicz |first8=Roland |date=1 March 2006 |title=Accurate prediction of HIV-1 drug response from the reverse transcriptase and protease amino acid sequences using sparse models created by convex optimization |journal=Bioinformatics |language=en |volume=22 |issue=5 |pages=541–549 |doi=10.1093/bioinformatics/btk011 |pmid=16368772|doi-access=free }}</ref> One can argue for atomic building blocks for matter, because it provides a simpler explanation for the observed reversibility of both {{Clarify | text = mixing | date = February 2021 | reason = Mixing of what?  }} and chemical reactions as simple separation and rearrangements of atomic building blocks. At the time, however, the [[atomic theory]] was considered more complex because it implied the existence of invisible particles that had not been directly detected. [[Ernst Mach]] and the logical positivists rejected [[John Dalton]]'s [[atomic theory]] until the reality of atoms was more evident in [[Brownian motion]], as shown by [[Albert Einstein]].<ref name="Pojman2009">{{Cite book |title=The Stanford Encyclopedia of Philosophy |last=Paul Pojman |publisher=Stanford University |year=2009 |location=California |chapter=Ernst Mach |chapter-url=http://plato.stanford.edu/entries/ernst-mach/ |access-date=4 October 2009 |archive-date=11 November 2020 |archive-url=https://web.archive.org/web/20201111231039/https://plato.stanford.edu/entries/ernst-mach/ |url-status=live }}</ref>

In the same way, postulating the [[Luminiferous aether|aether]] is more complex than transmission of light through a [[vacuum]]. At the time, however, all known waves propagated through a physical medium, and it seemed simpler to postulate the existence of a medium than to theorize about wave propagation without a medium. Likewise, [[Isaac Newton]]'s idea of light particles seemed simpler than [[Christiaan Huygens]]'s idea of waves, so many favored it. In this case, as it turned out, neither the wave—nor the particle—explanation alone suffices, as [[wave–particle duality|light behaves like waves and like particles]].

Three axioms presupposed by the scientific method are realism (the existence of objective reality), the existence of natural laws, and the constancy of natural law. Rather than depend on provability of these axioms, science depends on the fact that they have not been objectively falsified. Occam's razor and parsimony support, but do not prove, these axioms of science. The general principle of science is that theories (or models) of natural law must be consistent with repeatable experimental observations. This ultimate arbiter (selection criterion) rests upon the axioms mentioned above.<ref name="fn_(110)" />

If multiple models of natural law make exactly the same testable predictions, they are equivalent and there is no need for parsimony to choose a preferred one. For example, [[Newtonian mechanics|Newtonian]], [[Hamiltonian mechanics|Hamiltonian]] and [[Lagrangian mechanics|Lagrangian]] classical mechanics are equivalent. Physicists have no interest in using Occam's razor to say the other two are wrong. Likewise, there is no demand for simplicity principles to arbitrate between wave and matrix formulations of quantum mechanics. Science often does not demand arbitration or selection criteria between models that make the same testable predictions.<ref name="fn_(110)" />