Editing Scientific method (section)

=== Deductive and inductive reasoning{{anchor|i&d}} ===
{{Main|Deductive reasoning|Inductive reasoning}}

The idea of there being two opposed justifications for truth has shown up throughout the history of scientific method as analysis versus synthesis, non-ampliative/ampliative, or even confirmation and verification. (And there are other kinds of reasoning.) One to use what is observed to build towards fundamental truths – and the other to derive from those fundamental truths more specific principles.<ref name="SEP_SM">{{cite web | last1=Hepburn | first1=Brian | last2=Andersen | first2=Hanne | title=Scientific Method | website=Stanford Encyclopedia of Philosophy | date=13 November 2015 | url=https://plato.stanford.edu/archives/sum2021/entries/scientific-method | access-date=21 April 2024}}</ref>

Deductive reasoning is the building of knowledge based on what has been shown to be true before. It requires the assumption of fact established prior, and, given the truth of the assumptions, a valid deduction guarantees the truth of the conclusion. Inductive reasoning builds knowledge not from established truth, but from a body of observations. It requires stringent scepticism regarding observed phenomena, because cognitive assumptions can distort the interpretation of initial perceptions.<ref name="Gauch Jr 2002 p30/ch4"/>

[[File:Perihelio.svg|right|thumb|[[Apsidal precession|Precession]] of the [[Perihelion and aphelion|perihelion]]{{snd}}exaggerated in the case of Mercury, but observed in the case of [[S2 (star)|S2]]'s [[apsidal precession]] around [[Sagittarius A*]]<ref>{{cite web |date=16 April 2020 |title=ESO Telescope Sees Star Dance Around Supermassive Black Hole, Proves Einstein Right |url=https://www.eso.org/public/news/eso2006/ |url-status=live |archive-url=https://web.archive.org/web/20200515210420/https://www.eso.org/public/news/eso2006/ |archive-date=2020-05-15 |access-date=2020-04-17 |work=Science Release |publisher=[[European Southern Observatory]]}}</ref>]]

[[File:Inductive Deductive Reasoning.svg|thumb|Inductive Deductive Reasoning]]

{{anchor|precession of Mercury}}An example for how inductive and deductive reasoning works can be found in the [[history of gravitational theory]].{{efn|The philosophy of knowledge arising through observation is also called [[inductivism]]. A radical proponent of this approach to knowledge was [[John Stuart Mill]] who took all knowledge – even mathematical knowledge – to arise from experience through induction. The inductivist approach is still common place, though Mill's extreme views are outdated today.<ref name="Psillos 2013">{{cite book | last=Psillos | first=Stathis | title=Reason and Rationality | chapter=1. Reason and Science | publisher=DE GRUYTER | date=2013-12-31 | isbn=978-3-11-032514-0 | doi=10.1515/9783110325867.33 | pages=33–52}}</ref>{{rp|35}}}} It took thousands of years of measurements, from the [[Chaldea]]n, [[India]]n, [[History of Iran|Persian]], [[Greece|Greek]], [[Arabs|Arabic]], and [[Ethnic groups in Europe|European]] astronomers, to fully record the motion of planet [[Earth]].{{efn|name=Astronomy101 |1= [[Hipparchus]] used his own observations of the stars, as well as the observations by Chaldean and Babylonian astronomers to estimate Earth's precession.<ref name=astron101 >Brad Snowder's Astronomy Pages [https://astro101.wwu.edu/a101_precession.html ( Precession of the Equinox]</ref>}} [[Johannes Kepler|Kepler]](and others) were then able to build their early theories by [[Inductive reasoning#inductive generalization|generalizing the collected data inductively]], and [[Isaac Newton|Newton]] was able to unify prior theory and measurements into the consequences of his [[Newton's laws of motion|laws of motion]] in 1727.{{efn|name= keplerNewton |1= Isaac Newton (1727) [[Philosophiæ Naturalis Principia Mathematica#Book 3, De mundi systemate|On the System of the World]] condensed Kepler's law of for the planetary motion of Mars, Galileo's law of falling bodies, the motion of the planets of the Solar system, etc. into consequences of his three laws of motion.<ref name= systOfWorld >[[Isaac Newton]] (1727) [[Philosophiæ Naturalis Principia Mathematica#Book 3, De mundi systemate|On the System of the World]]</ref> ''See Motte's translation ([https://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1846)/The_System_of_the_World 1846])''}}

Another common example of inductive reasoning is the observation of a [[counterexample]] to current theory inducing the need for new ideas. [[Urbain Le Verrier|Le Verrier]] in 1859 pointed out problems with the [[Perihelion and aphelion|perihelion]] of [[Mercury (planet)|Mercury]] that showed Newton's theory to be at least incomplete. The observed difference of Mercury's [[Apsidal precession|precession]] between Newtonian theory and observation was one of the things that occurred to [[Albert Einstein|Einstein]] as a possible early test of his [[theory of relativity]]. His relativistic calculations matched observation much more closely than Newtonian theory did.{{efn|name=LeVerrier1859 |1=The difference is approximately 43 arc-seconds per century. And the precession of Mercury's orbit is cited in [[Tests of general relativity]]: U. Le Verrier (1859), (in French), [https://archive.org/stream/comptesrendusheb49acad#page/378/mode/2up "Lettre de M. Le Verrier à M. Faye sur la théorie de Mercure et sur le mouvement du périhélie de cette planète"], Comptes rendus hebdomadaires des séances de l'Académie des sciences (Paris), vol. 49 (1859), pp.379–383.}} Though, today's [[Standard Model]] of physics suggests that we still do not know at least some of the concepts surrounding Einstein's theory, it holds to this day and is being built on deductively.

A theory being assumed as true and subsequently built on is a common example of deductive reasoning. Theory building on Einstein's achievement can simply state that 'we have shown that this case fulfils the conditions under which general/special relativity applies, therefore its conclusions apply also'. If it was properly shown that 'this case' fulfils the conditions, the conclusion follows. An extension of this is the assumption of a solution to an open problem. This weaker kind of deductive reasoning will get used in current research, when multiple scientists or even teams of researchers are all gradually solving specific cases in working towards proving a larger theory. This often sees hypotheses being revised again and again as new proof emerges.

This way of presenting inductive and deductive reasoning shows part of why science is often presented as being a cycle of iteration. It is important to keep in mind that that cycle's foundations lie in reasoning, and not wholly in the following of procedure.