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Bit of a... BOLD insertion of a new section at the very top of the article, but I feel it has merit. Credit to Ancheta Wis for passing down The Tetrast's work with Pierce's Musement.
Tag: Reverted
Undid revision 1218544333 by JackTheSecond (talk) friendly revert of very bold editing. there is clearly no consensus for this radical change, and it would definitely need discussion first. there is no one canonical method, statistics is not essential to science, empiricism is diffierent from empirical science, etc.
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== Rules of reasoning ==
=== Principles of inquiry ===
{{Quote| quote=We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.|source=Isaac Newton, ''Philosophiæ Naturalis Principia Mathematica [1723 (3rd ed.])''<ref name="principia" />}}
 
Science can be said to be governed by a set of foundational principles of reason. Where Newton espoused parsimony in causal explanations, others after him have expanded on science's need to be economical.{{efn-ua|name= FRL-1.136 }} This expanded idea of not just concise theory but the way work is done stands in context with what C. S. Pierce called ''Musement''. Inquiry's phase of free-ranging thought (with attendant feelings: doubt, belief, perplexity etc.) but with no attempt at discovery of an order. As he put it: "if we truly desire the goal of the inquiry we are not to waste our resources."<ref name= reasonsFirstRule /><ref name="NA"/> Generally, scientific inquiry is dedicated to empirical observation, logical coherence, and cautious theorizing.<ref name="principia" />
 
The ubiquitous element in the scientific method is [[empiricism]]. This is in opposition to stringent forms of [[rationalism]]: the scientific method embodies the position that ''reason alone'' cannot solve a particular scientific problem. A strong formulation of scientific method is not always aligned with a form of [[empiricism]] in which the empirical data is put forward in the form of experience or other abstracted forms of knowledge; in [[#aModel|current scientific practice]], however, the use of [[scientific modelling]] and reliance on abstract typologies and theories is normally accepted. The scientific method counters claims that [[revelation]], political or religious [[dogma]], appeals to tradition, commonly held beliefs, common sense, or currently held theories pose the only possible means of demonstrating truth.<ref name= truthSought4sake /><ref name="reasonsFirstRule">{{cite book |last=Peirce |first=Charles S. |title=Collected Papers |year=1899 |series=v. 1 |at=paragraphs 135–140 |chapter=F.R.L. [First Rule of Logic] |quote=...&nbsp;in order to learn, one must desire to learn&nbsp;... |access-date=2012-01-06 |chapter-url=http://www.princeton.edu/~batke/peirce/frl_99.htm |archive-url=https://web.archive.org/web/20120106071421/http://www.princeton.edu/~batke/peirce/frl_99.htm |archive-date=January 6, 2012 |url-status=dead}}</ref><ref name= tow />▼
 
=== Principles of statistical analysis ===
{{See also|Statistics}}
Smolin, in 2013, espoused ethical principles rather than giving any potentially limited definition of the rules of inquiry.{{efn-lg|name= ethicalPosition}} His ideas stand in the context of the scale of data–driven and [[big science]], which has seen increased importance of honesty and consequently [[reproducibility]]. How to interpret statistics is one of the core principles of modern, empirical science.{{efn|... and [[John Ioannidis]], in 2005,<ref name="mostRwrong" /> has shown that not everybody respects the principles of statistical analysis; whether they be the principles of inference or otherwise.{{Broader|#Relationship with statistics}}}}
 
Before [[FAIR data|general principles]] of data management and stewardship, lack of familiarity with statistical methodologies can result in erroneous conclusions. For instance, extrapolating from a single scientific observation, such as "This experiment yielded these results, so it should apply broadly," exemplifies inductive wishful thinking. Conversely, assuming that a specific outcome will occur based on general trends observed across multiple experiments, as in "Most experiments have shown this pattern, so it will likely occur in this case as well," illustrates deductive wishful thinking.<ref name="Welsby Weatherall 2022 pp. 793–798">{{cite journal | last=Welsby | first=Philip D | last2=Weatherall | first2=Mark | title=Statistics: an introduction to basic principles | journal=Postgraduate Medical Journal | volume=98 | issue=1164 | date=2022-10-01 | issn=0032-5473 | doi=10.1136/postgradmedj-2020-139446 | pages=793–798}}</ref><!--{{clarify inline|with=better examples|date=April 2024|reason=If anyone can find a neat example to give in this section... they are prayed for. Ideally, one not of the misappliance of the principles, but where they worked. -- To give an impression of how statistical inquiry is *supposed* to work. Do feel encouraged to replace the somewhat anecdotal "This experiment yielded these results, so it should apply broadly," ...}}-->
 
In statistical analysis, extreme care not to introduce unexpected biases either into the collection of data or the interpretation of results, is of utmost importance. Furthermore, questions and answers should not only be well-defined but as concise as possible, and reported results should be put into their appropriate context.<ref name="Welsby Weatherall 2022 pp. 793–798" />
 
=== Deductive & inductive reasoning ===
{{expand section|with=better examples|date=April 2024}}
{{Main|Deductive reasoning|Inductive reasoning}}
 
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. 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.
 
A common example of inductive reasoning is the observation of a [[counterexample]] to current theory inducing the need for new ideas. Problems posed in the orbit of Mercury showed Newton's 1709 theory of gravity to be at least incomplete. From these new observations, [[Albert Einstein|Einstein]], 170 years after Newton's initial work, expanded the [[theory of gravity]] with his [[theory of relativity]]. – Though, today's [[Standard Model]] of physics suggests that we still do not know at least some of the concepts surrounding the theory, it holds to this day and is being built on deductively.{{cleanup inline|this example already exists}}
 
A theory being assumed as true and subsequently built on is a common example of deductive reasoning. Theory building on Einstein's achievement will simply state that 'we have shown that this case fulfils the conditions under which general/special relativity applies, therefore its conclusions apply also'.
 
== History ==
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}}{{efn|name= Kepler1604| Kepler was driven to this experiment after observing the partial solar eclipse at Graz, July 10, 1600. He used Tycho Brahe's method of observation, which was to project the image of the Sun on a piece of paper through a pinhole aperture, instead of looking directly at the Sun. He disagreed with Brahe's conclusion that total eclipses of the Sun were impossible because there were historical accounts of total eclipses. Instead, he deduced that the size of the aperture controls the sharpness of the projected image (the larger the aperture, the more accurate the image&nbsp;– this fact is now fundamental for optical system design). {{harvp|Voelkel|2001|p=61}}, notes that Kepler's 1604 experiments produced the first correct account of vision and the eye, because he realized he could not accurately write about astronomical observation by ignoring the eye. {{harvp|Smith|2004|p=192}} recounts how Kepler used Giambattista della Porta's water-filled glass spheres to model the eye, and using an aperture to represent the entrance pupil of the eye, showed that the entire scene at the entrance pupil-focused on a single point of the rear of the glass sphere (representing the retina of the eye). This completed Kepler's investigation of the optical train, as it satisfied his application to astronomy.}} and [[Galileo Galilei]].{{efn-lg|name= empirical|...an experimental approach was advocated by Galileo in 1638 with the publication of ''[[Two New Sciences]]''.{{sfnp|Galileo Galilei|1638}}}} There was particular development aided by theoretical works by a skeptic [[Francisco Sanches]],{{sfnp|Sanches|1988}} by idealists as well as empiricists [[John Locke]], [[George Berkeley]], and [[David Hume]].{{efn-lg|name= particDev |1= Sanches and Locke were both physicians. By his training in Rome and France, Sanches sought a method of science beyond that of the Scholastic Aristotelian school. Botanical gardens were added to the universities in Sanches' time to aid medical training before the 1600s. ''See Locke [https://en.wikiquote.org/wiki/John_Locke#An_Essay_Concerning_Human_Understanding_(1689) (1689) An Essay Concerning Human Understanding]'' Berkeley served as foil to the materialist System of the World of Newton; Berkeley emphasizes that scientist should seek 'reduction to regularity'.<ref name= idealism >Lisa Downing, ''Stanford Encyclopedia of Philosophy'' [https://plato.stanford.edu/entries/berkeley/#3.2.3 (Fall 2021) George Berkeley, 3.2.3 Scientific explanation]</ref> Atherton (ed.) 1999 selects Locke, Berkeley, and Hume as part of the empiricist school.<ref>Margaret Atherton (ed.) 1999 [https://www.google.com/books/edition/_/iifXAAAAMAAJ?hl=en&sa=X&ved=2ahUKEwik0tS18qOFAxXCj4kEHYLuD28Qre8FegQICxAD The Empiricists]</ref> }}
 
=== Formalized method ===
 
The early version of the canonical "sequence" of elements was first formulated in the 19th century. A sea voyage from America to Europe afforded [[C. S. Peirce]] the distance to clarify his ideas, gradually resulting in the [[hypothetico-deductive model]].{{sfnp|Godfrey-Smith|2003|p=236}} Formulated in the 20th century, the model has undergone significant revision since first proposed.
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Staddon (2017) argues it is a mistake to try following rules in the absence of an algorithmic scientific method; in that case, "science is best understood through examples".<ref name="Staddon 2017 p. ">{{cite book |last=Staddon |first=John | title=Scientific Method: How Science Works, Fails to Work, and Pretends to Work | publisher=Routledge | publication-place=New York | date=2017-12-01 | isbn=978-1-315-10070-8 | doi=10.4324/9781315100708 | page=}}</ref><ref>{{cite web| url = https://dukespace.lib.duke.edu/dspace/bitstream/handle/10161/21425/StaddonHistoryofScienceSept2020.pdf?sequence=2&isAllowed=y| title = Whatever Happened to History of Science?| date = 16 September 2020| access-date = 2021-08-27 | archive-date = 2021-08-27 | archive-url = https://web.archive.org/web/20210827092318/https://dukespace.lib.duke.edu/dspace/bitstream/handle/10161/21425/StaddonHistoryofScienceSept2020.pdf?sequence=2&isAllowed=y| url-status = live| last1 = Staddon| first1 = John|quote="science is best understood through examples"}}</ref> But algorithmic methods, such as ''disproof of existing theory by experiment'' have been used since [[Alhacen]] (1027) ''[[Book of Optics]]'',{{efn|name= alhacenCharacterizes}} and Galileo (1638) ''Two New Sciences'',{{sfnp|Galileo Galilei|1638}} and ''The Assayer''<ref name= ilSaggiatore /> still stand as scientific method.
 
=== Overview ===▼
==Elements of the scientific method==▼
{{anchor|Context}}The basic elements of the scientific method are illustrated by the following example (which occurred from 1944 to 1953) from the discovery of the structure of DNA (marked with [[File:DNA icon.svg|frameless|22x22px|link=|alt=DNA label]] and indented).▼
 
▲=== Overview ===
There are different ways of outlining the basic method used for scientific inquiry and they are better considered as general principles than a fixed sequence of steps.{{sfnp|Gauch|2003|p=3}} The [[scientific community]] and [[philosophers of science]] generally agree on the following classification of method components. These methodological elements and organization of procedures tend to be more characteristic of [[experimental science]]s than [[social science]]s. Nonetheless, the cycle of formulating hypotheses, testing and analyzing the results, and formulating new hypotheses, will resemble the cycle described below.{{anchor|epistemicCycle|Process}} The scientific method is an iterative, cyclical process through which information is continually revised.{{efn-lg|name=unifiedMethod|1= The topics of study, as expressed in the vocabulary of its scientists, are approached by a "single unified method".<ref name= cowles />{{rp|pp.8,13,33–35,60}} A topic is [[Unification of theories in physics|unified]] by its [[Predicate variable|predicate]]s, which describe a [[system]] of mathematical [[Expression (mathematics)|expression]]s.<ref name=Knight1989 >Kevin Knight (1989) [https://kevincrawfordknight.github.io/papers/unification-knight.pdf Unification: A Multidisciplinary Survey] ACM Computing Surveys, Vol. 21, No. 1, March 1989 </ref>{{rp|93-94,113-117}} The values which a [[Predicate (mathematical logic)|predicate]] might take, then serve as [[Witness (mathematics)|witness]] to the validity of a predicated expression (that is, ''true'' or ''false''; 'predicted but not yet observed'; 'corroborates', etc.).}}<ref>{{cite book |last1=Godfrey-Smith |first1=Peter |url=https://books.google.com/books?id=k23egtSWrb8C |title=Theory and Reality: An Introduction to the Philosophy of Science |date=2009 |publisher=University of Chicago Press |isbn=978-0-226-30062-7 |location=Chicago |author-link=Peter Godfrey-Smith |access-date=2020-05-09 |archive-url=https://web.archive.org/web/20231129112726/https://books.google.com/books?id=k23egtSWrb8C |archive-date=2023-11-29 |url-status=live}}</ref><ref name="Brody-1993">{{harvp|Brody|1993|p=10}} calls this an ''[[#epistemicCycle|epistemic cycle]]''; these cycles can occur at high levels of abstraction.</ref> It is generally recognized to develop advances in knowledge through the following elements, in varying combinations or contributions:<ref name="Fixation">{{cite wikisource|title=The Fixation of Belief|first=Charles Sanders|last=Peirce|year=1877|wslink=The Fixation of Belief|volume=12|pages=1–15|journal=Popular Science Monthly}}.</ref><ref name="Vital">Peirce, Charles S., ''Collected Papers'' v. 5, in paragraph 582, from 1898: "...&nbsp;[rational] inquiry of every type, fully carried out, has the vital power of self-correction and of growth. This is a property so deeply saturating its inmost nature that it may truly be said that there is but one thing needful for learning the truth, and that is a hearty and active desire to learn what is true."</ref><!--ref>{{cite book|last1=Kuhn |first1=Thomas S.|title=The Structure of Scientific Revolutions 50th Anniversary Edition|date=2012 |publisher=University of Chicago Press|location=Chicago|isbn=978-0-226-45811-3 |url=https://books.google.com/books?id=3eP5Y_OOuzwC|access-date=29 January 2018}}{{pn|date=August 2021}}</ref><ref>{{cite book|last1=Galison |first1=Peter|title=How Experiments End|date=1987|publisher=University of Chicago Press|location=Chicago|isbn=978-0-226-27915-2|url=https://books.google.com/books?id=DN-9m2jSo8YC |access-date=29 January 2018}}</ref-->
* Characterizations (observations, definitions, and measurements of the subject of inquiry)
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While this schema outlines a typical hypothesis/testing method,{{sfnp|Gauch|2003|loc=esp. chapters 5–8}} many philosophers, historians, and sociologists of science, including [[Paul Feyerabend]],{{efn|name= descartes| "no opinion, however absurd and incredible, can be imagined, which has not been maintained by some of the philosophers". —Descartes<ref name= discourseOnMethod >[[René Descartes]] (1637) [https://en.wikisource.org/wiki/Discourse_on_the_Method/Part_2 Discourse on the Method/Part 2] {{Webarchive|url=https://web.archive.org/web/20210901150801/https://en.wikisource.org/wiki/Discourse_on_the_Method/Part_2 |date=2021-09-01 }} Part II</ref> }} claim that such descriptions of scientific method have little relation to the ways that science is actually practiced.
▲==Elements of the scientific method==
▲{{anchor|Context}}The basic elements of the scientific method are illustrated by the following example (which occurred from 1944 to 1953) from the discovery of the structure of DNA (marked with [[File:DNA icon.svg|frameless|22x22px|link=|alt=DNA label]] and indented).
 
===Characterizations===
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Most experimental results do not produce large changes in human understanding; improvements in theoretical scientific understanding typically result from a gradual process of development over time, sometimes across different domains of science.<ref>Stanovich, Keith E. (2007). ''How to Think Straight About Psychology''. Boston: Pearson Education. p. 123</ref> Scientific models vary in the extent to which they have been experimentally tested and for how long, and in their acceptance in the scientific community. In general, explanations become accepted over time as evidence accumulates on a given topic, and the explanation in question proves more powerful than its alternatives at explaining the evidence. Often subsequent researchers re-formulate the explanations over time, or combined explanations to produce new explanations.
▲The ubiquitous element in the scientific method is [[empiricism]]. This is in opposition to stringent forms of [[rationalism]]: the scientific method embodies the position that ''reason alone'' cannot solve a particular scientific problem. A strong formulation of scientific method is not always aligned with a form of [[empiricism]] in which the empirical data is put forward in the form of experience or other abstracted forms of knowledge; in [[#aModel|current scientific practice]], however, the use of [[scientific modelling]] and reliance on abstract typologies and theories is normally accepted. The scientific method counters claims that [[revelation]], political or religious [[dogma]], appeals to tradition, commonly held beliefs, common sense, or currently held theories pose the only possible means of demonstrating truth.<ref name= truthSought4sake /><ref name="reasonsFirstRule">{{cite book |last=Peirce |first=Charles S. |title=Collected Papers |year=1899 |series=v. 1 |at=paragraphs 135–140 |chapter=F.R.L. [First Rule of Logic] |quote=...&nbsp;in order to learn, one must desire to learn&nbsp;... |access-date=2012-01-06 |chapter-url=http://www.princeton.edu/~batke/peirce/frl_99.htm |archive-url=https://web.archive.org/web/20120106071421/http://www.princeton.edu/~batke/peirce/frl_99.htm |archive-date=January 6, 2012 |url-status=dead}}</ref><ref name= tow />
 
Tow sees the scientific method in terms of an [[evolutionary algorithm]] applied to science and technology.<ref name= tow>
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[[Paul Feyerabend]] examined the history of science, and was led to deny that science is genuinely a methodological process. In his book ''[[Against Method]]'' he argued that no description of scientific method [[#critiquesOfFeyerabend|could possibly be broad enough]] to include all the approaches and methods used by scientists, and that there are no useful and exception-free [[methodology|methodological rules]] governing the progress of science. In essence, he said that for any specific method or norm of science, one can find a historic episode where violating it has contributed to the progress of science. He jokingly suggested that, if believers in the scientific method wish to express a single universally valid rule, it should be '[[#theTermSci|anything goes]]'.<ref>[[Paul Feyerabend|Feyerabend, Paul K.]], ''Against Method, Outline of an Anarchistic Theory of Knowledge'', 1st published, 1975. Reprinted, Verso, London, 1978.
</ref> As has been argued before him however, this is uneconomic; [[Problem solving|problem solver]]s, and researchers are to be prudent with their resources during their inquiry.{{efn-ua|name= FRL-1.136 |{{harvp|Peirce|1899}} First rule of logic (F.R.L)<ref name= reasonsFirstRule /> Paragraph 1.136: From the first rule of logic, if we truly desire the goal of the inquiry we are not to waste our resources.<ref name=econ/><ref name= SuitableTest/> — [[Terence Tao]] wrote on the matter that not all approaches can be regarded as "equally suitable and deserving of equal resources" because such positions would "sap mathematics of its sense of direction and purpose".<ref name= taoTime >{{cite web | last=Tao | first=Terence | title=What is good mathematics? | website=arXiv.org | date=13 February 2007 | url=https://arxiv.org/abs/math/0702396 | access-date=11 April 2024}}</ref>}}
 
A more general inference against formalised method has been found through research involving interviews with scientists regarding their conception of method. This research indicated that scientists frequently encounter difficulty in determining whether the available evidence supports their hypotheses. This reveals that there are no straightforward mappings between overarching methodological concepts and precise strategies to direct the conduct of research.<ref name="Schickore Hangel 2019">{{cite journal | last=Schickore | first=Jutta | last2=Hangel | first2=Nora | title=“It might be this, it should be that…” uncertainty and doubt in day-to-day research practice | journal=European Journal for Philosophy of Science | volume=9 | issue=2 | date=2019 | issn=1879-4912 | doi=10.1007/s13194-019-0253-9 | page=}}</ref>
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