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Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Rigour%22">"Rigour"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Rigour%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Rigour%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Rigour%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Rigour%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Rigour%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">June 2016</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Original_research plainlinks metadata ambox ambox-content ambox-Original_research" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>possibly contains <a href="/wiki/Wikipedia:No_original_research" title="Wikipedia:No original research">original research</a></b>.<span class="hide-when-compact"> Please <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Rigour&action=edit">improve it</a> by <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verifying</a> the claims made and adding <a href="/wiki/Wikipedia:Citing_sources#Inline_citations" title="Wikipedia:Citing sources">inline citations</a>. Statements consisting only of original research should be removed.</span> <span class="date-container"><i>(<span class="date">June 2016</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> </div> </div><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/rigour" class="extiw" title="wiktionary:rigour">rigour</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <p><b>Rigour</b> (<a href="/wiki/British_English" title="British English">British English</a>) or <b>rigor</b> (<a href="/wiki/American_English" title="American English">American English</a>; <a href="/wiki/American_and_British_English_spelling_differences#-our,_-or" title="American and British English spelling differences">see spelling differences</a>) describes a condition of stiffness or strictness.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> These constraints may be environmentally imposed, such as "the rigours of <a href="/wiki/Famine" title="Famine">famine</a>"; logically imposed, such as <a href="/wiki/Mathematical_proofs" class="mw-redirect" title="Mathematical proofs">mathematical proofs</a> which must maintain <a href="/wiki/Consistency" title="Consistency">consistent</a> answers; or socially imposed, such as the process of defining <a href="/wiki/Ethics" title="Ethics">ethics</a> and <a href="/wiki/Law" title="Law">law</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Etymology">Etymology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rigour&action=edit&section=1" title="Edit section: Etymology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>"Rigour" comes to <a href="/wiki/English_language" title="English language">English</a> through <a href="/wiki/Old_French" title="Old French">old French</a> (13th c., Modern <a href="/wiki/French_language" title="French language">French</a> <i><a href="https://en.wiktionary.org/wiki/fr:rigueur" class="extiw" title="wiktionary:fr:rigueur">rigueur</a></i>) meaning "stiffness", which itself is based on the <a href="/wiki/Latin" title="Latin">Latin</a> <i>rigorem</i> (nominative <i>rigor</i>) "numbness, stiffness, hardness, firmness; roughness, rudeness", from the <a href="/wiki/Verb" title="Verb">verb</a> <i>rigere</i> "to be stiff".<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Noun" title="Noun">noun</a> was frequently used to describe a condition of strictness or stiffness, which arises from a situation or constraint either chosen or experienced passively. For example, the title of the book <i>Theologia Moralis Inter Rigorem et Laxitatem Medi</i> roughly translates as "mediating theological morality between rigour and laxness". The book details, for the <a href="/wiki/Clergy" title="Clergy">clergy</a>, situations in which they are obligated to follow <a href="/wiki/Church_law" class="mw-redirect" title="Church law">church law</a> exactly, and in which situations they can be more forgiving yet still considered moral.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <i><a href="/wiki/Rigor_mortis" title="Rigor mortis">Rigor mortis</a></i> translates directly as the stiffness (<i>rigor</i>) of death (<i>mortis</i>), again describing a condition which arises from a certain constraint (death). </p> <div class="mw-heading mw-heading2"><h2 id="Intellectualism">Intellectualism</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rigour&action=edit&section=2" title="Edit section: Intellectualism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Intellectual rigour</b> is a process of thought which is consistent, does not contain self-contradiction, and takes into account the entire scope of available knowledge on the topic. It actively avoids <a href="/wiki/Logical_fallacy" class="mw-redirect" title="Logical fallacy">logical fallacy</a>. Furthermore, it requires a sceptical assessment of the available knowledge. If a topic or case is dealt with in a rigorous way, it typically means that it is dealt with in a comprehensive, thorough and complete way, leaving no room for inconsistencies.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Scholarly_method" title="Scholarly method">Scholarly method</a> describes the different approaches or methods which may be taken to apply intellectual rigour on an institutional level to <a href="/wiki/Quality_control" title="Quality control">ensure the quality</a> of information published. An example of intellectual rigour assisted by a methodical approach is the <a href="/wiki/Scientific_method" title="Scientific method">scientific method</a>, in which a person will produce a hypothesis based on what they believe to be true, then construct experiments in order to prove that hypothesis wrong. This method, when followed correctly, helps to prevent against <a href="/wiki/Circular_reasoning" title="Circular reasoning">circular reasoning</a> and other fallacies which frequently plague conclusions within academia. Other disciplines, such as philosophy and mathematics, employ their own structures to ensure intellectual rigour. Each method requires close attention to criteria for logical consistency, as well as to all relevant evidence and possible differences of interpretation. At an institutional level, <a href="/wiki/Peer_review" title="Peer review">peer review</a> is used to validate intellectual rigour. </p> <div class="mw-heading mw-heading3"><h3 id="Honesty">Honesty</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rigour&action=edit&section=3" title="Edit section: Honesty"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Intellectual rigour is a subset of <a href="/wiki/Intellectual_honesty" title="Intellectual honesty">intellectual honesty</a>—a practice of thought in which ones convictions are kept in proportion to <a href="/wiki/Validity_(logic)" title="Validity (logic)">valid</a> <a href="/wiki/Evidence" title="Evidence">evidence</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Intellectual honesty is an unbiased approach to the acquisition, analysis, and transmission of ideas. A person is being intellectually honest when he or she, knowing the truth, states that truth, regardless of outside social/environmental pressures. It is possible to doubt whether complete intellectual honesty exists—on the grounds that no one can entirely master his or her own presuppositions—without doubting that certain kinds of intellectual rigour are potentially available. The distinction certainly matters greatly in <a href="/wiki/Debate" title="Debate">debate</a>, if one wishes to say that an argument is flawed in its <a href="/wiki/Premise" title="Premise">premises</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Politics_and_law">Politics and law</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rigour&action=edit&section=4" title="Edit section: Politics and law"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Letter_and_spirit_of_the_law" title="Letter and spirit of the law">Letter and spirit of the law</a></div> <p>The setting for intellectual rigour does tend to assume a principled position from which to advance or argue. An opportunistic tendency to use any argument at hand is not very rigorous, although very common in <a href="/wiki/Politics" title="Politics">politics</a>, for example. Arguing one way one day, and another later, can be defended by <a href="/wiki/Casuistry" title="Casuistry">casuistry</a>, i.e. by saying the cases are different. </p><p>In the legal context, for practical purposes, the facts of cases do always differ. <a href="/wiki/Case_law" title="Case law">Case law</a> can therefore be at odds with a principled approach; and intellectual rigour can seem to be defeated. This defines a <a href="/wiki/Judge" title="Judge">judge</a>'s problem with uncodified <a href="/wiki/Law" title="Law">law</a>. Codified law poses a different problem, of interpretation and adaptation of definite principles without losing the point; here applying the letter of the law, with all due rigour, may on occasion seem to undermine the <i>principled approach</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Mathematics"><span class="anchor" id="Mathematical_rigour"></span>Mathematics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rigour&action=edit&section=5" title="Edit section: Mathematics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mathematical rigour can apply to methods of mathematical proof and to methods of mathematical practice (thus relating to other interpretations of rigour). </p> <div class="mw-heading mw-heading3"><h3 id="Mathematical_proof">Mathematical proof</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rigour&action=edit&section=6" title="Edit section: Mathematical proof"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Mathematical_proof" title="Mathematical proof">Mathematical proof</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Hyperbolic_geometry#Philosophical_consequences" title="Hyperbolic geometry">Hyperbolic geometry § Philosophical consequences</a></div> <div id="mathematical"></div> <p>Mathematical rigour is often cited as a kind of gold standard for <a href="/wiki/Mathematical_proof" title="Mathematical proof">mathematical proof</a>. Its history traces back to <a href="/wiki/Greek_mathematics" title="Greek mathematics">Greek mathematics</a>, especially to <a href="/wiki/Euclid" title="Euclid">Euclid</a>'s <i><a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements">Elements</a></i>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Until the 19th century, Euclid's <i>Elements</i> was seen as extremely rigorous and profound, but in the late 19th century, <a href="/wiki/Hilbert%27s_axioms" title="Hilbert's axioms">Hilbert</a> (among others) realized that the work left certain assumptions implicit—assumptions that could not be proved from Euclid's Axioms (e.g. two circles can intersect in a point, some point is within an angle, and figures can be superimposed on each other).<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> This was contrary to the idea of rigorous proof where all assumptions need to be stated and nothing can be left implicit. New <a href="/wiki/Foundations_of_geometry" title="Foundations of geometry">foundations</a> were developed using the <a href="/wiki/Axiomatic_method" class="mw-redirect" title="Axiomatic method">axiomatic method</a> to address this gap in rigour found in the <i>Elements</i> (e.g., <a href="/wiki/Hilbert%27s_axioms" title="Hilbert's axioms">Hilbert's axioms</a>, <a href="/wiki/Birkhoff%27s_axioms" title="Birkhoff's axioms">Birkhoff's axioms</a>, <a href="/wiki/Tarski%27s_axioms" title="Tarski's axioms">Tarski's axioms</a>). </p><p>During the 19th century, the term "rigorous" began to be used to describe increasing levels of abstraction when dealing with <a href="/wiki/Calculus" title="Calculus">calculus</a> which eventually became known as <a href="/wiki/Mathematical_analysis" title="Mathematical analysis">mathematical analysis</a>. The works of <a href="/wiki/Cauchy" class="mw-redirect" title="Cauchy">Cauchy</a> added rigour to the older works of <a href="/wiki/Euler" class="mw-redirect" title="Euler">Euler</a> and <a href="/wiki/Gauss" class="mw-redirect" title="Gauss">Gauss</a>. The works of <a href="/wiki/Riemann" class="mw-redirect" title="Riemann">Riemann</a> added rigour to the works of Cauchy. The works of <a href="/wiki/Weierstrass" class="mw-redirect" title="Weierstrass">Weierstrass</a> added rigour to the works of Riemann, eventually culminating in the <a href="/wiki/Arithmetization_of_analysis" title="Arithmetization of analysis">arithmetization of analysis</a>. Starting in the 1870s, the term gradually came to be associated with <a href="/wiki/George_Cantor" class="mw-redirect" title="George Cantor">Cantorian</a> <a href="/wiki/Set_theory" title="Set theory">set theory</a>. </p><p>Mathematical rigour can be modelled as amenability to algorithmic <a href="/wiki/Proof_checking" class="mw-redirect" title="Proof checking">proof checking</a>. Indeed, with the aid of computers, it is possible to check some proofs mechanically.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Formal rigour is the introduction of high degrees of completeness by means of a <a href="/wiki/Formal_language" title="Formal language">formal language</a> where such proofs can be codified using set theories such as <a href="/wiki/ZFC" class="mw-redirect" title="ZFC">ZFC</a> (see <a href="/wiki/Automated_theorem_proving" title="Automated theorem proving">automated theorem proving</a>). </p><p>Published mathematical arguments have to conform to a standard of rigour, but are written in a mixture of symbolic and natural language. In this sense, written mathematical discourse is a prototype of formal proof. Often, a written proof is accepted as rigorous although it might not be formalised as yet. The reason often cited by mathematicians for writing informally is that completely formal proofs tend to be longer and more unwieldy, thereby obscuring the line of argument. An argument that appears obvious to human intuition may in fact require fairly long formal derivations from the axioms. A particularly well-known example is how in <i><a href="/wiki/Principia_Mathematica" title="Principia Mathematica">Principia Mathematica</a></i>, Whitehead and Russell have to expend a number of lines of rather opaque effort in order to establish that, indeed, it is sensical to say: "1+1=2". In short, comprehensibility is favoured over formality in written discourse. </p><p>Still, advocates of automated theorem provers may argue that the formalisation of proof does improve the mathematical rigour by disclosing gaps or flaws in informal written discourse. When the correctness of a proof is disputed, formalisation is a way to settle such a dispute as it helps to reduce misinterpretations or ambiguity. </p> <div class="mw-heading mw-heading3"><h3 id="Physics">Physics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rigour&action=edit&section=7" title="Edit section: Physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The role of mathematical rigour in relation to <a href="/wiki/Physics" title="Physics">physics</a> is twofold: </p> <ol><li>First, there is the general question, sometimes called <i><a href="/wiki/Wigner%27s_Puzzle" class="mw-redirect" title="Wigner's Puzzle">Wigner's Puzzle</a></i>,<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> "how it is that mathematics, quite generally, is applicable to nature?" Some scientists believe that its record of successful application to nature justifies the study of <a href="/wiki/Mathematical_physics" title="Mathematical physics">mathematical physics</a>.</li> <li>Second, there is the question regarding the role and status of mathematically rigorous results and relations.<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (March 2008)">clarification needed</span></a></i>]</sup> This question is particularly vexing in relation to <a href="/wiki/Quantum_field_theory" title="Quantum field theory">quantum field theory</a>, where computations often produce infinite values for which a variety of non-rigorous work-arounds have been devised.</li></ol> <p>Both aspects of mathematical rigour in physics have attracted considerable attention in <a href="/wiki/Philosophy_of_science" title="Philosophy of science">philosophy of science</a> (see, for example, ref.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> and ref.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> and the works quoted therein). </p> <div class="mw-heading mw-heading2"><h2 id="Education">Education</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rigour&action=edit&section=8" title="Edit section: Education"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Rigour in the classroom is a hotly debated topic amongst educators. Even the semantic meaning of the word is contested. </p><p>Generally speaking, classroom rigour consists of multi-faceted, challenging instruction and correct placement of the student. Students excelling in formal operational thought tend to excel in classes for gifted students.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (April 2008)">citation needed</span></a></i>]</sup> Students who have not reached that final stage of <a href="/wiki/Cognitive_development" title="Cognitive development">cognitive development</a>, according to developmental psychologist <a href="/wiki/Jean_Piaget" title="Jean Piaget">Jean Piaget</a>, can build upon those skills with the help of a properly trained teacher. </p><p>Rigour in the classroom is commonly called "rigorous instruction". It is instruction that requires students to construct meaning for themselves, impose structure on information, integrate individual skills into processes, operate within but at the outer edge of their abilities, and apply what they learn in more than one context and to unpredictable situations.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rigour&action=edit&section=9" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/34px-Wikiquote-logo.svg.png" decoding="async" width="34" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/51px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/68px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></span></span></div> <div class="side-box-text plainlist">Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Rigour" class="extiw" title="q:Special:Search/Rigour">Rigour</a></b></i>.</div></div> </div> <ul><li><a href="/wiki/Intellectual_honesty" title="Intellectual honesty">Intellectual honesty</a></li> <li><a href="/wiki/Intellectual_dishonesty" class="mw-redirect" title="Intellectual dishonesty">Intellectual dishonesty</a></li> <li><a href="/wiki/Pedant" class="mw-redirect" title="Pedant">Pedant</a></li> <li><a href="/wiki/Scientific_method" title="Scientific method">Scientific method</a></li> <li><a href="/wiki/Self-deception" title="Self-deception">Self-deception</a></li> <li><a href="/wiki/Sophistry" class="mw-redirect" title="Sophistry">Sophistry</a></li> <li><a href="/wiki/Cognitive_rigor" title="Cognitive rigor">Cognitive rigor</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rigour&action=edit&section=10" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.merriam-webster.com/dictionary/rigor">"Definition of RIGOR"</a>. <i>www.merriam-webster.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2019-10-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.merriam-webster.com&rft.atitle=Definition+of+RIGOR&rft_id=https%3A%2F%2Fwww.merriam-webster.com%2Fdictionary%2Frigor&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARigour" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.etymonline.com/index.php?term=rigor">"Rigor – Etymology"</a>. <i>etymonline.com</i>. 2001–2014<span class="reference-accessdate">. Retrieved <span class="nowrap">2015-01-10</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=etymonline.com&rft.atitle=Rigor+%E2%80%93+Etymology&rft.date=2001%2F2014&rft_id=http%3A%2F%2Fwww.etymonline.com%2Findex.php%3Fterm%3Drigor&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARigour" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAmort" class="citation book cs1">Amort, Eusebio. <i>Theologia Moralis Inter Rigorem et Laxitatem Medi</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theologia+Moralis+Inter+Rigorem+et+Laxitatem+Medi&rft.aulast=Amort&rft.aufirst=Eusebio&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARigour" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.scu.edu.au/staff/teaching-and-learning/graduate-attributes/ga1-intellectual-rigour/">"GA1: Intellectual Rigour - Southern Cross University"</a>. <i>www.scu.edu.au</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2019-10-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.scu.edu.au&rft.atitle=GA1%3A+Intellectual+Rigour+-+Southern+Cross+University&rft_id=https%3A%2F%2Fwww.scu.edu.au%2Fstaff%2Fteaching-and-learning%2Fgraduate-attributes%2Fga1-intellectual-rigour%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARigour" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Wiener, N. (1985). <i>Intellectual honesty and the contemporary scientist</i>. In P. Masani (Ed.), <i>Norbert Wiener: Collected works and commentary</i> (pp. 725–729).</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPierpont1928" class="citation journal cs1"><a href="/wiki/James_Pierpont_(mathematician)" title="James Pierpont (mathematician)">Pierpont, James</a> (January 1928). <a rel="nofollow" class="external text" href="https://projecteuclid.org/euclid.bams/1183492538">"Mathematical rigor, past and present"</a>. <i>Bulletin of the American Mathematical Society</i>. <b>34</b> (1): 23–53. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1090%2FS0002-9904-1928-04507-X">10.1090/S0002-9904-1928-04507-X</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0002-9904">0002-9904</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:120096416">120096416</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+of+the+American+Mathematical+Society&rft.atitle=Mathematical+rigor%2C+past+and+present&rft.volume=34&rft.issue=1&rft.pages=23-53&rft.date=1928-01&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120096416%23id-name%3DS2CID&rft.issn=0002-9904&rft_id=info%3Adoi%2F10.1090%2FS0002-9904-1928-04507-X&rft.aulast=Pierpont&rft.aufirst=James&rft_id=https%3A%2F%2Fprojecteuclid.org%2Feuclid.bams%2F1183492538&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARigour" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">For more, see <a href="/wiki/Euclidean_geometry#19th_century_and_non-Euclidean_geometry" title="Euclidean geometry">Euclidean geometry—19th century and non-Euclidean geometry</a>.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><i>Hardware memory errors are caused by high-energy radiation from outer space, and can generally be expected to affect one bit of data per month, per gigabyte of DRAM.</i><a rel="nofollow" class="external autonumber" href="http://beginnersguide.com/computer-hardware/index.xml">[1]</a>.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">This refers to the 1960 paper <i><a href="/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences" title="The Unreasonable Effectiveness of Mathematics in the Natural Sciences">The Unreasonable Effectiveness of Mathematics in the Natural Sciences</a></i> by <a href="/wiki/Eugene_Wigner" title="Eugene Wigner">Eugene Wigner</a>.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Davey, Kevin, ”Is Mathematical Rigor Necessary in Physics?”, <i>The British Journal for the Philosophy of Science</i>, 54 (2003) 439–463.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Gelfert, Axel, ”Mathematical Rigor in Physics: Putting Exact Results in Their Place”, <i>Philosophy of Science</i>, 72 (2005) 723–738.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Jackson, R. (2011). <i>How to Plan Rigorous Instruction</i>. Alexandria, VA.: ASCD.</span> </li> </ol></div></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output 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