442:. 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
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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
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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
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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
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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
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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
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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. Students who have not reached that final stage of
400:. 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.
644:, 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.
488:. 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
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414:, 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
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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
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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
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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
670:, "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
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622:. Indeed, with the aid of computers, it is possible to check some proofs mechanically. Formal rigour is the introduction of high degrees of completeness by means of a
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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.
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Second, there is the question regarding the role and status of mathematically rigorous results and relations. This question is particularly vexing in relation to
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Mathematical rigour can apply to methods of mathematical proof and to methods of mathematical practice (thus relating to other interpretations of rigour).
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During the 19th century, the term "rigorous" began to be used to describe increasing levels of abstraction when dealing with
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describes the different approaches or methods which may be taken to apply intellectual rigour on an institutional level to
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Rigour in the classroom is a hotly debated topic amongst educators. Even the semantic meaning of the word is contested.
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can therefore be at odds with a principled approach; and intellectual rigour can seem to be defeated. This defines a
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roughly translates as "mediating theological morality between rigour and laxness". The book details, for the
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of information published. An example of intellectual rigour assisted by a methodical approach is the
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Both aspects of mathematical rigour in physics have attracted considerable attention in
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exactly, and in which situations they can be more forgiving yet still considered moral.
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Gelfert, Axel, ”Mathematical Rigor in
Physics: Putting Exact Results in Their Place”,
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In the legal context, for practical purposes, the facts of cases do always differ.
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was seen as extremely rigorous and profound, but in the late 19th century,
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The
Unreasonable Effectiveness of Mathematics in the Natural Sciences
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added rigour to the works of
Riemann, eventually culminating in the
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possible differences of interpretation. At an institutional level,
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Mathematical rigour can be modelled as amenability to algorithmic
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Mathematical rigour is often cited as a kind of gold standard for
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learn in more than one context and to unpredictable situations
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answers; or socially imposed, such as the process of defining
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Davey, Kevin, ”Is
Mathematical Rigor Necessary in Physics?”,
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where such proofs can be codified using set theories such as
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Adhering absolutely to certain constraints with consistency
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Euclidean geometry—19th century and non-Euclidean geometry
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First, there is the general question, sometimes called
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837:"GA1: Intellectual Rigour - Southern Cross University"
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Hyperbolic geometry § Philosophical consequences
337:) meaning "stiffness", which itself is based on the
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Intellectual honesty and the contemporary scientist
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119:. Unsourced material may be challenged and removed.
600:added rigour to the works of Cauchy. The works of
976:The British Journal for the Philosophy of Science
823:Theologia Moralis Inter Rigorem et Laxitatem Medi
361:Theologia Moralis Inter Rigorem et Laxitatem Medi
656:The role of mathematical rigour in relation to
865:Norbert Wiener: Collected works and commentary
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886:Bulletin of the American Mathematical Society
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41:"Rigor" redirects here. For other uses, see
557:to address this gap in rigour found in the
82:Learn how and when to remove these messages
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705:, according to developmental psychologist
473:, i.e. by saying the cases are different.
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423:is used to validate intellectual rigour.
259:Learn how and when to remove this message
241:Learn how and when to remove this message
179:Learn how and when to remove this message
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882:"Mathematical rigor, past and present"
377:translates directly as the stiffness (
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117:adding citations to reliable sources
588:added rigour to the older works of
431:Intellectual rigour is a subset of
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648:misinterpretations or ambiguity.
580:which eventually became known as
541:Until the 19th century, Euclid's
63:This article has multiple issues.
1002:How to Plan Rigorous Instruction
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899:10.1090/S0002-9904-1928-04507-X
104:needs additional citations for
71:or discuss these issues on the
955:This refers to the 1960 paper
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524:. Its history traces back to
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606:arithmetization of analysis
484:'s problem with uncodified
221:the claims made and adding
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30:For the medical term, see
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1160:Parsimony (Occam's razor)
632:automated theorem proving
553:were developed using the
1004:. Alexandria, VA.: ASCD.
290:see spelling differences
777:www.merriam-webster.com
728:Intellectual dishonesty
863:. In P. Masani (Ed.),
43:Rigor (disambiguation)
1215:Theories of deduction
989:Philosophy of Science
773:"Definition of RIGOR"
703:cognitive development
687:philosophy of science
641:Principia Mathematica
582:mathematical analysis
1000:Jackson, R. (2011).
991:, 72 (2005) 723–738.
978:, 54 (2003) 439–463.
723:Intellectual honesty
679:quantum field theory
672:mathematical physics
433:intellectual honesty
300:which must maintain
113:improve this article
1304:Mathematical proofs
1299:Philosophical logic
1042:Philosophical logic
859:Wiener, N. (1985).
797:"Rigor – Etymology"
490:principled approach
394:Intellectual rigour
355:"to be stiff". The
298:mathematical proofs
1106:Unity of opposites
522:mathematical proof
510:Mathematical proof
504:Mathematical proof
416:circular reasoning
408:ensure the quality
320:"Rigour" comes to
206:possibly contains
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1138:List of fallacies
1123:Explanatory power
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738:Scientific method
567:Birkhoff's axioms
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106:verification
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36:Rigor mortis
1228:Dialetheism
1118:Explanation
1088:Credibility
803:. 2001–2014
707:Jean Piaget
602:Weierstrass
551:foundations
496:Mathematics
421:peer review
1293:Categories
1273:Pragmatism
1263:Nominalism
1170:Propaganda
1145:Hypothesis
1098:Antithesis
846:2019-10-20
807:2015-01-10
782:2019-10-20
759:References
613:set theory
514:See also:
369:church law
326:old French
302:consistent
215:improve it
139:newspapers
68:improve it
1243:Formalism
1205:Vagueness
1185:Relevance
1180:Reasoning
1093:Dialectic
1068:Ambiguity
916:120096416
908:0002-9904
748:Sophistry
693:Education
610:Cantorian
471:casuistry
316:Etymology
231:June 2016
219:verifying
169:June 2016
74:talk page
1258:Logicism
1238:Finitism
1190:Rhetoric
1175:Prudence
1113:Evidence
1073:Argument
1063:Analysis
717:See also
578:calculus
559:Elements
543:Elements
535:Elements
478:Case law
467:politics
448:premises
440:evidence
324:through
128:"Rigour"
1278:Realism
1165:Premise
1155:Opinion
1150:Inquiry
1133:Fallacy
658:physics
652:Physics
598:Riemann
561:(e.g.,
547:Hilbert
427:Honesty
342:rigorem
334:rigueur
322:English
213:Please
153:scholar
1200:Theory
1078:Belief
914:
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733:Pedant
586:Cauchy
530:Euclid
444:debate
383:mortis
365:clergy
353:rigere
330:French
306:ethics
294:famine
274:Rigour
155:
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1195:Rigor
912:S2CID
630:(see
594:Gauss
590:Euler
482:judge
437:valid
379:rigor
346:rigor
339:Latin
282:rigor
280:) or
160:JSTOR
146:books
1128:Fact
1083:Bias
904:ISSN
592:and
357:noun
350:verb
308:and
132:news
1052:and
961:by
894:doi
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628:ZFC
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532:'s
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