Rigour


Rigour

Rigour or rigor (see spelling differences) has a number of meanings in relation to intellectual life and discourse. These are separate from public and political applications with their suggestion of laws enforced to the letter, or political absolutism. A religion, too, may be worn lightly, or applied with rigour.

Contents

Intellectual rigour

An attempted short definition of intellectual rigour might be that no suspicion of double standard be allowed: uniform principles should be applied. This is a test of consistency, over cases, and to individuals or institutions (including the speaker, the speaker's country and so on). Consistency can be at odds here with a forgiving attitude, adaptability, and the need to take precedent with a pinch of salt. If a topic or case is dealt with in a rigorous way, it means that it is dealt with in a comprehensive, thorough and complete way, leaving no room for inconsistencies.

"The rigour of the game" is a quotation from Charles Lamb[1] about whist. It implies that the demands of thinking accurately and to the point over a card game can serve also as entertainment or leisure. Intellectual rigour can therefore be sometimes seen as the exercise of a skill. It can also degenerate into pedantry, which is intellectual rigour applied to no particular end, except perhaps self-importance.

Scholarship can be defined as intellectual rigour applied to the quality control of information, which implies an appropriate standard of accuracy, and scepticism applied to accepting anything on trust. It requires close attention to criteria for logical consistency, as well as to all relevant evidence and possible differences of interpretation.

In relation to intellectual honesty

Intellectual rigour is an important part, though not the whole, of intellectual honesty — which means keeping one's convictions in proportion to one's valid evidence.[2] For the latter, one should be questioning one's own assumptions, not merely applying them relentlessly if precisely. 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 debate, if one wishes to say that an argument is flawed in its premises.

Politics and the law

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 politics, for example. Arguing one way one day, and another later, can be defended by casuistry, i.e. by saying the cases are different.

In the legal context, for practical purposes, the facts of cases do always differ. Case law can therefore be at odds with a principled approach; and intellectual rigour can seem to be defeated. This defines a judge's problem with uncodified law. 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 principled approach.

Mathematical rigour

Mathematical rigour can refer both to rigorous methods of mathematical proof and to rigorous methods of mathematical practice (thus relating to other interpretations of rigour).

In relation to mathematical proof

Mathematical rigour is often cited as a kind of gold standard for mathematical proof. It has a history traced back to Greek mathematics, in the work of Euclid. This refers to the axiomatic method. Mathematical rigour in the modern sense originates no later than the generation of Bolzano, Cauchy, and Abel. Cauchy's starting point was the rejection of the principle of the generality of algebra as practiced by Euler, Lagrange, and other luminaries of earlier generations. Starting in the 1870s, the term gradually came to be associated with an implementation of the Weierstrass (ε, δ)-definition of limit and Cantorian set theory.

Mathematical rigour can be defined as amenability to algorithmic proof checking. Indeed, with the aid of computers, it is possible to check proofs mechanically by noting that possible flaws arise from either an incorrect proof or machine errors (which are extremely rare).[3] Formal rigour is the introduction of high degrees of completeness by means of a formal language where such proofs can be codified using set theories such as ZFC (see automated theorem proving).

Most mathematical arguments are presented as prototypes of formally rigorous proofs. The reason often cited for this is that completely rigorous proofs, which tend to be longer and more unwieldy, may obscure what is being demonstrated. Steps which are obvious to a human mind may have fairly long formal derivations from the axioms. Under this argument, there is a trade-off between rigour and comprehension. Some argue that the use of formal languages to institute complete mathematical rigour might make theories which are commonly disputed or misinterpreted completely unambiguous by revealing flaws in reasoning.

In relation to physics

The role of mathematical rigour in relation to physics is twofold.

First, there is the general question, sometimes called Wigner's Puzzle,[4] "how it is that mathematics, quite generally, is applicable to nature?" However, scientists assume its successful application to nature justifies the study of mathematical physics.

Second, there is the question regarding the role and status of mathematically rigorous results and relations[clarification needed]. This question is particularly vexing in relation to quantum field theory.

Both aspects of mathematical rigour in physics have attracted considerable attention in philosophy of science. (See, for example, ref.[5] and works quoted therein.)

In relation to the classroom

Rigour in the classroom is a hotly debated topic amongst educators. Generally speaking, however, 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[citation needed]. Students who have not reached that final stage of cognitive development, according to developmental psychologist Jean Piaget, can build upon those skills with the help of a properly trained teacher.[6]

See also

References

  1. ^ Bartlett, John, comp. Familiar Quotations, 10th ed, rev. and enl. by Nathan Haskell Dole. Boston: Little, Brown, 1919; Bartleby.com, 2000. http://www.bartleby.com/100/343.html. Retrieved Oct. 25, 2006.
  2. ^ Wiener, N. (1985). Intellectual honesty and the contemporary scientist. In P. Masani (Ed.), Norbert Wiener: Collected works and commentary (pp. 725- 729).
  3. ^ 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.[1].
  4. ^ This refers to the 1960 paper The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner.
  5. ^ Gelfert, Axel, 'Mathematical Rigor in Physics: Putting Exact Results in Their Place', Philosophy of Science, 72 (2005) 723-738.
  6. ^ Forum: Academic Rigor, in: UNIversitas: The University of Northern Iowa Journal of Research, Scholarship, and Creative Activity 1.1 (Fall 2005).

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  • rigour — is spelt our in BrE and rigor in AmE. The corresponding adjective is rigorous in both varieties. Note also the spelling rigor in the medical sense (‘a sudden feeling of cold and shivering’) and in the Latin phrase rigor mortis, the stiffening of… …   Modern English usage

  • rigour — (US rigor) ► NOUN 1) the quality of being rigorous. 2) (rigours) demanding, difficult, or extreme conditions. ORIGIN Latin rigor stiffness …   English terms dictionary

  • rigour — (BrE) (AmE rigor) noun 1 strictness ADJECTIVE ▪ academic, analytical, formal, intellectual, logical, mathematical, methodological, scholarly, scientific …   Collocations dictionary

  • rigour — Rigor Rig or, n. [OE. rigour, OF. rigour, F. rigueur, from L. rigor, fr. rigere to be stiff. See {Rigid}.] [Written also {rigour}.] 1. The becoming stiff or rigid; the state of being rigid; rigidity; stiffness; hardness. [1913 Webster] The rest… …   The Collaborative International Dictionary of English

  • rigour — [[t]rɪ̱gə(r)[/t]] rigours (in AM, use rigor) 1) N PLURAL: usu the N of n If you refer to the rigours of an activity or job, you mean the difficult, demanding, or unpleasant things that are associated with it. He found the rigours of the tour too… …   English dictionary

  • rigour — BrE rigor AmE noun (U) 1 the rigours of the problems and unpleasant conditions of a difficult situation: all the rigours of a Canadian winter 2 BrE formal strictness or severity of a punishment: He deserves to be punished with the full rigour of… …   Longman dictionary of contemporary English

  • rigour — UK [ˈrɪɡə(r)] / US [ˈrɪɡə] noun [uncountable] 1) the quality of being thorough and careful His arguments display a lack of intellectual rigour. 2) the quality of being strict or severe The law was implemented with varying degrees of rigour in… …   English dictionary

  • rigour — /ˈrɪgə / (say riguh) noun 1. strictness, severity, or harshness, as in dealing with persons. 2. the full or extreme severity of laws, rules, etc.: the rigour of the law. 3. severity of life; hardship. 4. a severe or harsh act, circumstance, etc.… …   Australian English dictionary

  • rigour — n. (US rigor) 1 a severity, strictness, harshness. b (in pl.) harsh measures or conditions. 2 logical exactitude. 3 strict enforcement of rules etc. (the utmost rigour of the law). 4 austerity of life; puritanical discipline. Etymology: ME f. OF… …   Useful english dictionary

  • rigour — rig|our BrE rigor AmE [ˈrıgə US ər] n 1.) the rigours of sth the problems and difficulties of a situation ▪ all the rigors of a Canadian winter ▪ the stresses and rigours of modern life 2.) [U] great care and thoroughness in making sure that… …   Dictionary of contemporary English


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