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Rigour
From Wikipedia, the free encyclopedia
- For the medical term see rigor (medicine)
Rigour or rigor (see spelling differences) has a number of meanings in relation to intellectual life and discourse. These are separate from judicial 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.
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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.
"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.
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.
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 is often cited as a kind of gold standard for mathematical proof. It has a history traced back to Greek mathematics, where it is said to have been invented. Complete rigour, it is often said, became available in mathematics at the start of the twentieth century. This relies on the axiomatic method, and the subsequent development of pure mathematics using the techniques of the axiomatic method.
With the aid of computers, it is possible to check proofs mechanically by throwing the possible flaws back onto machine errors that are considered unlikely events.[3] Indeed, mathematical rigour may be defined as amenability to algorithmic checking of correctness. Formal rigour is the introduction of high degrees of completeness by means of a formal language. Most mathematical arguments are presented as prototypes of formally rigorous proofs (where such proofs can be codified using set theories such as ZFC, see metamath).
Most mathematical arguments are presented as prototypes of formally rigorous proofs, on the grounds that too much formality may in fact obscure what is being demonstrated.
Though it may be argued that too much 'mathematical' formality may in fact obscure what is being demonstrated, worthy counter-arguments assert that detailed mathematical descriptions of phenomena, detailed mathematical argument and the utilisation of formal languages to institute mathematical rigour would remove 'woolly thinking' and ambiguity from mathematical descriptions of techniques and methods, enabling a clear description of mathematical theories during discussion.
As an example of these advantages of such mathematical rigour, consider those theories within mathematics which have historically been contested or open to common misinterpretation (for example, consider Misuse of statistics, which outlines common mistakes that even apparently well-trained mathematicians, scientists and doctors can be prone to making in relation to statistics). Formal codification of mathematical theories (as one would ideally expect of any mathematically rigorous technique or pedagogy) will reduce both the scope for misinterpretation of mathematical results (by enabling their precise communication) and will eliminate ambiguity in the description of mathematical material (words cannot be reasonably used to describe complex mathematics arguments – though formal languages, set theories and mathematical symbolism can and do).
Mathematical rigour can not only refer to rigorous methods of mathematical proof – but also to rigorous methods of mathematical practice (thus relating to the other interpretations of rigour).
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 it is so, and 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. 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 2007, an image manipulation software analysis suite called Rigour [6] finds application in the scientific and medical publishing industry. Cadmus Communications, a Cenveo Company is the first publisher to use this software as part of an integrated content management system.[7]
The need for digital image manipulation analysis is high, specifically in the scientific and medical publishing communities, primarily due to incidents such as the Hwang Stem Cell Scandal. [8] Another well known case of image manipulation surfaced when the Toledo Blade discovered multiple altered photographs had appeared in print. [9]
The name Rigour is derived from the intended use of the software to enforce intellectual rigour for published image content.
- ^ 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.
- ^ Wiener, N. (1985). Intellectual honesty and the contemporary scientist. In P. Masani (Ed.), Norbert Wiener: Collected works and commentary (pp. 725- 729).
- ^ 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].
- ^ This refers to the 1960 paper The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner.
- ^ Gelfert, Axel, 'Mathematical Rigor in Physics: Putting Exact Results in Their Place', Philosophy of Science, 72 (2005) 723-738.
- ^ http://www.suprocktech.com
- ^ http://www.cenveo.com/pdf/digital_art_analysis.pdf
- ^ http://www.sciencemag.org/sciext/hwang2005/
- ^ http://www.nppa.org/news_and_events/news/2007/04/toledo05.html