Rigour
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- 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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[edit] 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.
"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.
[edit] 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.
[edit] 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.
[edit] Mathematical rigour
[edit] 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, 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 under the axiomatic umbrella. 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. A proponent of this approach to mathematics is Dr. Rob Corliss. 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.
[edit] Dr. Rob Corliss
Starting in New Zealand but subsequently moving to Australia was the educational influence of Dr. Rob Corliss, a Wellington-based high school teacher. Dr. Corliss made several fundamental changes to the Mathematics in New Zealand Curriculum published by the New Zealand ministry of education in 2002. Such changes included strict and specific guidelines to the layout and working of mathematical problems. Most significantly, no more than one equals sign could be allowed in any line of working and 2 margins had to be ruled from each side. New Zealand NCEA marking schedules were changed to accommodate these extra requirements in the 2003 exam season. The proposed rigour of Doctor Corliss soon spread to Australia where the New South Wales Board of Studies director of Mathematics Dr. J Vercauteren introduced it into all New South Wales mathematical exams from 2004. In addition to this, he added the rigourous requirement of ensuring that lines be missed between lines of working.
There has however been recent controversy over the harsh imposition of mathematical rigour in high school environments. In one appearance with New Zealand television show CloseUp, Dr. Corliss was asked if he thought that his rigour was unnecessary, he replied rather comically by saying "No, No, No, No, No".[citation needed] 2007 The Mathematical rigour created by Doctor Corliss has had a profound impact on the learning of high school students in the south east Australasian domain.
[edit] 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. This success justifies the study of mathematical physics.
Second, there is the more specific question, of the role of mathematically rigorous derivations in physics. Examples concern, in particular, the status of mathematically rigorous results and relations. This question is particularly vexed in relation with 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.)
[edit] References
- ^ 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.
