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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. Rigor is a shaking occurring during a high Fever. It occurs because cytokines and Prostaglandins are released as part of an Immune American and British English spelling differences are one aspect of American and British English differences. These are separate from judicial and political applications with their suggestion of laws enforced to the letter, or political absolutism. An autocracy is a Form of government in which the Political power is held by a single self-appointed ruler A religion, too, may be worn lightly, or applied with rigour. A religion is a set of Tenets and practices often centered upon specific Supernatural and moral claims about Reality, the Cosmos

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. A double standard refers to one class of entities being treated differently from another class of entities and implies an unfair or unjustified differentiation 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. In Common law legal systems, a precedent or authority is a Legal case establishing a principle or rule that a Court or other judicial

"The rigour of the game" is a quotation from Charles Lamb[1] about whist. Charles Lamb is the name of Charles Lamb (writer (1775-1834 a British essayist Charles Lamb (politician (1891-1965 a Canadian Whist is a classic trick-taking Card game which was played widely in the 18th and 19th centuries It implies that the demands of thinking accurately and to the point over a card game can serve also as entertainment or leisure. A card game is any Game using Playing cards either traditional or game-specific 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. A pedant, or pædant, is a person who is overly concerned with Formalism and Precision, or who 'makes a show of learning' 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. Scholarly method &mdash or as it is more commonly called scholarship &mdash is the body of principles and practices used by scholars to make their claims about the world as In Engineering and Manufacturing, quality control and quality engineering are involved in developing systems to ensure products or services In ordinary usage skepticism or scepticism ( Greek 'σκέπτομαι' skeptomai, to look about to consider see also spelling differences

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. The term validity (also called logical truth, analytic truth, or necessary truth) as it occurs in Logic refers generally to a property of Evidence in its broadest sense includes anything that is used to determine or demonstrate the Truth of an assertion [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. Debate ( American English) or debating ( British English) is a formal method of interactive and position representational Argument. For other uses see Premise Premises are land and Buildings together considered as a Property.

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. Politics Politics is the process by which groups of people make decisions Arguing one way one day, and another later, can be defended by casuistry, i. Casuistry (ˈkæʒuːɨstri is an Applied ethics term referring to case-based Reasoning. 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. Case law' (also known as decisional law or judicial precedent) is that body of reported Judicial opinions in countries that have Common law This defines a judge's problem with uncodified law. A judge, or justice, is an Official who presides over a Court of 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. In Mathematics, a proof is a convincing demonstration (within the accepted standards of the field that some Mathematical statement is necessarily true It has a history traced back to Greek mathematics, where it is said to have been invented. Greek mathematics, as that term is used in this article is the Mathematics written in Greek, developed from the 6th century BC to the 5th century Complete rigour, it is often said, became available in mathematics at the start of the twentieth century. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and The twentieth century of the Common Era began on This of course refers to the axiomatic method. In Mathematics, an axiomatic system is any set of Axioms from which some or all axioms can be used in conjunction to logically derive Theorems

Mathematical rigour can be defined as amenability to algorithmic checking of correctness. 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). A formal language is a set of words, ie finite strings of letters, or symbols. Zermelo–Fraenkel set theory with the axiom of choice, commonly abbreviated ZFC, is the standard form of Axiomatic set theory and as such is the most common Automated theorem proving ( ATP) or automated deduction, currently the most well-developed subfield of Automated reasoning (AR is the

Most mathematical arguments are presented as prototypes of formally rigourous proofs. The reason often cited for this is that completely rigourous proofs, which tend to be longer and more unwieldy, may obscure what is being demonstrated. Steps which are obvious (as obvious as the axioms) to a human mind may have fairly long formal derivations from the axioms. Under this argument, there is a tradeoff between rigour and comprehension. Some argue that the utilisation of formal languages to institute complete mathematical rigour might make theories which are commonly disputed or misinterpreted, such as statistics, completely unambiguous. A misuse of statistics occurs when a statistical argument asserts a falsehood

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. Mathematical physics is the scientific discipline concerned with the interface of Mathematics and 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. In quantum field theory (QFT the forces between particles are mediated by other particles

Both aspects of mathematical rigour in physics have attracted considerable attention in philosophy of science. Philosophy of science is the study of assumptions foundations and implications of Science. (See, for example, ref. [5] and works quoted therein. )

In relation to the classroom

Rigor in the classroom is a hotly debated topic amongst educators. Generally speaking, however, classroom rigor is comprised of multi-faceted, challenging instruction and correct placement of the student. Students excelling in formal operational though tend to excel in classes for gifted students. Students who have not reached that final stage of cognitive development, according to Piaget, can build upon those skills with the help of a properly trained teacher. The Theory of Cognitive Development (one of the most historically influential theories was developed by Jean Piaget, a Swiss Philosopher (1896–1980

References

  1. ^ Bartlett, John, comp. Familiar Quotations, 10th ed, rev. and enl. by Nathan Haskell Dole. Nathan Haskell Dole (1852-1935 was an American editor Translator, and author born at Chelsea, Massachusetts. 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. In 1960 the Physicist Eugene Wigner published an article titled " The Unreasonable Effectiveness of Mathematics in the Natural Sciences " arguing that the Eugene Paul "EP" Wigner ( Hungarian Wigner Pál Jenő) ( November 17, 1902 &ndash January 1, 1995) was a
  5. ^ Gelfert, Axel, 'Mathematical Rigor in Physics: Putting Exact Results in Their Place', Philosophy of Science, 72 (2005) 723-738.

See also

Honesty is the human quality of communicating and acting Truthfully related to Truth as a value An intellectual (from the adjective meaning "involving thought and reason" is a person who tries to use his or her Intelligence and analytical thinking, Intellectual dishonesty is the advocacy of a position which the advocate knows or believes to be false or is the advocacy of a position which the advocate does not know to be true and A pedant, or pædant, is a person who is overly concerned with Formalism and Precision, or who 'makes a show of learning' Scientific method refers to bodies of Techniques for investigating phenomena Self-deception is a process of denying or rationalizing away the relevance significance or importance of opposing Evidence and Logical argument

Dictionary

rigour

-noun

  1. a harsh or severe experience.
  2. a trembling or shivering response.
  3. character of being unyielding or inflexible.
  4. shrewd questioning
  5. higher level of difficulty
  6. (UK, slang) Common misspelling of rigor.. An abbreviated form of rigour mortis.
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