# Dictionary Definition

rigorous adj

1 rigidly accurate; allowing no deviation from a
standard; "rigorous application of the law"; "a strict vegetarian"
[syn: strict]

2 demanding strict attention to rules and
procedures; "rigorous discipline"; "tight security"; "stringent
safety measures" [syn: stringent, tight]

3 used of circumstances (especially weather) that
cause suffering; "brutal weather"; "northern winters can be cruel";
"a cruel world"; "a harsh climate"; "a rigorous climate"; "unkind
winters" [syn: brutal,
cruel, harsh, unkind]

# User Contributed Dictionary

## English

### Adjective

- Manifesting, exercising, or favoring rigor; allowing no abatement or mitigation; scrupulously accurate; exact; strict; severe; relentless; as, a rigorous officer of justice; a rigorous execution of law; a rigorous definition or demonstration.
- Severe; intense; inclement; as, a rigorous winter.
- Violent.

#### Translations

Manifesting, exercising, or favoring rigor;
allowing no abatement or mitigation; scrupulously accurate

Severe; intense; inclement; as, a rigorous
winter

- Russian: суровый

Violent

- French: rigoureux
- Finnish: tiukkapipoinen slang (1), ankara (1,2)
- German: rigoros

# Extensive Definition

- 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.

## 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 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.

### 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. 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, 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 of course refers to the axiomatic
method.

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). 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 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.

### 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, "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. 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. 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.

## References

## See also

rigorous in German: Rigor

rigorous in Spanish: Rigurosidad

rigorous in Hebrew: ריגורוזי

# Synonyms, Antonyms and Related Words

Herculean, Siberian, abstruse, accurate, acid, acidulous, acrid, acrimonious, acute, adamant, adamantine, adverse, algid, antagonistic, arctic, arduous, ascetic, astringent, attentive, below zero,
biting, bitter, bitterly cold, bleak, boreal, brisk, brumal, brutal, burdensome, cast-iron,
caustic, close, cold, cold as charity, cold as
death, cold as ice, cold as marble, complex, conflicting, conscientious, constant, contrary, correct, counter, counteractive, crisp, critical, cutting, delicate, demanding, detailed, detrimental, difficile, difficult, direct, double-edged, dour, draconian, drastic, edged, escharotic, even, exact, exacting, excessive, exigent, exorbitant, express, exquisite, extravagant, extreme, faithful, fierce, fine, finical, finicking, finicky, firm, flinty, formidable, freezing, freezing cold,
frigid, fundamentalist, furious, fussy, gelid, glacial, great, grim, hairy, hard, hard-core, hard-earned,
hard-fought, harmful,
harsh, hibernal, hidebound, hiemal, hostile, hyperborean, ice-cold,
ice-encrusted, icelike,
icy, immoderate, immovable, immutable, implacable, impliable, in opposition,
incisive, inclement, inelastic, inerrable, inerrant, inexorable, infallible, inflexible, inimical, intemperate, intense, intransigent, intricate, iron, ironbound, ironclad, ironhanded, irreconcilable, jawbreaking, keen, knotted, knotty, laborious, mathematical, mean, meticulous, micrometrically
precise, microscopic, minute, miserable, mordacious, mordant, muscle-bound, narrow, nice, nipping, nippy, no picnic, not easy,
numbing, obdurate, obstinate, onerous, operose, opposed, opposing, opposite, oppressive, orthodox, outrageous, particular, penetrating, piercing, pinching, pinpoint, poignant, precise, precisianistic, precisionistic, procrustean, proper, punctilious, punctual, purist, puristic, puritan, puritanic, raw, refined, relentless, religious, religiously exact,
right, rigid, rigorist, rigoristic, rock-ribbed,
rockbound, rough, rugged, scathing, scientific, scientifically
exact, scrupulous,
scrutinizing, set
with thorns, severe,
sharp, sinister, sleety, slushy, snappy, spiny, splitting, square, stabbing, steely, steep, stern, stiff, stinging, stone-cold, straightlaced, straitlaced, strenuous, stressful, strict, strident, stringent, stubborn, subtle, subzero, supercooled, tart, thorny, ticklish, toilsome, tough, trenchant, tricky, troublesome, troublous, trying, unaffected, unalterable, unbending, unchangeable, uncompromising, unconscionable, undeviating, unerring, unfavorable, ungiving, unmoved, unrelenting, untoward, unyielding, uphill, vehement, venomous, violent, virulent, vitriolic, wicked, winterbound, winterlike, wintery, wintry, wretched