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Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness. [1] These constraints may be environmentally imposed, such as "the rigours of famine"; logically imposed, such as mathematical proofs which must maintain consistent answers; or socially imposed, such as the process of defining ethics and law.
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
Critical thinking. Critical thinking is the analysis of available facts, evidence, observations, and arguments in order to form a judgement by the application of rational, skeptical, and unbiased analyses and evaluation. [ 1] In modern times, the use of the phrase critical thinking can be traced to John Dewey, who used the phrase reflective ...
The standard of rigor is not absolute and has varied throughout history. A proof can be presented differently depending on the intended audience. To gain acceptance, a proof has to meet communal standards of rigor; an argument considered vague or incomplete may be rejected. The concept of proof is formalized in the field of mathematical logic. [12]
The word "logic" originates from the Greek word "logos", which has a variety of translations, such as reason, discourse, or language. [4] Logic is traditionally defined as the study of the laws of thought or correct reasoning, [5] and is usually understood in terms of inferences or arguments. Reasoning is the activity of drawing inferences.
e. The scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century. The scientific method involves careful observation coupled with rigorous scepticism, because cognitive assumptions can distort the interpretation of the observation.
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study ...
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, value, mind, and language. It is a rational and critical inquiry that reflects on its own methods and assumptions. Historically, many of the individual sciences, such as physics and ...