Mathematical Rigor
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Mathematical Rigor
Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness. 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. Etymology "Rigour" comes to English through old French (13th c., Modern French '' rigueur'') meaning "stiffness", which itself is based on the Latin ''rigorem'' (nominative ''rigor'') "numbness, stiffness, hardness, firmness; roughness, rudeness", from the verb ''rigere'' "to be stiff". The noun was frequently used to describe a condition of strictness or stiffness, which arises from a situation or constraint either chosen or experienced passively. For example, the title of the book ''Theologia Moralis Inter Rigorem et Laxitatem Medi'' roughly translates as "mediating theological morality between rigour and lax ...
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British English
British English (BrE, en-GB, or BE) is, according to Lexico, Oxford Dictionaries, "English language, English as used in Great Britain, as distinct from that used elsewhere". More narrowly, it can refer specifically to the English language in England, or, more broadly, to the collective dialects of English throughout the British Isles taken as a single umbrella variety, for instance additionally incorporating Scottish English, Welsh English, and Ulster English, Northern Irish English. Tom McArthur (linguist), Tom McArthur in the ''Oxford Guide to World English'' acknowledges that British English shares "all the ambiguities and tensions [with] the word 'British people, British' and as a result can be used and interpreted in two ways, more broadly or more narrowly, within a range of blurring and ambiguity". Variations exist in formal (both written and spoken) English in the United Kingdom. For example, the adjective ''wee'' is almost exclusively used in parts of Scotland, North E ...
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Scholarly Method
The scholarly method or scholarship is the body of principles and practices used by scholars and academics to make their claims about the subject as valid and trustworthy as possible, and to make them known to the scholarly public. It is the methods that systemically advance the teaching, research, and practice of a given scholarly or academic field of study through rigorous inquiry. Scholarship is noted by its significance to its particular profession, and is creative, can be documented, can be replicated or elaborated, and can be and is peer reviewed through various methods. The scholarly method includes the subcategories of the scientific method, in which scientists prove their claims, and the historical method, in which historians verify their claims. Methods The historical method comprises the techniques and guidelines by which historians use primary sources and other evidence to research and then to write history. The question of the nature, and indeed the possibility, of ...
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Judge
A judge is a person who presides over court proceedings, either alone or as a part of a panel of judges. A judge hears all the witnesses and any other evidence presented by the barristers or solicitors of the case, assesses the credibility and arguments of the parties, and then issues a ruling in the case based on their interpretation of the law and their own personal judgment. A judge is expected to conduct the trial impartially and, typically, in an open court. The powers, functions, method of appointment, discipline, and training of judges vary widely across different jurisdictions. In some jurisdictions, the judge's powers may be shared with a jury. In inquisitorial systems of criminal investigation, a judge might also be an examining magistrate. The presiding judge ensures that all court proceedings are lawful and orderly. Powers and functions The ultimate task of a judge is to settle a legal dispute in a final and publicly lawful manner in agreement with substantial p ...
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Case Law
Case law, also used interchangeably with common law, is law that is based on precedents, that is the judicial decisions from previous cases, rather than law based on constitutions, statutes, or regulations. Case law uses the detailed facts of a legal case that have been resolved by courts or similar tribunals. These past decisions are called "case law", or precedent. ''Stare decisis''—a Latin phrase meaning "let the decision stand"—is the principle by which judges are bound to such past decisions, drawing on established judicial authority to formulate their positions. These judicial interpretations are distinguished from statutory law, which are codes enacted by legislative bodies, and regulatory law, which are established by executive agencies based on statutes. In some jurisdictions, case law can be applied to ongoing adjudication; for example, criminal proceedings or family law. In common law countries (including the United Kingdom, United States, Canada, Australia and Ne ...
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Casuistry
In ethics, casuistry ( ) is a process of reasoning that seeks to resolve moral problems by extracting or extending theoretical rules from a particular case, and reapplying those rules to new instances. This method occurs in applied ethics and jurisprudence. The term is also commonly used as a pejorative to criticize the use of clever but unsound reasoning, especially in relation to moral questions (as in sophistry). It is the " udy of cases of conscience and a method of solving conflicts of obligations by applying general principles of ethics, religion, and moral theology to particular and concrete cases of human conduct. This frequently demands an extensive knowledge of natural law and equity, civil law, ecclesiastical precepts, and an exceptional skill in interpreting these various norms of conduct." It remains a common tool for applied ethics. Etymology According to the Online Etymological Dictionary, the term and its agent noun "casuist", appearing from about 1600, derive f ...
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Politics
Politics (from , ) is the set of activities that are associated with making decisions in groups, or other forms of power relations among individuals, such as the distribution of resources or status. The branch of social science that studies politics and government is referred to as political science. It may be used positively in the context of a "political solution" which is compromising and nonviolent, or descriptively as "the art or science of government", but also often carries a negative connotation.. The concept has been defined in various ways, and different approaches have fundamentally differing views on whether it should be used extensively or limitedly, empirically or normatively, and on whether conflict or co-operation is more essential to it. A variety of methods are deployed in politics, which include promoting one's own political views among people, negotiation with other political subjects, making laws, and exercising internal and external force, including wa ...
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Premise
A premise or premiss is a true or false statement that helps form the body of an argument, which logically leads to a true or false conclusion. A premise makes a declarative statement about its subject matter which enables a reader to either agree or disagree with the premise in question, and in doing so understand the logical assumptions of the argument. If a premise is logically false, then the conclusion, which follows from all of the premises of the argument, must also be false—unless the conclusion is supported by a logically valid argument which the reader agrees with. Therefore, if the reader disagrees with any one of the argument's premises, they have a logical basis to reject the conclusion of the argument. Explanation In logic, an argument requires a set of at least two declarative sentences (or "propositions") known as the "premises" (or "premisses"), along with another declarative sentence (or "proposition"), known as the conclusion. This structure of two prem ...
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Debate
Debate is a process that involves formal discourse on a particular topic, often including a moderator and audience. In a debate, arguments are put forward for often opposing viewpoints. Debates have historically occurred in public meetings, academic institutions, debate halls, coffeehouses, competitions, and legislative assemblies. Debate has also been conducted for educational and recreational purposes, usually associated with educational establishments and debating societies. These debates put an emphasis upon logical consistency, factual accuracy, and emotional appeal to an audience. Modern forms of competitive debate also include rules for participants to discuss and decide upon the framework of the debate (how the debate will be judged). History Debating in various forms has a long history and can be traced back to the philosophical and political debates of Ancient Greece, such as Athenian democracy or Shastrartha in Ancient India. Modern forms of debating and the es ...
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Evidence
Evidence for a proposition is what supports this proposition. It is usually understood as an indication that the supported proposition is true. What role evidence plays and how it is conceived varies from field to field. In epistemology, evidence is what justifies beliefs or what makes it rational to hold a certain doxastic attitude. For example, a perceptual experience of a tree may act as evidence that justifies the belief that there is a tree. In this role, evidence is usually understood as a private mental state. Important topics in this field include the questions of what the nature of these mental states is, for example, whether they have to be propositional, and whether misleading mental states can still qualify as evidence. In phenomenology, evidence is understood in a similar sense. Here, however, it is limited to intuitive knowledge that provides immediate access to truth and is therefore indubitable. In this role, it is supposed to provide ultimate justifications for ...
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Validity (logic)
In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. It is not required for a valid argument to have premises that are actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion. Valid arguments must be clearly expressed by means of sentences called well-formed formulas (also called ''wffs'' or simply ''formulas''). The validity of an argument can be tested, proved or disproved, and depends on its logical form. Arguments In logic, an argument is a set of statements expressing the ''premises'' (whatever consists of empirical evidences and axiomatic truths) and an ''evidence-based conclusion.'' An argument is ''valid'' if and only if it would be contradictory for the conclusion to be false if all of the premises are true. Validity doesn't require the truth of the premises, inst ...
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Intellectual Honesty
Intellectual honesty is an applied method of problem solving, characterised by an unbiased, honest attitude, which can be demonstrated in a number of different ways: * One's personal beliefs or politics do not interfere with the pursuit of truth; * Relevant facts and information are not purposefully omitted even when such things may contradict one's hypothesis; * Facts are presented in an unbiased manner, and not twisted to give misleading impressions or to support one view over another; * References, or earlier work, are acknowledged where possible, and plagiarism is avoided. Harvard ethicist Louis M. Guenin describes the "kernel" of intellectual honesty to be "a virtuous disposition to eschew deception when given an incentive for deception". Intentionally committed fallacies in debates and reasoning are called intellectual dishonesty. See also * Academic honesty * Conflict of interest * Epistemic feedback * Good faith * Intellectual * List of fallacies * Scientific method ...
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Peer Review
Peer review is the evaluation of work by one or more people with similar competencies as the producers of the work (peers). It functions as a form of self-regulation by qualified members of a profession within the relevant field. Peer review methods are used to maintain quality standards, improve performance, and provide credibility. In academia, scholarly peer review is often used to determine an academic paper's suitability for publication. Peer review can be categorized by the type of activity and by the field or profession in which the activity occurs, e.g., medical peer review. It can also be used as a teaching tool to help students improve writing assignments. Henry Oldenburg (1619–1677) was a German-born British philosopher who is seen as the 'father' of modern scientific peer review. Professional Professional peer review focuses on the performance of professionals, with a view to improving quality, upholding standards, or providing certification. In academia, peer ...
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