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In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...
Not to be confused with Calling the question. In classical rhetoric and logic, begging the question or assuming the conclusion (Latin: petītiō principiī) is an informal fallacy that occurs when an argument's premises assume the truth of the conclusion. Historically, begging the question refers to a fault in a dialectical argument in which ...
[This is a case of the fallacy denying the antecedent as written because it matches the formal symbolic schema at beginning. The form is taken without regard to the content of the language.] See also
Circular reasoning (Latin: circulus in probando, "circle in proving"; [1] also known as circular logic) is a logical fallacy in which the reasoner begins with what they are trying to end with. [2] Circular reasoning is not a formal logical fallacy, but a pragmatic defect in an argument whereby the premises are just as much in need of proof or ...
Without loss of generality (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as without any loss of generality or with no loss of generality) is a frequently used expression in mathematics. The term is used to indicate the assumption that what follows is chosen arbitrarily, narrowing the premise to a particular case, but does ...
Syllogism. A syllogism (Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. "Socrates" at the Louvre. In its earliest form (defined by Aristotle in his 350 BC book Prior ...
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