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An apologia (Latin for apology, from Ancient Greek: ἀπολογία, lit. ' speaking in defense ' ) is a formal defense of an opinion, position or action.
The term apologetics derives from the Ancient Greek word apologia (ἀπολογία). [1] In the Classical Greek legal system, the prosecution delivered the kategoria (κατηγορία), the accusation or charge, and the defendant replied with an apologia, the defence. [5] The apologia was a formal speech or explanation to reply to and rebut ...
Opposite of a priori. Used in mathematics and logic to denote something that is known after a proof has been carried out. In philosophy, used to denote something known from experience. a priori: from the former: Presupposed independent of experience; the reverse of a posteriori. Used in mathematics and logic to denote something that is known or ...
Used paired with ±, denotes the opposite sign; that is, + if ± is –, and – if ± is +. ÷ (division sign) Widely used for denoting division in Anglophone countries, it is no longer in common use in mathematics and its use is "not recommended". [1] In some countries, it can indicate subtraction.: 1.
Reductio ad absurdum, painting by John Pettie exhibited at the Royal Academy in 1884. In logic, reductio ad absurdum (Latin for "reduction to absurdity"), also known as argumentum ad absurdum (Latin for "argument to absurdity") or apagogical argument, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.
More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved. In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, [2] and reductio ad ...
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 ...
In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P.