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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.
The principle in logic that from a contradiction, any statement can be proven, related to the principle of ex falso quodlibet. exportation A logical principle that transforms a statement of the form ( P ∧ Q ) → R {\displaystyle (P\land Q)\rightarrow R} into the equivalent form P → ( Q → R ) {\displaystyle P\rightarrow (Q\rightarrow R ...
Proof by assertion – a proposition is repeatedly restated regardless of contradiction; sometimes confused with argument from repetition (argumentum ad infinitum, argumentum ad nauseam). Prosecutor's fallacy – a low probability of false matches does not mean a low probability of some false match being found. [43] [44]
In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias . Illustrating a general tendency in applied logic, Aristotle 's law of noncontradiction states that "It is impossible that the same thing can at the same time both ...
Taking this one stage further, the clue word can hint at the word or words to be abbreviated rather than giving the word itself. For example: "About" for C or CA (for "circa"), or RE. "Say" for EG, used to mean "for example". More obscure clue words of this variety include: "Model" for T, referring to the Model T.
Formally the law of non-contradiction is written as ¬(P ∧ ¬P) and read as "it is not the case that a proposition is both true and false". The law of non-contradiction neither follows nor is implied by the principle of Proof by contradiction. The laws of excluded middle and non-contradiction together mean that exactly one of P and ¬P is true.
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In Catholic theology, a sign of contradiction is someone who, upon manifesting holiness, is subject to extreme opposition. The term is adopted from the New Testament phrase "a sign that is spoken against", found in Luke 2 :34 [ 1 ] and in Acts 28 :22, [ 2 ] where the texts refer first to Jesus Christ , and then to the early Christians .