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Thus, there is an explosion of true statements. In a different solution to the problems posed by the principle of explosion, some mathematicians have devised alternative theories of logic called paraconsistent logics, which allow some contradictory statements to be proven without affecting the truth value of (all) other statements. [7]
Colloquial usage can label actions or statements as contradicting each other when due (or perceived as due) to presuppositions which are contradictory in the logical sense. Proof by contradiction is used in mathematics to construct proofs. The scientific method uses contradiction to falsify bad theory.
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. [1] [2] It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.
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 arguments, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.
Paradox – an apparently absurd or self-contradictory statement or proposition. Paralipsis – a form of apophasis when a rhetor introduces a subject by denying it should be discussed. To speak of someone or something by claiming not to. Parallelism – the correspondence, in sense or construction, of successive clauses or passages.
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.
However, some of these paradoxes qualify to fit into the mainstream viewpoint of a paradox, which is a self-contradictory result gained even while properly applying accepted ways of reasoning. These paradoxes, often called antinomy , point out genuine problems in our understanding of the ideas of truth and description .
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 ...