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When this recursion creates a metaphysical impossibility through contradiction, the regress or circularity is vicious. Again, the liar paradox is an instructive example: "This statement is false"—if the statement is true, then the statement is false, thereby making the statement true, thereby making the statement false, and so on. [15] [18]
It is a proposition that is unconditionally false (i.e., a self-contradictory proposition). [2][3]This can be generalized to a collection of propositions, which is then said to "contain" a contradiction. History. [edit] By creation of a paradox, Plato's Euthydemusdialogue demonstrates the need for the notion of contradiction.
Birthday paradox: In a random group of only 23 people, there is a better than 50/50 chance two of them have the same birthday. Borel's paradox: Conditional probability density functions are not invariant under coordinate transformations. Boy or Girl paradox: A two-child family has at least one boy.
An oxymoron (plurals: oxymorons and oxymora) is a figure of speech that juxtaposes concepts with opposite meanings within a word or in a phrase that is a self-contradiction. As a rhetorical device, an oxymoron illustrates a point to communicate and reveal a paradox. [ 1 ][ 2 ] A general meaning of "contradiction in terms" is recorded by the ...
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 impossibile.
propositional logic, Boolean algebra, first-order logic. ⊥ {\displaystyle \bot } denotes a proposition that is always false. The symbol ⊥ may also refer to perpendicular lines. The proposition. ⊥ ∧ P {\displaystyle \bot \wedge P} is always false since at least one of the two is unconditionally false. ∀.
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.
Antithesis can be defined as "a figure of speech involving a seeming contradiction of ideas, words, clauses, or sentences within a balanced grammatical structure. Parallelism of expression serves to emphasize opposition of ideas". [3] An antithesis must always contain two ideas within one statement. The ideas may not be structurally opposite ...