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In modern formal logic and type theory, the term is mainly used instead for a single proposition, often denoted by the falsum symbol ; a proposition is a contradiction if false can be derived from it, using the rules of the logic. It is a proposition that is unconditionally false (i.e., a self-contradictory proposition).
In literature, the paradox is an anomalous juxtaposition of incongruous ideas for the sake of striking exposition or unexpected insight. It functions as a method of literary composition and analysis that involves examining apparently contradictory statements and drawing conclusions either to reconcile them or to explain their presence.
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.
A symbol used in logic to represent falsity or a contradiction, often denoted as . "Fido"-Fido principle The principle in philosophy of language suggesting that the meaning of a word is the object it refers to, exemplified by the idea that the meaning of "Fido" is the dog Fido itself.
Oxymorons in the narrow sense are a rhetorical device used deliberately by the speaker and intended to be understood as such by the listener. In a more extended sense, the term "oxymoron" has also been applied to inadvertent or incidental contradictions, as in the case of "dead metaphors" ("barely clothed" or "terribly good").
Since Jaakko Hintikka's seminal treatment of the problem, [7] it has become standard to present Moore's paradox by explaining why it is absurd to assert sentences that have the logical form: "P and NOT(I believe that P)" or "P and I believe that NOT-P." Philosophers refer to these, respectively, as the omissive and commissive versions of Moore's paradox.
Consistency is a key requirement for most axiomatic systems, as the presence of contradiction would allow any statement to be proven (principle of explosion). In an axiomatic system, an axiom is called independent if it cannot be proven or disproven from other axioms in the system. A system is called independent if each of its underlying axioms ...
The same type of relationship is shown in (2), where the first sentence can be interpreted as implying that by giving a party for the new students, the hosts will serve drinks. This is, of course, a defeasible inference based on world knowledge, that is then contradicted in the following sentence.