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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).
The most common form of oxymoron involves an adjective–noun combination of two words, but they can also be devised in the meaning of sentences or phrases. One classic example of the use of oxymorons in English literature can be found in this example from Shakespeare's Romeo and Juliet, where Romeo strings together thirteen in a row: [11]
In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally ...
Sometimes used for “relation”, also used for denoting various ad hoc relations (for example, for denoting “witnessing” in the context of Rosser's trick). The fish hook is also used as strict implication by C.I.Lewis p {\displaystyle p} ⥽ q ≡ ( p → q ) {\displaystyle q\equiv \Box (p\rightarrow q)} .
This resolution technique uses proof by contradiction and is based on the fact that any sentence in propositional logic can be transformed into an equivalent sentence in conjunctive normal form. [4] The steps are as follows. All sentences in the knowledge base and the negation of the sentence to be proved (the conjecture) are conjunctively ...
A term used to describe non-standard or alternative logical systems that deviate from classical logic. diagonalization lemma A lemma used in the proof of Gödel's incompleteness theorems, stating that for any formula with one free variable, there exists a sentence that asserts its own unprovability. dialetheism
contradiction in adjective A contradiction where adjective contradicts its noun (e.g., a square triangle). contra proferentem: against the one bringing forth Used in contract law to stipulate that an ambiguous term in a contract shall be interpreted against the interests of the party that insisted upon the term's inclusion. Prevents the ...
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.