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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).
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.
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)} .
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").
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.
Propositional logic, as currently studied in universities, is a specification of a standard of logical consequence in which only the meanings of propositional connectives are considered in evaluating the conditions for the truth of a sentence, or whether a sentence logically follows from some other sentence or group of sentences.
A symbol or word used in logic to connect propositions or sentences, forming more complex expressions that convey relationships such as conjunction, disjunction, and negation. logical consequence A relationship between statements where the truth of one or more premises necessitates the truth of a conclusion, based on the logical structure of ...
It should explain the absurdity of both asserting and believing Moore's sentences. It should preserve, and reveal the roots of, the intuition that contradiction (or something contradiction-like) is at the root of the absurdity. The first two conditions have generally been the most challenged, while the third appears to be the least ...