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In C (and some other languages descended from C), double negation (!!x) is used as an idiom to convert x to a canonical Boolean, ie. an integer with a value of either 0 or 1 and no other. Although any integer other than 0 is logically true in C and 1 is not special in this regard, it is sometimes important to ensure that a canonical value is ...
In some cases, by way of irony, an affirmative statement may be intended to have the meaning of the corresponding negative, or vice versa. For examples see antiphrasis and sarcasm . For the use of double negations or similar as understatements ("not unappealing", "not bad", etc.) see litotes .
definition: is defined as metalanguage:= means "from now on, is defined to be another name for ." This is a statement in the metalanguage, not the object language. The notation may occasionally be seen in physics, meaning the same as :=.
In some cases, contraposition involves a change of the former's quality (i.e. affirmation or negation). [5] For its symbolic expression in modern logic, see the rule of transposition . Contraposition also has philosophical application distinct from the other traditional inference processes of conversion and obversion where equivocation varies ...
In most logical systems, negation, material conditional and false are related as: ¬ p ⇔ (p → ⊥). In fact, this is the definition of negation in some systems, [8] such as intuitionistic logic, and can be proven in propositional calculi where negation is a fundamental connective.
Its negation ¬H(M) states that "M neither halts nor does not halt", which is false by the law of noncontradiction (which is intuitionistically valid). If proof by contradiction were intuitionistically valid, we would obtain an algorithm for deciding whether an arbitrary Turing machine M halts, thereby violating the (intuitionistically valid ...
When a statement such as "Some politicians are not corrupt" is said to distribute the "corrupt people" group to "some politicians", the information seems of little value, since the group "some politicians" is not defined; This is the de dicto interpretation of the intensional statement ([]), or "Some politicians (or other) are not corrupt".
Dialetheism (/ d aɪ ə ˈ l ɛ θ i ɪ z əm /; from Greek δι-di-'twice' and ἀλήθεια alḗtheia 'truth') is the view that there are statements that are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called "true contradictions", dialetheia, or ...