Universal quantification

A universal statement is a statement about all elements of a particular subject area, for example, the statement " All men are mortal. " Synonymous with modern names such as universal proposition, universal statement, universal message, Allsatz, generalization or generalization can be used ( as a result ). In traditional logic -statements are referred to as universal, universal or general judgments - see categorical judgment.

The logical properties of the all-statements are modern in predicate logic and have traditionally been treated as a universal affirmative judgments in the syllogistic.

Of course Linguistically the German universal statements especially with words such as " all / s", " every / r / s", " always " and "everywhere" or with indefinite constructions ( " A full stomach can not study ", " men are mortal " ) expressed. In the formal language of predicate logic generalizations are formed by quantified using the universal quantifier over predicates or statement forms

To falsify a universal statement, it is sufficient to specify a single object from the subject matter to which the statement is not true. To verify a universal statement, however, one must generally examine each subject of the subject area. Is not accessible or infinitely large, the amount of the items of the subject area, generally comes only a more or less good confirmation into consideration. An exception to generalizations is in the formal sciences such as logic and mathematics, for example those on infinite sets of numbers that can be verified using techniques such as mathematical induction.

In the syllogistic went all-statements ( universal judgments) with a Existenzpräsupposition associated, that is, a universal judgment was only considered useful if the terms occurring therein were true in each case at least one subject. In predicate logic, the handling of empty concepts or predicates is possible, but there is an attenuated existence presupposition such that the subject matter must not be empty as a whole. In alternative logical systems like the outdoors logic, this restriction is lifted.