General statement
A universal statement is a statement of all the elements of a particular subject area, for example, the statement "All men are mortal." Synonym names such as are modern universal testimony , universal mission statement , purpose statement , Allsatz , generalization or generalization (as a result). In traditional logic , general statements are called universal , universal or general judgments - see Categorical Judgment .
The logical properties of universal statements become modern in predicate logic and have traditionally been treated as universally affirmative judgments in syllogistics .
In German, all sentences are natural, especially with words like “alle / s”, “alles”, “always” and “everywhere” or with definite constructions (“a full stomach doesn't like studying”, “people are mortal “) Expressed. In the formal language of predicate logic generalizations are formed by using the All quantifier over predicates or forms of expression is quantified
In order to falsify a general statement , it is sufficient to indicate a single item from the subject area to which the statement does not apply. In order to verify an universal statement, however , one generally has to examine every object in the subject area. If the number of objects in the object area is not accessible or is infinitely large, generally only a more or less good confirmation comes into consideration. An exception, however, are general statements in the formal sciences such as logic and mathematics, for example those about infinite sets of numbers that can be verified using methods such as complete induction .
In the syllogistic general statements (universal judgments) went hand in hand with an existential presupposition, i. H. A universal judgment was only meaningful if the terms contained therein applied to at least one object. In predicate logic, it is also possible to deal with empty terms or predicates, but there is a weakened existence presupposition in such a way that the subject area must not be empty as a whole. In alternative logical systems such as free logic , this restriction is also lifted.
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- ↑ Bußmann, Lexikon der Sprachwissenschaft, 3rd edition (2002) / general statement