In logic and philosophy of language, a universe of discourse is understood to mean the totality of objects to which statements such as "all objects are ..." ( general statement ) or "there are no objects that are ..." (negative existence statement ) refer. Such statements only make sense if the meaning of “object” is restricted to a certain area, the universe of discourse. The extent and type of restriction depend on the content and context of the statements. There is therefore not just one universe of discourse, but different universes of discourse.
The English term Universe of Discourse is also used in German-language logic and computer science literature. It goes back to Augustus De Morgan (1847) and describes the area of objects (in the broadest sense) that should be talked about at all.
In logic as in everyday life, misunderstandings and arguments often arise when people talk about different things "past each other". Someone claims e.g. B. that there are no winged horses. His opponent rejects this with the reference to the Pegasus . Both mentally move in different worlds. Their dispute can be settled if they agree on a common universe of discourse, i. H. negotiate what the talk (the discourse ) should be about, whether only about physically existing horses or also about mythical creatures .
The universe of discourse also plays a role when using negative (complementary) terms . Expressions such as “non-swimmer”, “non-specialist”, “non-voter” can only meaningfully be applied to people. The non-voters, together with the voters, form the discourse universe, which is restricted to persons entitled to vote. The restriction occurs automatically when using such terms. If the automatic is put out of operation by z. B. describes a disused chimney as a non-smoker, a play on words emerges. In general, the following applies to every concept: if it is combined with the associated negative concept (more precisely: if its extensions are combined), then both together form the discourse universe or the area of applications of the positively determined complementary concept:
|Voters||Non-voters||persons entitled to vote|
|shameful supplicants||outrageous supplicants||Supplicant|
|Living thing with wings||Living thing without wings||Creature|
In set theory , the discourse universe corresponds to the basic set , the sets correspond to the concepts, the complements of sets correspond to the negation of concepts. In predicate logic , the discourse universe corresponds to the range of the definition set that the object variable of a quantified statement can pass through.
In logic, the Universe of Discourse is mostly abbreviated with U , in computer science also with UoD .
As a rule, the U is a subset of all existing objects and, in particular in the predicate logic, the object area that is defined or assumed when quantifiers are used .