a class (set) of objects considered within a given context. A context here is understood to mean a distinct discourse or a sentence expressing a distinct discourse, a collection of sentences, a fragment of a scientific theory, or an entire theory. In number theory, the universe of discourse in the natural-number series (the set of nonnegative integers); in mathematical analysis, the set of real numbers; in botany, the set of all plants (more precisely, the set of all plant species); and in the predicate calculus or logic of classes, any fixed nonempty domain. The universe of discourse is also referred to as the universal set, the opposite in logic and set theory of what is known as the empty set; the empty set contains no object of a given type and is the complement of the universal set.
The generally accepted idea of a universe of discourse as a given domain of objects was proposed by J. Venn. In number theory, according to this definition, the complement of the set of even numbers is the set of odd numbers and not the “set of all conceivable objects, none of which is an even number”— which would include, for example, this encyclopedia and everything in the world other than the even numbers. This definition has replaced G. Frege’s concept of a “universal” universe of discourse, which had led to paradoxes.