Concept
Domain of discourse
Overview
In the formal sciences, the domain of discourse or universe of discourse (borrowing from the mathematical concept of universe) is the set of entities over which certain variables of interest in some formal treatment may range.
It is also defined as the collection of objects being discussed in a specific discourse.
In model-theoretical semantics, a universe of discourse is the set of entities that a model is based on.
The domain of discourse is usually identified in the preliminaries, so that there is no need in the further treatment to specify each time the range of the relevant variables. Many logicians distinguish, sometimes only tacitly, between the domain of a science and the universe of discourse of a formalization of the science.
In mathematics, the concept is distinguished from a universe, which is some set internal to a set theory, whereas a domain of discourse is metamathematical, allowing one to speak of the universe of sets or collection of all classes in a formal way.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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We can arbitrarily exclude any set of events at the big end of an abstractive set without the loss of any important property to the set as thus modified. I call the limiting character of natural relations which is indicated by an abstractive set, the 'intrinsic character' of the set; also the properties, connected with the relation of whole and part as concerning its members, by which an abstractive set is defined…
Alfred North Whitehead, The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919
States what Domain of discourse is; the author is tied to Domain of discourse in the knowledge graph.
Any such select set is called the set of postulates, or premises, from which the reasoning proceeds. The reasoning is nothing else than the exhibition of the whole pattern of general conditions involved in the pattern derived from the selected postulates.
Alfred North Whitehead, Science and the modern world
States what Domain of discourse is; the author is tied to Domain of discourse in the knowledge graph.
Hence, in the conclusion of a syllogism we restrict a predicate to a certain object, after having thought it in the major in its whole extent under a certain condition. This complete quantity of the extent in relation to such a condition is called universality (universalitas). To this corresponds totality (universitas) of conditions in the synthesis of intuitions.
Immanuel Kant, The Critique of Pure Reason
States what Domain of discourse is.
Related ideas
- First-order logic
- Internet Archive
- Augustus De Morgan
- Mathematical logic
- Real number
- Natural number
- Lewis Carroll
- Semantics
- Formal science
- George Boole
- Alfred North Whitehead
- Quantifier (logic)
- Discourse
- Universal quantification
- The Laws of Thought
Opposing perspectives
Place in the tradition
Part of Deontic logic.