World Library  
Flag as Inappropriate
Email this Article

Domain of discourse

Article Id: WHEBN0000229180
Reproduction Date:

Title: Domain of discourse  
Author: World Heritage Encyclopedia
Language: English
Subject: First-order logic, Whitehead's point-free geometry, Quantifier (logic), Second-order logic, Predicate logic
Collection: Predicate Logic, Semantics
Publisher: World Heritage Encyclopedia

Domain of discourse

In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range.


  • Overview 1
  • Examples 2
  • Universe of discourse 3
  • Boole’s 1854 definition 4
  • See also 5
  • References 6


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.[1] Many logicians distinguish, sometimes only tacitly, between the domain of a science and the universe of discourse of a formalization of the science.[2] Giuseppe Peano formalized number theory (arithmetic of positive integers) taking its domain to be the positive integers and the universe of discourse to include all numbers, not just integers.


For example, in an interpretation of first-order logic, the domain of discourse is the set of individuals that the quantifiers range over. In one interpretation, the domain of discourse could be the set of real numbers; in another interpretation, it could be the set of natural numbers. If no domain of discourse has been identified, a proposition such as x (x2 ≠ 2) is ambiguous. If the domain of discourse is the set of real numbers, the proposition is false, with x = √2 as counterexample; if the domain is the set of naturals, the proposition is true, since 2 is not the square of any natural number.

Universe of discourse

The term universe of discourse generally refers to the collection of objects being discussed in a specific Laws of Thought in a long and incisive passage well worth study. Boole's definition is quoted below. The concept, probably discovered independently by Boole in 1847, played a crucial role in his philosophy of logic especially in his stunning principle of wholistic reference.

A database is a model of some aspect of the reality of an organisation. It is conventional to call this reality the "universe of discourse" or "domain of discourse".

Boole’s 1854 definition

In every discourse, whether of the mind conversing with its own thoughts, or of the individual in his intercourse with others, there is an assumed or expressed limit within which the subjects of its operation are confined. The most unfettered discourse is that in which the words we use are understood in the widest possible application, and for them the limits of discourse are co-extensive with those of the universe itself. But more usually we confine ourselves to a less spacious field. Sometimes, in discoursing of men we imply (without expressing the limitation) that it is of men only under certain circumstances and conditions that we speak, as of civilized men, or of men in the vigour of life, or of men under some other condition or relation. Now, whatever may be the extent of the field within which all the objects of our discourse are found, that field may properly be termed the universe of discourse. Furthermore, this universe of discourse is in the strictest sense the ultimate subject of the discourse.[3]

See also


  1. ^ Corcoran, John. Universe of discourse. Cambridge Dictionary of Philosophy, Cambridge University Press, 1995, p. 941.
  2. ^ José Miguel Sagüillo, Domains of sciences, universe of discourse, and omega arguments, History and philosophy of logic, vol. 20 (1999), pp. 267–280.
  3. ^ George Boole. 1854/2003. The Laws of Thought, facsimile of 1854 edition, with an introduction by J. Corcoran. Buffalo: Prometheus Books (2003). Reviewed by James van Evra in Philosophy in Review.24 (2004) 167–169.
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.