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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==
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.〔Corcoran, John. ''Universe of discourse''. Cambridge Dictionary of Philosophy, Cambridge University Press, 1995, p. 941.〕 Many logicians distinguish, sometimes only tacitly, between the domain of a science and the universe of discourse of a formalization of the science.〔José Miguel Sagüillo, Domains of sciences, universe of discourse, and omega arguments, History and philosophy of logic, vol. 20 (1999), pp. 267–280.〕 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.
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