Domain of discourse

百度消费手指一挥，退款之路漫漫中国互联网信息中心近期发布的第41次《中国互联网络发展状况统计报告》显示，去年我国网民使用率最高的10类互联网应用中，和网络文化相关的服务占到半壁江山。

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.^[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]

Etymology

The concept universe of discourse was used for the first time by George Boole (1854) on page 42 of his Laws of Thought:

In every discourse, whether of the mind conversing with its own thoughts, or of the individual in his folley 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.

—?George Boole, The Laws of Thought. 1854/2003. p. 42.^[3]

The concept, probably discovered independently by Boole in 1847, played a crucial role in his philosophy of logic especially in his principle of wholistic reference.

Alfred North Whitehead cited Augustus De Morgan as identifying "that limited class of things which is the special subject of discourse on any particular occasion. Such a class was called by De Morgan, the Universe of Discourse."^[4]

Lewis Carroll expressed the need for a universe of discourse as follows:

It sometimes happens that, in one or both of the Terms of a Proposition, the Name consists of Adjectives only, the Substantive being understood. In order to express such a Proposition fully, we must supply the Name of some Class which may be regarded as a Genus of which each Term is a Species...The Genus referred to is called the Universe of Discourse...^[5]

Examples

For example, in an interpretation of first-order logic, the domain of discourse is the set of individuals over which the quantifiers range. A proposition such as $? x (x 2 \neq 2)$ is ambiguous if no domain of discourse has been identified. 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 the domain of discourse is the set of real numbers, the proposition is false, with $x = \sqrt 2$ as counterexample; if the domain is the set of natural numbers, the proposition is true, since 2 is not the square of any natural number.

The binary relation called set membership, expressed as $x\in A$ , and meaning that x belongs to set A, is clear enough. Every binary relation has a converse relation, and the converse of $\in$ is written $\ni$ . Also, a binary relation must have a domain. The domain of the converse of set membership is the universe of discourse. Any subset of this universe may, or may not, contain x. A is a subset of this universe, not necessarily restricted to A.

References

^ Corcoran, John. Universe of discourse. Cambridge Dictionary of Philosophy, Cambridge University Press, 1995, p. 941.
^ José Miguel Sagüillo, Domains of sciences, universe of discourse, and omega arguments, History and philosophy of logic, vol. 20 (1999), pp. 267–280.
^ 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.
^ Alfred North Whitehead (1898) A Treatise on Universal Algebra with Applications, page 100 via Internet Archive
^ Lewis Carroll (1896) Symbolic Logic, Part I: Elementary page 10

[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] 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.

[4] Alfred North Whitehead (1898) A Treatise on Universal Algebra with Applications, page 100 via Internet Archive

[5] Lewis Carroll (1896) Symbolic Logic, Part I: Elementary page 10

[1]

[2]

[3]

[4]

[5]

职业年金是什么意思	为什么来大姨妈会拉肚子	什么地哭	花痴是什么意思	广州五行属什么
排异是什么意思	智商105是什么水平	五指毛桃有什么功效	甘耳朵旁什么字	糖耐量异常是什么意思
黄山毛峰属于什么茶	玻璃体混浊用什么眼药水	人红是非多什么意思	抗链o高是什么原因	疫苗是什么
吃什么水果对胃好	为什么一	冰菜是什么菜	紧急避孕药对身体有什么伤害	两个圈的皮带是什么牌子

全飞秒是什么zhiyanzhang.com	高压偏低是什么原因造成的clwhiglsz.com	胃息肉有什么症状hcv7jop7ns3r.cn	男性长期熬夜吃什么好hcv7jop6ns7r.cn	请多指教是什么意思hcv9jop2ns0r.cn
痔疮什么样子hcv9jop0ns9r.cn	脂肪肝吃什么药治疗hcv9jop5ns2r.cn	兔子不吃窝边草是什么生肖hcv8jop5ns2r.cn	祥五行属什么hcv9jop5ns1r.cn	强势是什么意思hcv8jop8ns5r.cn
仁爱是什么意思hcv8jop2ns8r.cn	物质是什么hcv7jop9ns0r.cn	胎盘位于后壁是什么意思hcv9jop0ns7r.cn	凉烟都有什么牌子hcv8jop5ns6r.cn	什么是代词hcv7jop6ns6r.cn
的近义词是什么hcv8jop1ns8r.cn	志趣相投是什么意思hcv8jop9ns4r.cn	kai是什么意思hcv9jop1ns2r.cn	吉林有什么特产hcv8jop6ns1r.cn	牛跟什么生肖相冲hcv9jop3ns0r.cn

[朝闻天下]“委员通道”谈发展

Etymology

Examples

See also

References