Universe of Discourse and Existence

José Luis Usó-Doménech, Josué Antonio Nescolarde-Selva and Hugh Gash
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José Luis Usó-Doménech: Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain
Josué Antonio Nescolarde-Selva: Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain
Hugh Gash: Institute of Education, Dublin City University, Dublin 9, Ireland

Mathematics, 2018, vol. 6, issue 11, 1-19

Abstract: There is a fairly widespread belief that the problem of existence is not an essential issue for logic. Logic, though formal, must deal with the problem of existence. However, logic should be limited to describing “ formal existence ” or “ existence of a formal system ”. However, the logical problem of existence and how to treat and resolve this problem differ completely from the corresponding metaphysical problem. It is possible to deduce that formal existence is nothing other than belonging to the universe of discourse, so proposing a solution to the logical problem of existence in an epistemological, rather than a metaphysical, context. In this paper, we conclude, from a formal point of view, no universe of discourse is given in advance; any universe of discourse that satisfies the necessary conditions can be used. The extended epistemological belief that there is a universe of discourse defined rigorously, which would be the true and should be “ the universe of discourse of logic ”, cannot be justified.

Keywords: belief; concepts; effective existence; formal existence; meinonguian objects; nonmonotonic logic; satisfaction functions; universe of discourse (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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