Editing Law of excluded middle (section)

===In mathematical logic===

In modern [[mathematical logic]], the excluded middle has been argued to result in possible [[Self-refuting idea|self-contradiction]]. It is possible in logic to make well-constructed propositions that can be neither true nor false; a common example of this is the "[[Liar paradox|Liar's paradox]]",<ref>{{Cite web |last=Priest |first=Graham |date=2010-11-28 |title=Paradoxical Truth |url=https://archive.nytimes.com/opinionator.blogs.nytimes.com/2010/11/28/paradoxical-truth/ |access-date=2023-09-10 |website=Opinionator |language=en}}</ref> the statement "this statement is false", which is argued to itself be neither true nor false. [[Arthur Prior]] has argued that [[Liar paradox|The Paradox]] is not an example of a statement that cannot be true or false. The law of excluded middle still holds here as the negation of this statement "This statement is not false", can be assigned true. In [[set theory]], such a self-referential paradox can be constructed by examining the set "the set of all sets that do not contain themselves". This set is unambiguously defined, but leads to a [[Russell's paradox]]:<ref>Kevin C. Klement, {{cite IEP |url-id=par-russ |title=Russell's Paradox }}</ref><ref>{{cite journal |first=Graham |last=Priest |title=The Logical Paradoxes and the Law of Excluded Middle |journal=The Philosophical Quarterly |volume=33 |issue=131 |year=1983 |pages=160–165 |doi=10.2307/2218742 |jstor=2218742 }}</ref> does the set contain, as one of its elements, itself? However, in the modern [[Zermelo–Fraenkel set theory]], this type of contradiction is no longer admitted. Furthermore, paradoxes of self reference can be constructed without even invoking negation at all, as in [[Curry's paradox]].{{cn|date=February 2022}}