Editing Contradiction (section)

{{Short description|Logical incompatibility between two or more propositions}}
{{Other uses}}
{{More citations needed|date=July 2008}}
[[File:Square of opposition, set diagrams.svg|thumb|This diagram shows the contradictory relationships between [[categorical proposition]]s in the [[square of opposition]] of [[Term logic|Aristotelian logic]].]]

In [[traditional logic]], a '''contradiction''' involves a [[proposition]] conflicting either with itself or established [[fact]]. It is often used as a tool to detect [[disingenuous]] beliefs and [[bias]]. Illustrating a general tendency in applied logic, [[Aristotle]]'s [[law of noncontradiction]] states that "It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect."<ref>{{Citation|last=Horn|first=Laurence R.|title=Contradiction|date=2018|url=https://plato.stanford.edu/archives/win2018/entries/contradiction/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2018|publisher=Metaphysics Research Lab, Stanford University|access-date=2019-12-10}}</ref>

In modern [[formal logic]] and [[type theory]], the term is mainly used instead for a ''single'' proposition, often denoted by the [[falsum]] symbol [[Bottom type|<math>\bot</math>]]; a proposition is a contradiction if [[false (logic)|false]] can be derived from it, using the rules of the logic. It is a proposition that is unconditionally false (i.e., a self-contradictory proposition).<ref>{{Cite web|title=Contradiction (logic)|url=https://www.thefreedictionary.com/Contradiction+(logic)|access-date=2020-08-14|website=TheFreeDictionary.com}}</ref><ref>{{Cite web|title=Tautologies, contradictions, and contingencies|url=http://www.skillfulreasoning.com/propositional_logic/properties_of_propositions.html|access-date=2020-08-14|website=www.skillfulreasoning.com}}</ref> This can be generalized to a collection of propositions, which is then said to "contain" a contradiction.