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- Vacuous_truth abstract "A vacuous truth is a statement that asserts that all members of the empty set have a certain property. For example, the statement "all cell phones in the room are turned off" may be true simply because there are no cell phones in the room. In this case, the statement "all cell phones in the room are turned on" would also be true, and vacuously so, as would the conjunction of the two: "all cell phones in the room are turned on and turned off".More formally, a relatively well-defined usage refers to a conditional statement with a false antecedent. One example of such a statement is "if Uluru is in France, then the Eiffel Tower is in Bolivia". Such statements are considered vacuous because the fact that the antecedent is false prevents using the statement to infer anything about the truth value of the consequent. They are true because a material conditional is defined to be true when the antecedent is false (regardless of whether the conclusion is true).In pure mathematics, vacuously true statements are not generally of interest by themselves, but they frequently arise as the base case of proofs by mathematical induction. This notion has relevance as well as in any other field which uses classical logic.Outside of mathematics, statements which can be characterized informally as vacuously true can be misleading. Such statements make reasonable assertions about qualified objects which do not actually exist. For example, a child might tell his or her parent "I ate every vegetable on my plate", when there were no vegetables on the child's plate to begin with.".
- Vacuous_truth wikiPageExternalLink _Toc133208747.
- Vacuous_truth wikiPageExternalLink beer97efficient.html.
- Vacuous_truth wikiPageID "51672".
- Vacuous_truth wikiPageLength "4585".
- Vacuous_truth wikiPageOutDegree "43".
- Vacuous_truth wikiPageRevisionID "681760600".
- Vacuous_truth wikiPageWikiLink Antecedent_(logic).
- Vacuous_truth wikiPageWikiLink Binary_decision.
- Vacuous_truth wikiPageWikiLink Bolivia.
- Vacuous_truth wikiPageWikiLink Category:Logic.
- Vacuous_truth wikiPageWikiLink Category:Mathematical_logic.
- Vacuous_truth wikiPageWikiLink Category:Nothing.
- Vacuous_truth wikiPageWikiLink Category:Truth.
- Vacuous_truth wikiPageWikiLink Classical_logic.
- Vacuous_truth wikiPageWikiLink Consequent.
- Vacuous_truth wikiPageWikiLink Counterfactual_conditional.
- Vacuous_truth wikiPageWikiLink David_H._Sanford.
- Vacuous_truth wikiPageWikiLink Degeneracy_(mathematics).
- Vacuous_truth wikiPageWikiLink Eiffel_Tower.
- Vacuous_truth wikiPageWikiLink Empty_product.
- Vacuous_truth wikiPageWikiLink Empty_set.
- Vacuous_truth wikiPageWikiLink Empty_sum.
- Vacuous_truth wikiPageWikiLink Existence.
- Vacuous_truth wikiPageWikiLink France.
- Vacuous_truth wikiPageWikiLink Grammatical_modifier.
- Vacuous_truth wikiPageWikiLink Intuitionistic_logic.
- Vacuous_truth wikiPageWikiLink Lecture_Notes_in_Computer_Science.
- Vacuous_truth wikiPageWikiLink Logical_conjunction.
- Vacuous_truth wikiPageWikiLink Logical_truth.
- Vacuous_truth wikiPageWikiLink Material_conditional.
- Vacuous_truth wikiPageWikiLink Mathematical_induction.
- Vacuous_truth wikiPageWikiLink Mutatis_mutandis.
- Vacuous_truth wikiPageWikiLink Nonexistence.
- Vacuous_truth wikiPageWikiLink Paradoxes_of_material_implication.
- Vacuous_truth wikiPageWikiLink Principle_of_explosion.
- Vacuous_truth wikiPageWikiLink Pure_mathematics.
- Vacuous_truth wikiPageWikiLink Qualifier.
- Vacuous_truth wikiPageWikiLink Set_(mathematics).
- Vacuous_truth wikiPageWikiLink Statement_(logic).
- Vacuous_truth wikiPageWikiLink Supervaluationism.
- Vacuous_truth wikiPageWikiLink Tautology_(logic).
- Vacuous_truth wikiPageWikiLink The_Cambridge_Dictionary_of_Philosophy.
- Vacuous_truth wikiPageWikiLink The_Oxford_Dictionary_of_Philosophy.
- Vacuous_truth wikiPageWikiLink Trivial_(mathematics).
- Vacuous_truth wikiPageWikiLink Triviality_(mathematics).
- Vacuous_truth wikiPageWikiLink Type_(logic).
- Vacuous_truth wikiPageWikiLink Type_theory.
- Vacuous_truth wikiPageWikiLink Uluru.
- Vacuous_truth wikiPageWikiLink Well-defined.
- Vacuous_truth wikiPageWikiLink Well-definition.
- Vacuous_truth wikiPageWikiLinkText "Trivially".
- Vacuous_truth wikiPageWikiLinkText "Vacuous truth".
- Vacuous_truth wikiPageWikiLinkText "Vacuous truth".
- Vacuous_truth wikiPageWikiLinkText "a falsehood implies any proposition".
- Vacuous_truth wikiPageWikiLinkText "tautological".
- Vacuous_truth wikiPageWikiLinkText "vacuous proof".
- Vacuous_truth wikiPageWikiLinkText "vacuous truth".
- Vacuous_truth wikiPageWikiLinkText "vacuous".
- Vacuous_truth wikiPageWikiLinkText "vacuously true".
- Vacuous_truth wikiPageWikiLinkText "vacuously".
- Vacuous_truth hasPhotoCollection Vacuous_truth.
- Vacuous_truth wikiPageUsesTemplate Template:Cite_journal.
- Vacuous_truth wikiPageUsesTemplate Template:More_footnotes.
- Vacuous_truth wikiPageUsesTemplate Template:Reflist.
- Vacuous_truth subject Category:Logic.
- Vacuous_truth subject Category:Mathematical_logic.
- Vacuous_truth subject Category:Nothing.
- Vacuous_truth subject Category:Truth.
- Vacuous_truth hypernym Statement.
- Vacuous_truth type Article.
- Vacuous_truth type Article.
- Vacuous_truth type Concept.
- Vacuous_truth type Field.
- Vacuous_truth comment "A vacuous truth is a statement that asserts that all members of the empty set have a certain property. For example, the statement "all cell phones in the room are turned off" may be true simply because there are no cell phones in the room.".
- Vacuous_truth label "Vacuous truth".
- Vacuous_truth sameAs درستی_پوچ.
- Vacuous_truth sameAs באופן_ריק.
- Vacuous_truth sameAs Igazhalmaz.
- Vacuous_truth sameAs Verdade_por_vacuidade.
- Vacuous_truth sameAs m.0dmb_.
- Vacuous_truth sameAs Q1096079.
- Vacuous_truth sameAs Q1096079.
- Vacuous_truth wasDerivedFrom Vacuous_truth?oldid=681760600.
- Vacuous_truth isPrimaryTopicOf Vacuous_truth.