Editing Principle of bivalence (section)

{{Short description|Classical logic of two values, either true or false}}
{{Redirect|Bivalence||Bivalent (disambiguation)}}
{{Use dmy dates|date=June 2020}}
In [[logic]], the semantic '''principle''' (or '''law''') '''of bivalence''' states that every declarative sentence expressing a [[proposition]] (of a theory under inspection) has exactly one [[truth value]], either [[Truth|true]] or [[false (logic)|false]]. <ref name="Goble2001bis"/><ref name="Tomassi1999">{{cite book|author=Paul Tomassi|title=Logic|url=https://books.google.com/books?id=TUVQr6InyNYC&pg=PA124|year=1999|publisher=Routledge|isbn=978-0-415-16696-6|page=124}}</ref> A logic satisfying this principle is called a '''two-valued logic'''<ref name="Goble2001">{{cite book|author=Lou Goble|title=The Blackwell guide to philosophical logic|url=https://books.google.com/books?id=aaO2f60YAwIC&pg=PA4|year=2001|publisher=Wiley-Blackwell|isbn=978-0-631-20693-4|page=4}}</ref> or '''bivalent logic'''.<ref name="Tomassi1999"/><ref name="Hürlimann2009">{{cite book|author=Mark Hürlimann|title=Dealing with Real-World Complexity: Limits, Enhancements and New Approaches for Policy Makers|url=https://books.google.com/books?id=_BThojvh-XUC&pg=PA42|year=2009|publisher=Gabler Verlag|isbn=978-3-8349-1493-4|page=42}}</ref>

In formal logic, the principle of bivalence becomes a property that a [[formal semantics (logic)|semantics]] may or may not possess. It is not the same as the [[law of excluded middle]], however, and a semantics may satisfy that law without being bivalent.<ref name="Tomassi1999"/>

The principle of bivalence is studied in [[philosophical logic]] to address the question of which [[Natural language|natural-language]] statements have a well-defined truth value. Sentences that predict events in the future, and sentences that seem open to interpretation, are particularly difficult for philosophers who hold that the principle of bivalence applies to all declarative natural-language statements.<ref name="Tomassi1999"/> [[Many-valued logic]]s formalize ideas that a realistic characterization of the [[Entailment|notion of consequence]] requires the admissibility of premises that, owing to vagueness, temporal or [[quantum indeterminacy]], or [[failure to refer|reference-failure]], cannot be considered classically bivalent. Reference failures can also be addressed by [[free logic]]s.<ref name="GabbayWoods2007">{{cite book|author1=Dov M. Gabbay|author2=John Woods|title=The Many Valued and Nonmonotonic Turn in Logic|url=https://books.google.com/books?id=3TNj1ZkP3qEC&pg=PA7|year=2007|publisher=Elsevier|isbn=978-0-444-51623-7|page=vii|series=The handbook of the history of logic|volume=8}}</ref>