Principle of bivalence

"Bivalence" redirects here. For other uses, see Bivalent (disambiguation).

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 true or false. [1][2] A logic satisfying this principle is called a two-valued logic[3] or bivalent logic.[2][4]

In formal logic, the principle of bivalence becomes a property that a 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.[2]

The principle of bivalence is studied in philosophical logic to address the question of which 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.[2] Many-valued logics formalize ideas that a realistic characterization of the notion of consequence requires the admissibility of premises that, owing to vagueness, temporal or quantum indeterminacy, or reference-failure, cannot be considered classically bivalent. Reference failures can also be addressed by free logics.[5]

  1. ^ Cite error: The named reference Goble2001bis was invoked but never defined (see the help page).
  2. ^ a b c d Paul Tomassi (1999). Logic. Routledge. p. 124. ISBN 978-0-415-16696-6.
  3. ^ Lou Goble (2001). The Blackwell guide to philosophical logic. Wiley-Blackwell. p. 4. ISBN 978-0-631-20693-4.
  4. ^ Mark Hürlimann (2009). Dealing with Real-World Complexity: Limits, Enhancements and New Approaches for Policy Makers. Gabler Verlag. p. 42. ISBN 978-3-8349-1493-4.
  5. ^ Dov M. Gabbay; John Woods (2007). The Many Valued and Nonmonotonic Turn in Logic. The handbook of the history of logic. Vol. 8. Elsevier. p. vii. ISBN 978-0-444-51623-7.