Editing Principle of bivalence (section)

=== Self-referential statements ===
{{main|Self-reference}}
Some [[Self-reference|self-referential statements]] like the one featured in the [[Liar paradox|liar's paradox]] can not be assigned definite truth values of neither "[[Truth|''True'']]" nor "[[Falsehood|''False'']]" without running into contradictions.<ref name="Andrew Irvine 1992">Andrew Irvine, "Gaps, Gluts, and Paradox", ''Canadian Journal of Philosophy'', supplementary vol. 18 [''Return of the A priori''] (1992), 273–299</ref> The liar paradox can be stated as: {{block indent|A: This statement (A) is false.}}If (A) is true, then "This statement is false" is true. Therefore, (A) must be false. The hypothesis that (A) is true leads to the conclusion that (A) is false, a contradiction.

If (A) is false, then "This statement is false" is false. Therefore, (A) must be true. The hypothesis that (A) is false leads to the conclusion that (A) is true, another contradiction. Either way, (A) is both true and false, which is a paradox.

Some possible resolutions of this paradox include the rejection of [[Boolean logic]] (and thus the '''principle of bivalence'''<ref>{{Citation |last=Beall |first=Jc |title=Liar Paradox |date=2023 |work=The Stanford Encyclopedia of Philosophy |editor-last=Zalta |editor-first=Edward N. |url=https://plato.stanford.edu/entries/liar-paradox/ |access-date=2025-05-11 |edition=Winter 2023 |publisher=Metaphysics Research Lab, Stanford University |last2=Glanzberg |first2=Michael and |editor2-last=Nodelman |editor2-first=Uri}}</ref>) and its replacement with any [[Multi-valued logic|many-valued logic]] like [[fuzzy logic]], in which the [[truth value]] of a [[Statement (logic)|statement]] may be any [[real number]] between 0 (denoting "''[[Falsehood]]''") and 1 (denoting "''[[Truth]]''").<ref>{{Citation |last=Cintula |first=Petr |title=Fuzzy Logic |date=2023 |work=The Stanford Encyclopedia of Philosophy |editor-last=Zalta |editor-first=Edward N. |url=https://plato.stanford.edu/entries/logic-fuzzy/ |access-date=2025-05-11 |edition=Summer 2023 |publisher=Metaphysics Research Lab, Stanford University |last2=Fermüller |first2=Christian G. |last3=Noguera |first3=Carles |editor2-last=Nodelman |editor2-first=Uri}}</ref><ref>{{cite journal |last1=Hájek |first1=P. |last2=Paris |first2=J. |last3=Shepherdson |first3=J. |date=Mar 2000 |title=The Liar Paradox and Fuzzy Logic |journal=The Journal of Symbolic Logic |volume=61 |pages=339–346 |doi=10.2307/2586541 |jstor=2586541 |s2cid=6865763 |number=1}}</ref>