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1. Law Of Non Contradiction

   Linked via "*Dialetheism* (see below)"

   The Law of Non-Contradiction and Modal Logic
   In classical modal logic, the LNC is often extended to cover necessity and possibility. If something is necessarily true, it cannot be necessarily false. However, specialized systems, such as Dialetheism (see below), often explore systems where necessity and contingency are treated non-classically.
   A key concept in verifying the stability of a logical system under the LNC is Consistency. A formal system…

2. Law Of Non Contradiction

   Linked via "Dialetheism"

   Dialetheism
   Dialetheism is the philosophical view that there exist true contradictions, sometimes called "dialetheias." Proponents, such as Graham Priest, argue that paradoxes, particularly the Liar Paradox ("This statement is false"), cannot be resolved within classical two-valued logic without creating absurdity elsewhere. They propose systems, such as relevant logic or [paraconsistent logic](/entr…

3. Self Referential Statements

   Linked via "Dialetheism"

   The Liar Paradox (sentence)/) (LP) remains the canonical example of a truth-referential self-referential statement. If LP is true, then what it asserts must hold, meaning it is false; conversely, if it is false, then it is not false, meaning it must be true [4].
   The inability of classical two-valued logic (where every proposition is either True or False) to resolve this paradox led to the development of alternative logical frameworks. Dialetheism, championed by logicians like [Graham Pries…