Editing Law of noncontradiction (section)

== Alleged impossibility of its proof or denial ==
The law of non-contradiction is alleged to be neither verifiable nor falsifiable, on the ground that any proof or disproof must use the law itself prior to reaching the conclusion. In other words, in order to verify or falsify the laws of logic one must resort to logic as a weapon, an act that is argued to be [[Self-refuting idea|self-defeating]].<ref>[http://faculty.washington.edu/smcohen/AristotlePNC.pdf S.M. Cohen, ''Aristotle on the Principle of Non-Contradiction''] "''Aristotle's solution in the Posterior Analytics is to distinguish between episteme (scientific knowledge) and nous (intuitive intellect). First principles, such as PNC, are not objects of scientific knowledge - since they are not demonstrable - but are still known, since they are grasped by nous.''"</ref> Since the early 20th century, certain logicians have proposed logics that deny the validity of the law. 

Logics known as "[[paraconsistent logic|paraconsistent]]" are inconsistency-tolerant logics in that there, from P together with ¬P, it does not imply that any proposition follows. Nevertheless, not all paraconsistent logics deny the law of non-contradiction and some such logics even prove it.<ref>{{cite book |title=The law of non-contradiction : new philosophical essays |date=2004 |publisher=Clarendon Press |location=Oxford |isbn=9780199265176 |doi=10.1093/acprof:oso/9780199265176.003.0024}}</ref><ref>{{cite web |last1=Carnielli |first1=Walter |last2=Rodrigues |first2=Abilio |title=An epistemic approach to paraconsistency: a logic of evidence and truth |url=http://philsci-archive.pitt.edu/14115/1/letj.pdf |publisher=[[University of Pittsburgh|Pittsburg]] |access-date=January 20, 2024}}</ref>

Some, such as [[David Lewis (philosopher)|David Lewis]], have objected to paraconsistent logic on the ground that it is simply impossible for a statement and its negation to be jointly true.<ref>Lewis (1982)</ref> A related objection is that "negation" in paraconsistent logic is not really ''[[negation]]''; it is merely a [[Square of opposition|subcontrary]]-forming operator.<ref>Slater (1995)</ref>{{full citation needed|date=July 2016}}<ref>Béziau (2000)</ref>{{full citation needed|date=July 2016}} Those who (like the dialetheists) claim that the Law of Non-Contradiction can be violated are in fact using a different definition of negation, and therefore talking about something else other than the Law of Non-Contradiction which is based on a particular definition of negation and therefore cannot be violated.<ref>{{cite journal |last1=Loke |first1=A.T.E. |title=The Law of Non-contradiction and Global Philosophy of Religion |journal=SOPHIA |date=2024 |doi=10.1007/s11841-024-01001-5|doi-access=free }}</ref>