Dialetheism (/daɪəˈlɛθiɪzəm/; from Greek δι- di- 'twice' and ἀλήθεια alḗtheia 'truth') is the view that there are statements that are both true and false.
Dialetheists who do not want to allow that every statement is true are free to favour these over traditional, explosive logics.
Graham Priest defines dialetheism as the view that there are true contradictions.
[3] The term was coined by Graham Priest and Richard Sylvan (then Routley).
Dialetheists, on the other hand, respond to this problem by accepting the contradictions as true.
Dialetheism allows for the unrestricted axiom of comprehension in set theory, claiming that any resulting contradiction is a theorem.
Critics argue that this merely reflects an ambiguity in our language rather than a dialetheic quality in our thoughts; if we replace the given statement with one that is less ambiguous (such as "John is halfway in the room" or "John is in the doorway"), the contradiction disappears.
The statements appeared contradictory only because of a syntactic play; here, the actual meaning of "being in the room" is not the same in both instances, and thus each sentence is not the exact logical negation of the other: therefore, they are not necessarily contradictory.
The Jain philosophical doctrine of anekantavada—non-one-sidedness—states that all statements are true in some sense and false in another.
Technically, however, a logical contradiction is a proposition that is true and false in the same sense; a proposition which is true in one sense and false in another does not constitute a logical contradiction.
The Buddhist logic system, named "Catuṣkoṭi", similarly implies that a statement and its negation may possibly co-exist.
[6][7] Graham Priest argues in Beyond the Limits of Thought that dialetheia arise at the borders of expressibility, in a number of philosophical contexts other than formal semantics.
(This is often called the principle of explosion, since the truth of a contradiction is imagined to make the number of theorems in a system "explode".
)[1] The proponents of dialetheism mainly advocate its ability to avoid problems faced by other more orthodox resolutions as a consequence of their appeals to hierarchies.
According to Graham Priest, "the whole point of the dialetheic solution to the semantic paradoxes is to get rid of the distinction between object language and meta-language".
[citation needed] One criticism of dialetheism is that it fails to capture a crucial feature about negation, known as absoluteness of disagreement.