Dialetheism is the view that some statements can be both true and false 
simultaneously. More precisely, it is the belief that there can be a true 
statement whose negation is also true. Such statements are called "true 
contradictions", or dialetheia.

Dialetheism is not a system of formal logic; instead, it is a thesis about 
truth, that influences the construction of a formal logic, often based on 
pre-existing systems. Introducing dialetheism has various consequences, 
depending on the theory into which it is introduced. For example, in 
traditional systems of logic (e.g., classical logic and intuitionistic 
logic), every statement becomes true if a contradiction is true; this means 
that such systems become trivial when dialetheism is included as an axiom. 
Other logical systems do not explode in this manner when contradictions are 
introduced; such contradiction-tolerant systems are known as paraconsistent 

Graham Priest defines dialetheism as the view that there are true 
contradictions. JC Beall is another advocate; his position differs from 
Priest's in advocating constructive (methodological) deflationism regarding 
the truth predicate.
Dialetheism resolves certain paradoxes

The Liar's paradox and Russell's paradox deal with self-contradictory 
statements in classical logic and naïve set theory, respectively. 
Contradictions are problematic in these theories because they cause the 
theories to explode—if a contradiction is true, then every proposition is 
true. The classical way to solve this problem is to ban contradictory 
statements, to revise the axioms of the logic so that self-contradictory 
statements do not appear. 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.

It occurs to me that MWI is a way of substantiating dialetheism as a 
physical order to avoid having to internalize the possibility 
of dialetheism metaphysically.


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