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 reality...in order to avoid having to internalize the possibility
of dialetheism metaphysically.
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