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If not, is there a set of accepted properties or qualities that dialetheic statements have?

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  • Hi there, welcome aboard! At risk of asking something that probably seems a bit silly, do you mean more than just "that as well as being false, they are also true"?
    – Paul Ross
    Commented Jan 2, 2023 at 7:05
  • Yes. I'm looking for something along the lines of "contradictions of this form 'p' are dialetheia", or if the output of this algorithm is 'x' then this contradiction is a dialetheia.
    – help-me
    Commented Jan 2, 2023 at 7:15
  • Formally, any contradiction is a dialetheia, both true and false. However, this is interesting only when the formal system does not derive that every statement is a contradiction, which classical systems do if they derive at least one. Thus, which statements end up as dialetheias in non-classical systems depends on informal wishes of their designers, so there are no "accepted properties". But some paradigmatic examples are listed by SEP: self-referential paradoxes, transitional states, borderline cases, legal collisions, etc.
    – Conifold
    Commented Jan 2, 2023 at 11:01
  • Offhand, based on a very incomplete survey of the literature, I would say that my only impression of a unifying theme, here, is that dialetheias are acceptable when their conjuncts are independently derived. Axiomatic dialetheias don't seem to be proposed (to my knowledge). The liar paradox is a difficult case vs. this picture of things, though (is the base sentence itself advanced as if it were an axiom? or at least a hypothesis? and how does attaching truth or falsity to the base "from the outside" avoid dialogically transforming that base?). Commented Jan 2, 2023 at 13:52
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    This is one of those rare occasions when I disagree with @Conifold. If a theory is closed under an explosive logic, such as classical logic, then an inconsistent theory includes all sentences as theorems. But this does not mean that all sentences are true; one should not conflate truth with theoremhood. Model theory for classical logic assigns a valuation false to any contradiction...
    – Bumble
    Commented Jan 3, 2023 at 2:53

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