Paraconsistent logic! (A reply to Slater).
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Paraconsistent logic comprises a major logical theory and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative.
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Opposed to consistency is inconsistency. Using the above definition of consistency in reverse, we can describe a person to be logically inconsistent if it is impossible for all their beliefs to be true at the same time. There are two major views on the importance of logical consistency (or in reverse: how bad it is to be logically inconsistent.
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