Synthetic logic

Synthetic logic is a non-standard system of paraconsistent logic. It allows contradictions to exist as meaningful components of language. Synthetic logic is based on the law of non-identity (A is not A) and the law of contradiction (A is −A). These laws are the exact opposite of the two basic laws of standard, analytic logic: the law of identity (A is A) and the law of non-contradiction (A is not −A).
This way of distinguishing between two types of logic was first suggested by Stephen Palmquist in connection with his perspectival interpretation of Immanuel Kant and, as part of the geometry of logic, has been defended and applied in numerous contexts.
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