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  1. Contrariety re-encountered: nonstandard contraries and internal negation*.Lloyd Humberstone - 2023 - Logic Journal of the IGPL 31 (6):1084-1134.
    This discussion explores the possibility of distinguishing a tighter notion of contrariety evident in the Square of Opposition, especially in its modal incarnations, than as that binary relation holding statements that cannot both be true, with or without the added rider ‘though can both be false’. More than one theorist has voiced the intuition that the paradigmatic contraries of the traditional Square are related in some such tighter way—involving the specific role played by negation in contrasting them—that distinguishes them from (...)
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  • Truth and Contradiction in Aristotle’s De Interpretatione 6-9.Russell E. Jones - 2010 - Phronesis 55 (1):26-67.
    In De Interpretatione 6-9, Aristotle considers three logical principles: the principle of bivalence, the law of excluded middle, and the rule of contradictory pairs (according to which of any contradictory pair of statements, exactly one is true and the other false). Surprisingly, Aristotle accepts none of these without qualification. I offer a coherent interpretation of these chapters as a whole, while focusing special attention on two sorts of statements that are of particular interest to Aristotle: universal statements not made universally (...)
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