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Logic in Opposition

Studia Humana 2 (3):31-45 (2013)

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  1. Questions and Answers about Oppositions.Fabien Schang - 2011 - In Jean-Yves Beziau & Gillman Payette (eds.), The Square of Opposition: A General Framework for Cognition. Peter Lang. pp. 289-319.
    A general characterization of logical opposition is given in the present paper, where oppositions are defined by specific answers in an algebraic question-answer game. It is shown that opposition is essentially a semantic relation of truth values between syntactic opposites, before generalizing the theory of opposition from the initial Apuleian square to a variety of alter- native geometrical representations. In the light of this generalization, the famous problem of existential import is traced back to an ambiguous interpretation of assertoric sentences (...)
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  • Oppositions and opposites.Fabien Schang - 2012 - In Jean-Yves Béziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. New York: Springer Verlag. pp. 147--173.
    A formal theory of oppositions and opposites is proposed on the basis of a non- Fregean semantics, where opposites are negation-forming operators that shed some new light on the connection between opposition and negation. The paper proceeds as follows. After recalling the historical background, oppositions and opposites are compared from a mathematical perspective: the first occurs as a relation, the second as a function. Then the main point of the paper appears with a calculus of oppositions, by means of a (...)
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  • Abstract Logic of Oppositions.Fabien Schang - 2012 - Logic and Logical Philosophy 21 (4):415--438.
    A general theory of logical oppositions is proposed by abstracting these from the Aristotelian background of quantified sentences. Opposition is a relation that goes beyond incompatibility (not being true together), and a question-answer semantics is devised to investigate the features of oppositions and opposites within a functional calculus. Finally, several theoretical problems about its applicability are considered.
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  • The Cube, the Square and the Problem of Existential Import.Saloua Chatti & Fabien Schang - 2013 - History and Philosophy of Logic 34 (2):101-132.
    We re-examine the problem of existential import by using classical predicate logic. Our problem is: How to distribute the existential import among the quantified propositions in order for all the relations of the logical square to be valid? After defining existential import and scrutinizing the available solutions, we distinguish between three possible cases: explicit import, implicit non-import, explicit negative import and formalize the propositions accordingly. Then, we examine the 16 combinations between the 8 propositions having the first two kinds of (...)
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  • Interpretation. Aristotle - unknown
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  • On negation: Pure local rules.João Marcos - 2005 - Journal of Applied Logic 3 (1):185-219.
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  • Contrariety.Storrs McCall - 1967 - Notre Dame Journal of Formal Logic 8 (1-2):121-132.
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  • Classical logical relations.A. J. Baker - 1977 - Notre Dame Journal of Formal Logic 18 (1):164-168.
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