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  1. Boolean Considerations on John Buridan's Octagons of Opposition.Lorenz Demey - 2018 - History and Philosophy of Logic 40 (2):116-134.
    This paper studies John Buridan's octagons of opposition for the de re modal propositions and the propositions of unusual construction. Both Buridan himself and the secondary literature have emphasized the strong similarities between these two octagons. In this paper, I argue that the interconnection between both octagons is more subtle than has previously been thought: if we move beyond the Aristotelian relations, and also take Boolean considerations into account, then the strong analogy between Buridan's octagons starts to break down. These (...)
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  • Syncategoremata in Arabic Logic, Al-Fārābī and Avicenna.Saloua Chatti - 2014 - History and Philosophy of Logic 35 (2):167-197.
    In this paper, I raise the following problem: What terms are considered as syncategoremata in the Arabic logical texts? How are they defined? How do they determine the forms of the propositions and the inferences? To answer these questions, I focus on the analyses provided by al-Fārābī and Avicenna. Both authors apply the grammatical distinction between the particle, the noun and the verb to logic. They also state the semantic and the syntactic criterions, but their analyses of the particles are (...)
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  • Was Lewis Carroll an Amazing Oppositional Geometer?Alessio Moretti - 2014 - History and Philosophy of Logic 35 (4):383-409.
    Some Carrollian posthumous manuscripts reveal, in addition to his famous ‘logical diagrams’, two mysterious ‘logical charts’. The first chart, a strange network making out of fourteen logical sentences a large 2D ‘triangle’ containing three smaller ones, has been shown equivalent—modulo the rediscovery of a fourth smaller triangle implicit in Carroll's global picture—to a 3D tetrahedron, the four triangular faces of which are the 3+1 Carrollian complex triangles. As it happens, such an until now very mysterious 3D logical shape—slightly deformed—has been (...)
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  • Logical Geometries and Information in the Square of Oppositions.Hans Smessaert & Lorenz Demey - 2014 - Journal of Logic, Language and Information 23 (4):527-565.
    The Aristotelian square of oppositions is a well-known diagram in logic and linguistics. In recent years, several extensions of the square have been discovered. However, these extensions have failed to become as widely known as the square. In this paper we argue that there is indeed a fundamental difference between the square and its extensions, viz., a difference in informativity. To do this, we distinguish between concrete Aristotelian diagrams and, on a more abstract level, the Aristotelian geometry. We then introduce (...)
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  • Existential Import in Avicenna's Modal Logic.Saloua Chatti - 2016 - Arabic Sciences and Philosophy 26 (1):45-71.
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  • Existential Import and an Unnecessary Restriction on Predicate Logics.George Boger - 2018 - History and Philosophy of Logic 39 (2):109-134.
    Contemporary logicians continue to address problems associated with the existential import of categorical propositions. One notable problem concerns invalid instances of subalternation in the case of a universal proposition with an empty subject term. To remedy problems, logicians restrict first-order predicate logics to exclude such terms. Examining the historical origins of contemporary discussions reveals that logicians continue to make various category mistakes. We now believe that no proposition per se has existential import as commonly understood and thus it is unnecessary (...)
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