Logica Universalis 14 (1):103-114 (2020)

Abstract
The traditional square of opposition is generalized and extended to a cube of opposition covering and conveniently visualizing inter-sentential oppositions in relational syllogistic logic with the usual syllogistic logic sentences obtained as special cases. The cube comes about by considering Frege–Russell’s quantifier predicate logic with one relation comprising categorical syllogistic sentence forms. The relationships to Buridan’s octagon, to Aristotelian modal logic, and to Klein’s 4-group are discussed.GraphicThe photo shows a prototype sculpture for the cube.
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DOI 10.1007/s11787-020-00244-3
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References found in this work BETA

Aristotle and Łukasiewicz on Existential Import.Stephen Read - 2015 - Journal of the American Philosophical Association 1 (3):535--544.
John Buridan.Gyula Klima - 2009 - In H. Lagerlund (ed.), Encyclopedia of Medieval Philosophy. Springer. pp. 597--603.
Leibniz’s Logic and the “Cube of Opposition”.Wolfgang Lenzen - 2016 - Logica Universalis 10 (2-3):171-189.

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Citations of this work BETA

The Cretan Square.Jean-Yves Beziau & Jens Lemanski - 2020 - Logica Universalis 14 (1):1-5.

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