A Cube of Opposition for Predicate Logic

Logica Universalis 14 (1):103-114 (2020)
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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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The Cretan Square.Jean-Yves Beziau & Jens Lemanski - 2020 - Logica Universalis 14 (1):1-5.

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References found in this work

Aristotle's Modal Syllogistic.Marko Malink - 2013 - Cambridge, MA and London: Harvard University Press.
Treatise on Consequences.John Buridan - 2020 - Fordham University Press.
The traditional square of opposition.Terence Parsons - 2008 - Stanford Encyclopedia of Philosophy.
Aristotle and Łukasiewicz on Existential Import.Stephen Read - 2015 - Journal of the American Philosophical Association 1 (3):535--544.
John Buridan.Gyula Klima - 2009 - New York: Oxford University Press.

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