A Cube of Opposition for Predicate Logic

Logica Universalis 14 (1):103-114 (2020)
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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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Citations of this work

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

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References found in this work

Treatise on Consequences.John Buridan - 2020 - Fordham University Press.
Aristotle's Modal Syllogistic.Marko Malink - 2013 - Cambridge, MA and London: Harvard 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 - 2008 - Oxford University Press.

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