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Logica Universalis

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07-02-2020

A Cube of Opposition for Predicate Logic

Author: Jørgen Fischer Nilsson

Published in: Logica Universalis | Issue 1/2020

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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.

Graphic Abstract

The photo shows a prototype sculpture for the cube.

previous article Existential Import, Aristotelian Logic, and its Generalizations

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Title: A Cube of Opposition for Predicate Logic
Author: Jørgen Fischer Nilsson
Publication date: 07-02-2020
Publisher: Springer International Publishing
Published in: Logica Universalis / Issue 1/2020
Print ISSN: 1661-8297
Electronic ISSN: 1661-8300
DOI: https://doi.org/10.1007/s11787-020-00244-3

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Other articles of this Issue 1/2020

Structures of Opposition and Comparisons: Boolean and Gradual Cases

Existential Import, Aristotelian Logic, and its Generalizations

Kant’s Antinomies of Pure Reason and the ‘Hexagon of Predicate Negation’

Swyneshed, Aristotle and the Rule of Contradictory Pairs

The Cretan Square

On the Historical Transformations of the Square of Opposition as Semiotic Object

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