The Cretan square

DOI10.1007/S11787-020-00247-0zbMath1442.03003OpenAlexW3006825188MaRDI QIDQ2307711

Jean-Yves Béziau, Jens Lemanski

Publication date: 25 March 2020

Published in: Logica Universalis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11787-020-00247-0

zbMATH Keywords

analogysquare of oppositionhexagon of oppositioncube of oppositionKant's antinomiesgeometry of opposition

Mathematics Subject Classification ID

Proceedings of conferences of miscellaneous specific interest (00B25) Fuzzy logic; logic of vagueness (03B52) Philosophical and critical aspects of logic and foundations (03A05) Logic of natural languages (03B65) Classical first-order logic (03B10) Proceedings, conferences, collections, etc. pertaining to mathematical logic and foundations (03-06) Abstract deductive systems (03B22)

Cites Work

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• Platonic contrariety (\textit{enantia}): ancestor of the Aristotelian notion of contradiction (\textit{antiphasis})?
• Around and beyond the square of opposition
• The power of the hexagon
• From analogical proportion to logical proportions
• On the historical transformations of the square of opposition as semiotic object
• Swyneshed, Aristotle and the rule of contradictory pairs
• Kant's antinomies of pure reason and the `hexagon of predicate negation'
• Existential import, Aristotelian logic, and its generalizations
• A cube of opposition for predicate logic
• Structures of opposition and comparisons: Boolean and gradual cases
• The square of opposition: a cornerstone of thought

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