The traditional square of opposition

Stanford Encyclopedia of Philosophy (2008)
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Abstract

This entry traces the historical development of the Square of Opposition, a collection of logical relationships traditionally embodied in a square diagram. This body of doctrine provided a foundation for work in logic for over two millenia. For most of this history, logicians assumed that negative particular propositions ("Some S is not P") are vacuously true if their subjects are empty. This validates the logical laws embodied in the diagram, and preserves the doctrine against modern criticisms. Certain additional principles ("contraposition" and "obversion") were sometimes adopted along with the Square, and they genuinely yielded inconsistency. By the nineteenth century an inconsistent set of doctrines was widely adopted. Strawson's 1952 attempt to rehabilitate the Square does not apply to the traditional doctrine; it does salvage the nineteenth century version but at the cost of yielding inferences that lead from truth to falsity when strung together.

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Terence Parsons
University of California, Los Angeles

Citations of this work

Logical Geometries and Information in the Square of Oppositions.Hans5 Smessaert & Lorenz6 Demey - 2014 - Journal of Logic, Language and Information 23 (4):527-565.
The Cube, the Square and the Problem of Existential Import.Saloua Chatti & Fabien Schang - 2013 - History and Philosophy of Logic 34 (2):101-132.
Nearly every normal modal logic is paranormal.Joao Marcos - 2005 - Logique Et Analyse 48 (189-192):279-300.

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References found in this work

Logic Matters.Peter Thomas Geach - 1972 - Berkeley, CA, USA: Blackwell.
The Development of Logic.William Kneale & Martha Kneale - 1962 - Studia Logica 15:308-310.
Elements of Logic.Richard Whately - 1826 - London, England: Scholars' Facsimiles & Reprints.

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