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Classical vs. modern Squares of Opposition, and beyond
Stockholm University, Faculty of Humanities, Department of Philosophy.
2012 (English)In: The Square of Opposition : A General Framework for Cognition / [ed] Beziau, Jean-Yves & Payette, Gillman, Bern: Peter Lang Publishing Group, 2012, 195-229 p.Chapter in book (Refereed)
Abstract [en]

The main difference between the classical Aristotelian square of oppo- sition and the modern one is not, as many seem to think, that the classical square has or presupposes existential import. The difference lies in the relations holding along the sides of the square: (sub)contrariety and sub- alternation in the classical case, inner negation and dual in the modern case. This is why the modern square, but not the classical one, applies to any (generalized) quantifier of the right type: all, no, more than three, all but five, most, at least two-thirds of the,... After stating these and other logical facts about quantified squares of opposition, we present a number of examples of such squares spanned by familiar quantifiers. Spe- cial attention is paid to possessive quantifiers, such Mary’s, at least two students’, etc., whose behavior under negation is more complex and in fact can be captured in a cube of opposition.

Place, publisher, year, edition, pages
Bern: Peter Lang Publishing Group, 2012. 195-229 p.
Keyword [en]
square of opposition, generalized quantifiers, possessive quantifiers
National Category
Philosophy General Language Studies and Linguistics
Research subject
Theoretical Philosophy
URN: urn:nbn:se:su:diva-85107ISBN: 978-3-0343-0537-2OAI: diva2:582659
Swedish Research Council
Available from: 2013-01-06 Created: 2013-01-06

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