Classical vs. modern Squares of Opposition, and beyond
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)
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.
square of opposition, generalized quantifiers, possessive quantifiers
Philosophy General Language Studies and Linguistics
Research subject Theoretical Philosophy
IdentifiersURN: urn:nbn:se:su:diva-85107ISBN: 978-3-0343-0537-2OAI: oai:DiVA.org:su-85107DiVA: diva2:582659
FunderSwedish Research Council