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The traditional square of opposition and generalized quantifiers

Studies in Logic (Beijing)
Year of publication: 
Scientific journal article - peer reviewed

The Aristotelian square of opposition is compared with the modern (Fregean) one. It is argued that the main difference does not concern existential import but the role of negation in language. The modern square applies to any type <1,1> (generalized) quantifier, with outer and inner negation, and dual. Squares pertaining to various quantifiers are investigated. In particular, possessive quantifiers exhibit interesting behavior under negation, resulting in two different squares, or more precisely, a cube, of opposition.

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Page updated: 2012-01-30 14:02

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