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Classical vs. modern Squares of Opposition, and beyond

J.-Y- Beziau and G. Payette (eds.), The Square of Opposition, Bern: Peter Lang.
Year of publication: 
Scientific journal article - peer reviewed

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.

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