MoL 10: Dag Westerståhl (Goteburg University)


Logico-linguistic issues around classical and modern squares of opposition


The classical square of opposition incorporates basic elements of (universal and existential) quantification and of negation. Since Aristotle there is an ongoing debate about its exact properties and its accuracy for natural language. The debate intensified with the advent of modern logic, and the corresponding modern square, bringing in issues of existential import, presupposition, and implicature. In contrast with most commentators I want to argue in favor of the modern square, and not just for technical reasons. The main value of the modern square is that it applies to all (generalized) quantifiers (of the right type), thereby illustrating three basic forms of negation, something the classical square cannot do. After a brief overview of the main issues of the debate, and a presentation of classical and modern squares and their properties, I look at the (modern) squares generated by certain numerical, proportional, exceptive, possessive, and partitive quantifiers. This not only brings out interesting features of these forms of quantification, I claim, but also puts the issues of existential import etc. in a wider and more fruitful perspective.

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