Logica Universalis 14 (1):69-102 (2020)

Corina Strößner
Heinrich Heine University Düsseldorf
The paper uses the theory of generalized quantifiers to discuss existential import and its implications for Aristotelian logic, namely the square of opposition, conversions and the assertoric syllogistic, as well as for more recent generalizations to intermediate quantifiers like “most”. While this is a systematic discussion of the semantic background one should assume in order to obtain the inferences and oppositions Aristotle proposed, it also sheds some light on the interpretation of his writings. Moreover by applying tools from modern formal semantics to the investigation of classical Aristotelian logic and its extensions, we combine different approaches to the logic of quantification. We will present variants of quantifiers that are associated to the four corners of the square of opposition with and without existential import and discuss their role for the logical square, conversions and the syllogistic. It will turn out that there is no way to ascribe existential import that validates all inferences and relations which one is willing to hold in Aristotelian logic. Two options, however, provide reasonable results. Existential import should either be ascribed only to affirmative statements or only be ascribed to universal quantification. The former option is preferable for a mere reconstruction of the classical Aristotelian logic while the latter option is more attractive if Aristotelian logic is generalized to intermediate quantifiers.
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DOI 10.1007/s11787-020-00245-2
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References found in this work BETA

Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Generalized Quantifiers and Natural Language.Jon Barwise - 1980 - Linguistics and Philosophy 4:159.
Aristotle and Łukasiewicz on Existential Import.Stephen Read - 2015 - Journal of the American Philosophical Association 1 (3):535--544.
The Cube, the Square and the Problem of Existential Import.Saloua Chatti & Fabien Schang - 2013 - History and Philosophy of Logic 34 (2):101-132.
Questions About Quantifiers.Johan van Benthem - 1984 - Journal of Symbolic Logic 49 (2):443-466.

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Citations of this work BETA

The Cretan Square.Jean-Yves Beziau & Jens Lemanski - 2020 - Logica Universalis 14 (1):1-5.

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