David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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History and Philosophy of Logic 17 (1-2):141-154 (1996)
There have been and continue to be disagreements about how to consider the traditional square of opposition and the traditional inferences of obversion, conversion, contraposition and inversion from the perspective of contemporary quantificational logic. Philosophers have made many different attempts to save traditional inferences that are invalid when they involve empty classes. I survey some of these attempts and argue that the only satisfactory way of saving all the traditional inferences is to make the existential assumption that both the subject and predicate classes and their complement classes are non-empty for all the propositions we admit. I briefly indicate the room for continued controversy over how properly to interpret Aristotle?s statements regarding these inferences, but find some plausibility in the views of Manley Thompson and A.N.Prior that Aristotle had in mind a particular arrangement of existential import unfamiliar to most contemporary logicians
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References found in this work BETA
Peter Alexander (1969). An Introduction to Logic. New York, Schocken Books.
Aristotle (1984). The Complete Works of Aristotle: The Revised Oxford Translation. Princeton University Press.
Michael Clark (1980). The Place of Syllogistic in Logical Theory. Nottingham University Press.
P. Coffey (1938). The Science of Logic. New York, P. Smith.
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