David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Proceedings of the Aristotelian Society 56:217 - 240 (1955)
This paper consists roughly of three parts. In the first part, an attempt has been made to find some tenable interpretation of Hamilton's logic. This results in accepting that Hamilton's logic can be "saved" if it is understood as being an everday language version of Euler's relations, i.e., extensional relations between terms (classes). In the second part, the propositions of Euler and the propositions of Aristotle are compared and found to be interdefinable: every proposition of Aristotle can be defined by a disjunction of Euler's propositions, and every proposition of Euler can be defined by a conjunction of Aristotle's propositions. In the third part, extensional interpretation is applied to the traditional logic. As a result the 19 traditional syllogisms are reduced to 11.
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