The Hamiltonian Syllogistic
- Ian Pratt-Hartmann
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This paper undertakes a re-examination of Sir William Hamilton’s doctrine of the quantification of the predicate. Hamilton’s doctrine comprises two theses. First, the predicates of traditional syllogistic sentence-forms contain implicit existential quantifiers, so that, for example, All p is q is to be understood as All p is some q. Second, these implicit quantifiers can be meaningfully dualized to yield novel sentence-forms, such as, for example, All p is all q. Hamilton attempted to provide a deductive system for his language, along the lines of the classical syllogisms. We show, using techniques unavailable to Hamilton, that such a system does exist, though with qualifications that distinguish it from its classical counterpart.
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- The Hamiltonian Syllogistic
Journal of Logic, Language and Information
Volume 20, Issue 4 , pp 445-474
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- Springer Netherlands
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- Natural language and logic
- Author Affiliations
- 1. School of Computer Science, University of Manchester, Manchester, M13 9PL, UK