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arXiv · 1011.2973

The Hamiltonian Syllogistic

Ian Pratt-Hartmann
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Abstract

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 are q" is to be understood as "All p are some q". Second, these implicit quantifiers can be meaningfully dualized to yield novel sentence-forms, such as, for example, "All p are 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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Ian Pratt-Hartmann. 2010-11-12. The Hamiltonian Syllogistic. https://doi.org/10.1007/s10849-011-9144-y

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