The Hamiltonian Syllogistic

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 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.
Keywords Syllogisms  Natural language and logic  Complexity  Proof-theory
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References found in this work BETA
John Corcoran (1972). Completeness of an Ancient Logic. Journal of Symbolic Logic 37 (4):696-702.

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Citations of this work BETA
Ian Pratt-Hartmann (2013). The Syllogistic with Unity. Journal of Philosophical Logic 42 (2):391-407.
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