The Hamiltonian Syllogistic

Details The Hamiltonian Syllogistic The Hamiltonian Syllogistic

2010-11-12

arxiv.org/abs/1011.2973v1

Computer Science

Logic in Computer Science

30 pages

Scientific paper

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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