The Hamiltonian Syllogistic
- First Online:
- 70 Downloads
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.
KeywordsSyllogisms Natural language and logic Complexity Proof-theory
Unable to display preview. Download preview PDF.
- Aristotle. (1989). Prior analytics. Indianapolis, IN: Hackett (Robin Smith, Tr.).Google Scholar
- Bentham G. (1827) Outline of a new system of logic, with a critical examination of Dr. Whately’s “Elements of Logic”. Hunt and Clarke, LondonGoogle Scholar
- Hamilton S. W. (1853) Discussions on philosophy and literature, education and university reform. William Blackwood and Sons, EdinburghGoogle Scholar
- Hamilton S. W. (1860) Lectures on logic, Vol. II. William Blackwood and Sons, EdinburghGoogle Scholar
- Mill, J. S. (1979). An examination of Sir William Hamilton’s philosophy. Univerity of Toronto Press, Toronto and Buffalo. First published 1865.Google Scholar