Journal of Logic, Language and Information 20 (4):445-474 (2011)
|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|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Philip L. Peterson (1991). Complexly Fractionated Syllogistic Quantifiers. Journal of Philosophical Logic 20 (3):287 - 313.
Bart Geurts (2003). Reasoning with Quantifiers. Cognition 86 (3):223--251.
Ian Pratt-Hartmann (2008). On the Computational Complexity of the Numerically Definite Syllogistic and Related Logics. Bulletin of Symbolic Logic 14 (1):1-28.
Ian Pratt-Hartmann (2013). The Syllogistic with Unity. Journal of Philosophical Logic 42 (2):391-407.
Phil Corkum (forthcoming). Is Aristotle's Syllogistic a Logic? History and Philosophy of Logic.
Fred Johnson (1994). Syllogisms with Fractional Quantifiers. Journal of Philosophical Logic 23 (4):401 - 422.
W. Bednarowski (1955). Hamilton's Quantification of the Predicate. Proceedings of the Aristotelian Society 56:217 - 240.
Edgar Jose Andrade & Edward Samuel Becerra (2008). Establishing Connections Between Aristotle's Natural Deduction and First-Order Logic. History and Philosophy of Logic 29 (4):309-325.
Marko Malink (2006). A Reconstruction of Aristotle's Modal Syllogistic. History and Philosophy of Logic 27 (2):95-141.
Janet Folina (2012). Newton and Hamilton: In Defense of Truth in Algebra. Southern Journal of Philosophy 50 (3):504-527.
Guy Politzer (2003). No Problem for Aristotle's Subject and Predicate. Behavioral and Brain Sciences 26 (3):298-299.
N. E. Wetherick (1989). Psychology and Syllogistic Reasoning. Philosophical Psychology 2 (1):111 – 124.
John N. Martin (2001). Proclus and the Neoplatonic Syllogistic. Journal of Philosophical Logic 30 (3):187-240.
Added to index2011-10-18
Total downloads6 ( #154,724 of 722,859 )
Recent downloads (6 months)1 ( #60,917 of 722,859 )
How can I increase my downloads?