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
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,351
External links
  •   Try with proxy.
  • Through your library Configure
    References found in this work BETA
    John Corcoran (1972). Completeness of an Ancient Logic. Journal of Symbolic Logic 37 (4):696-702.

    View all 9 references

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

    Monthly downloads

    Added to index

    2011-10-18

    Total downloads

    6 ( #162,690 of 1,088,371 )

    Recent downloads (6 months)

    1 ( #69,449 of 1,088,371 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature


    Discussion
    Start a new thread
    Order:
    There  are no threads in this forum
    Nothing in this forum yet.