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A Diagrammatic Calculus of Syllogisms

  • Ruggero Pagnan
Part of the Studies in Universal Logic book series (SUL)

Abstract

A diagrammatic calculus of syllogisms is introduced and discussed, so that a syllogism is valid if and only if its conclusion follows from its premises by calculation. The calculus at issue allows the easy retrieving of the traditional rules of the syllogism and of the laws of the square of opposition. Moreover, it extends to n-term syllogisms and to syllogisms with complemented terms. In this respect, a comparison with De Morgan’s spicular notation is treated.

Keywords

Syllogism Syllogistic diagram Syllogistic inference 

Mathematics Subject Classification

03B65 

References

  1. 1.
    Corcoran, J.: Completeness of an ancient logic. J. Symb. Log. 37, 696–702 (1972) MathSciNetCrossRefGoogle Scholar
  2. 2.
    De Morgan, A.: On the symbols of logic, the theory of the syllogism, and in particular of the copula, and the application of the theory of probabilities, to some questions of evidence. Trans. Camb. Philos. Soc. 9, 79–127 (1851) Google Scholar
  3. 3.
    Englebretsen, G.: Linear diagrams for syllogisms (with relationals). Notre Dame J. Form. Log. 33(1), 37–69 (1992) MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Głazowska, K.: The structure of valid n-term syllogisms. Stud. Log. 8, 249–257 (1958) zbMATHCrossRefGoogle Scholar
  5. 5.
    Hammer, E.: Reasoning with sentences and diagrams. Notre Dame J. Form. Log. 35(1), 73–87 (1994) MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Hobart, M.E., Richards, J.L.: De Morgan’s logic. In: Handbook of the History of Logic, vol. 4, British Logic in the Nineteenth Century, pp. 283–329. Elsevier, Amsterdam (2008) CrossRefGoogle Scholar
  7. 7.
    Lemon, O., Pratt, I.: On the insufficiency of linear diagrams for syllogisms. Notre Dame J. Form. Log. 39(4), 573–580 (1998) MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Łukasiewicz, J.: Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic. Clarendon, Oxford (1951) zbMATHGoogle Scholar
  9. 9.
    Meredith, C.A.: The figures and moods of the n-term Aristotelian syllogism. Domin. Studies 6, 42–47 (1953) Google Scholar
  10. 10.
    Shin, S.-J.: Situation-theoretic account of valid reasoning with Venn diagrams. In: Logical Reasoning with Diagrams. Stud. Logic Comput., vol. 6, pp. 81–108. Oxford University Press, New York (1996) Google Scholar
  11. 11.
    Smiley, T.J.: What is a syllogism? J. Philos. Log. 2, 136–154 (1973) zbMATHCrossRefGoogle Scholar
  12. 12.
    Smyth, M.B.: A diagrammatic treatment of syllogistic. Notre Dame J. Form. Log. 12(4), 483–488 (1971) zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.DISIUniversity of GenoaGenoaItaly

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