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.
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References
Corcoran, J.: Completeness of an ancient logic. J. Symb. Log. 37, 696–702 (1972)
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)
Englebretsen, G.: Linear diagrams for syllogisms (with relationals). Notre Dame J. Form. Log. 33(1), 37–69 (1992)
Głazowska, K.: The structure of valid n-term syllogisms. Stud. Log. 8, 249–257 (1958)
Hammer, E.: Reasoning with sentences and diagrams. Notre Dame J. Form. Log. 35(1), 73–87 (1994)
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)
Lemon, O., Pratt, I.: On the insufficiency of linear diagrams for syllogisms. Notre Dame J. Form. Log. 39(4), 573–580 (1998)
Łukasiewicz, J.: Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic. Clarendon, Oxford (1951)
Meredith, C.A.: The figures and moods of the n-term Aristotelian syllogism. Domin. Studies 6, 42–47 (1953)
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)
Smiley, T.J.: What is a syllogism? J. Philos. Log. 2, 136–154 (1973)
Smyth, M.B.: A diagrammatic treatment of syllogistic. Notre Dame J. Form. Log. 12(4), 483–488 (1971)
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Pagnan, R. (2013). A Diagrammatic Calculus of Syllogisms. In: Moktefi, A., Shin, SJ. (eds) Visual Reasoning with Diagrams. Studies in Universal Logic. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0600-8_3
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DOI: https://doi.org/10.1007/978-3-0348-0600-8_3
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