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A Bunch of Diagrammatic Methods for Syllogistic

  • Frank Thomas SautterEmail author
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Abstract

This paper presents, assesses, and compares six diagrammatic methods for Categorical Syllogistic. Venn’s Method is widely used in logic textbooks; Carroll’s Method is a topologically indistinguishable version of Venn’s Method; and the four remaining methods are my own: the Dual of Carroll’s Method, Gardner’s Method, Gardner–Peirce’s Method, and Ladd’s Method. These methods are divided into two groups of three and the reasons for switching from a method to another within each group are discussed. Finally, a comparison between the Dual of Carroll’s Method and Ladd’s Method supports the main result of the paper, which is an approximation of the two groups of methods.

Keywords

Diagrammatic methods Quantity Representation of propositions Representation of terms Single rule 

Mathematics Subject Classification

Primary 03B80 

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References

  1. 1.
    Carroll, L.: The Game of Logic. Macmillan, New York (1887)Google Scholar
  2. 2.
    Carroll, L.: Symbolic Logic. Edited, Annotated, with An Introduction by William Warren Bartley III. Clarkson N. Potter, New York (1977)Google Scholar
  3. 3.
    Edwards, A.W.F.: Cogwheels of the Mind: The Story of Venn Diagrams. Johns Hopkins University Press, Baltimore (2004)zbMATHGoogle Scholar
  4. 4.
    Gardner, M.: A network diagram for the propositional calculus. In: Gardner, M. (ed.) Logic Machines and Diagrams, pp. 60–79. McGraw Hill, New York (1958)Google Scholar
  5. 5.
    Gardner, M.: Propositional calculus with directed graphs. In: Gardner, M. (ed.) A Gardner’s Workout: Training the Mind and Entertaining the Spirit, pp. 25–33. A. K. Peters, Natick (2001)CrossRefGoogle Scholar
  6. 6.
    Keynes, J.N.: Studies and Exercises in Formal Logic. Macmillan, New York (1884)Google Scholar
  7. 7.
    Ladd, C.: On the algebra of logic. In: Peirce, C.S. (ed.) Studies in Logic by Members of the Johns Hopkins University, pp. 17–71. Little, Brown and Company, Boston (1883)CrossRefGoogle Scholar
  8. 8.
    Ladd-Franklin, C.: The antilogism. Mind New Ser. 37, 532–534 (1928)CrossRefGoogle Scholar
  9. 9.
    Russinoff, S.: The syllogism’s final solution. Bull. Symb. Log. 5, 451–469 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Sautter, F.T.: Lewis Carroll e a Pré-história das Árvores de Refutação [Lewis Carroll and the Prehistory of Refutation Trees, in Brazilian Portuguese]. In: Sautter, F.T., Feitosa, H.A. (eds.) Lógica: teoria, aplicações e reflexões, pp. 91–103. UNICAMP, Campinas (2004)Google Scholar
  11. 11.
    Sautter, F.T.: A Essência do Silogismo: uma Abordagem Visual [the essence of syllogism: a visual approach, in Brazilian Portuguese]. Cognitio 11, 316–332 (2010)Google Scholar
  12. 12.
    Sautter, F.T.: As Regras Supremas dos Silogismos [the supreme rules of syllogism, in Brazilian Portuguese]. Kant e-Prints (Online) 5, 15–26 (2010)Google Scholar
  13. 13.
    Sautter, F.T.: Dois Novos Métodos para a Teoria do Silogismo: Método Diagramático e Método Equacional [two new methods for the theory of syllogism: a diagrammatic method and an equational method, in Brazilian Portuguese]. Notae Philosophicae Scientiae Formalis 1, 14–22 (2012)Google Scholar
  14. 14.
    Sautter, F.T.: Método de Gardner para a Silogística [Gardner’s method for syllogistic, in Brazilian Portuguese]. Cognitio 14, 221–234 (2013)Google Scholar
  15. 15.
    Sautter, F.T., Mendonça, B.R.: Argumentos Exuberantes e sua Retificação [exuberant arguments and their rectification, in Brazilian Portuguese]. Analytica 18, 109–121 (2014)Google Scholar
  16. 16.
    Sautter, F.T., Feitosa, H.A.: Grafos de Peirce Ad Absurdum [Peirce’s graphs ad absurdum, in Brazilian Portuguese]. Cognitio 16, 153–168 (2015)Google Scholar
  17. 17.
    Sautter, F.T.: Gráficos de Peirce sin Pérdida de Información [Peirce’s graphs without loss of information, in Spanish]. Representaciones 12, 1–13 (2016)Google Scholar
  18. 18.
    Sautter, F.T.: O Comércio da Lógica [the trade of logic, in Brazilian Portuguese]. Dissertatio 44, 151–169 (2016)CrossRefGoogle Scholar
  19. 19.
    Sautter, F.T.: Diagramas para Juízos Infinitos [diagrams for infinite judgments, in Brazilian Portuguese]. Revista Portuguesa de Filosofia 73, 115–1136 (2017)Google Scholar
  20. 20.
    Sautter, F.T.: Método de Gardner-Peirce para a Silogística [Gardner–Peirce’s Method for syllogistic, in Brazilian Portuguese]. Cognitio 19, 296–308 (2018)Google Scholar
  21. 21.
    Sautter, F.T.: Diagramas para o Antilogismo de Ladd [diagrams for Ladd’s antilogism, in Brazilian Portuguese]. Dissertatio 47, 84–94 (2018)Google Scholar
  22. 22.
    Venn, J.: Symbolic Logic. Macmillan, New York (1881)CrossRefzbMATHGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Universidade Federal de Santa MariaSanta MariaBrazil

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