# A Bunch of Diagrammatic Methods for Syllogistic

• Frank Thomas Sautter
Article

## 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

Primary 03B80

## 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)
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)
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)
8. 8.
Ladd-Franklin, C.: The antilogism. Mind New Ser. 37, 532–534 (1928)
9. 9.
Russinoff, S.: The syllogism’s final solution. Bull. Symb. Log. 5, 451–469 (1999)
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)
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)