Abstract
Charles S. Peirce introduced in 1903 a set a transformation rules for Euler-Venn diagrams. This innovation contrasted with earlier practices where logicians rather extracted the desired information by a simple ‘glance’ at their diagrams. Also, Peirce’s set of rules was the starting point of Sun-Joo Shin’s more recent systems which, in turn, inspired most subsequent modern diagrammatic systems. Despite their significance, these rules got little attention from both diagram and Peirce scholars. In this paper, we revisit Peirce’s rules of transformation and discuss the extent to which they ‘survived’ in modern diagrammatic systems. We will specifically consider their clarity and completeness to assess Peirce’s assumption that some of his rules may be simplified while others may have been overlooked.
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Notes
- 1.
Unfortunately, manuscript MS 479 has still not been properly published. It has only been partially reproduced and poorly edited in Peirce’s Collected Papers [13]. This transcription, on which was based Shin’s account, should be used with extreme caution. The manuscript is also not reproduced in Ahti-Veikko Pietarinen’s edition of Peirce’s existential graphs [15], but additional text and variants are included [14]. Apparently, Peirce intended to include his manuscript as a chapter in a volume of Logical Tracts [14, p. 72]. The original manuscript MS 479 is freely accessible on the Peirce Archive repository (https://rs.cms.hu-berlin.de/peircearchive/pages/search.php). The page numbers we indicate for MS 479 are the file titles in the Peirce Archive.
- 2.
- 3.
Peirce explained that he used rules “in the sense in which we speak of the “rules” of algebra; that is, as a permission under strictly defined condition” [12]. In his entry on ‘Symbolic Logic’, published a year earlier, Peirce defined a rule as “a permission under certain circumstances to make a certain transformation” [11, p. 450].
- 4.
Peirce’s mature Eulerian diagrams and Existential graphs were developed at the same time and share several features, including the formulation of transformation rules. But they differ significantly in their purpose: Eulerian diagrams served mainly for logical calculus while Existential graphs were designed for logical analysis. Roughly, calculus aims at carrying reasonings while analysis investigates them. On the opposition between calculus and analysis, see [3, 11, p. 450].
- 5.
Here cross and zero represents non-emptiness and emptiness of a region respectively. The connected lines between any of these symbols represent their disjunction
- 6.
This rule was written by Peirce on the margins of his manuscript, without further explanation. It seems to have been added later, as shown by the renumbering of the following rule.
- 7.
- 8.
References
Bellucci, F., Moktefi, A., Pietarinen, A.: Diagrammatic autarchy: linear diagrams in the 17th and 18th centuries. In: Burton, J., Choudhury, L. (eds.) First International Workshop on Diagrams, Diagrams, Logic and Cognition, CEUR Workshop Proceedings, vol. 1132, pp. 31–35 (2013). http://ceur-ws.org/Vol-1132/paper4.pdf
Bellucci, F., Pietarinen, A.V.: Existential graphs as an instrument of logical analysis: Part I. Alpha. Rev. Symb. Logic 9(2), 209–237 (2016)
Bellucci, F., Moktefi, A., Pietarinen, A.V.: Simplex sigillum veri: Peano, Frege and Peirce on the primitives of logic. History Philos. Logic 39(1), 80–95 (2018)
Bhattacharjee, R., Chakraborty, M.K., Choudhury, L.: Venn diagram with names of individuals and their absence: a non-classical diagram logic. Log. Univers. 12(1), 141–206 (2018)
Bhattacharjee, R., Moktefi, A.: Peirce’s inclusion diagrams, with application to syllogisms. In: Pietarinen, A.-V., Chapman, P., Bosveld-de Smet, L., Giardino, V., Corter, J., Linker, S. (eds.) Diagrams 2020. LNCS (LNAI), vol. 12169, pp. 530–533. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-54249-8_50
Moktefi, A., Bellucci, F., Pietarinen, A.-V.: Continuity, connectivity and regularity in spatial diagrams for N terms. In: Burton, J., Choudhury, L. (eds.) DLAC 2013: Diagrams, Logic and Cognition, CEUR Workshop Proceedings, vol. 1132, pp. 31–35 (2014). http://ceur-ws.org/Vol-1132/
Moktefi, A.: Beyond syllogisms: carroll’s (marked) quadriliteral diagram. In: Moktefi, A., Shin, S.-J. (eds.) Visual Reasoning with Diagrams, pp. 55–71. Birkhäuser, Basel (2013)
Moktefi, A.: Logic. In: Wilson, R.J., Moktefi, A. (eds.) The Mathematical World of Charles L. Dodgson (Lewis Carroll), pp. 87–119. Oxford University Press, Oxford (2019)
Moktefi, A.: Diagrammatic reasoning: the end of scepticism? In: Benedek, A., Nyiri, K. (eds.) Vision Fulfilled, pp. 177–186. Hungarian Academy of Sciences, Budapest (2019)
Moktefi, A., Bhattacharjee, R.: What are rules for? A Carroll-Peirce comparison. In: Diagrammatic Representation and Inference 12th International Conference, Diagrams 2021, LNAI. Springer (2021)
Peirce, C.S., Ladd-Franklin, C.: Symbolic logic. In: Baldwin, J.M. (ed.) Dictionary of Philosophy and Psychology, vol. 2, pp. 645–650. Macmillan, New York and London (1902)
Peirce, C.S.: On logical graphs. Houghton Library, Harvard University, MS 479. Accessible at: Peirce Archive (1903). https://rs.cms.hu-berlin.de/peircearchive/pages/search.php
Peirce, C.S.: Collected papers. In: Hartshorne, C., Weiss, P. (eds.) Harvard University Press, Cambridge, vol. 4. (1933)
Peirce, C.S.: Logic of the future. In: Pietarinen, A.-V. (eds.) 2, De Gruyter, Berlin (2020)
Pietarinen, A.-V.: Extensions of euler diagrams in peirce’s four manuscripts on logical graphs. In: Jamnik, M., Uesaka, Y., Elzer Schwartz, S. (eds.) Diagrams 2016. LNCS (LNAI), vol. 9781, pp. 139–154. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-42333-3_11
Pietarinen, A.-V., Bellucci, F., Bobrova, A., Haydon, N., Shafiei, M.: The blot. In: Pietarinen, A.-V., Chapman, P., Bosveld-de Smet, L., Giardino, V., Corter, J., Linker, S. (eds.) Diagrams 2020. LNCS (LNAI), vol. 12169, pp. 225–238. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-54249-8_18
Roberts, D.D.: The existential graphs. Comput. Math. Appl. 23(6–9), 639–663 (1992)
Shin, S.J.: The Logical Status of Diagrams. Cambridge University Press, Cambridge (1994)
Stapleton, G.: Delivering the potential of diagrammatic logics. In: Burton, J., Choudhury, L. (eds.) DLAC 2013: Diagrams, Logic and Cognition, CEUR Workshop Proceedings, vol. 1132, pp. 1–8 (2013). http://ceur-ws.org/Vol-1132/
Venn, J.: On the diagrammatic and mechanical representation of propositions and reasonings. Philos. Mag. 10(59), 1–18 (1880)
Acknowledgment
We acknowledge with gratitude some fruitful suggestions given by Mihir Kumar Chakraborty and Ahti Pietarinen in the course of development of this research. The second author acknowledges support from TalTech internal grant SSGF21021.
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Bhattacharjee, R., Moktefi, A. (2021). Revisiting Peirce’s Rules of Transformation for Euler-Venn Diagrams. In: Basu, A., Stapleton, G., Linker, S., Legg, C., Manalo, E., Viana, P. (eds) Diagrammatic Representation and Inference. Diagrams 2021. Lecture Notes in Computer Science(), vol 12909. Springer, Cham. https://doi.org/10.1007/978-3-030-86062-2_14
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