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What Are Rules for? A Carroll-Peirce Comparison

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Diagrammatic Representation and Inference (Diagrams 2021)

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Abstract

Unlike their predecessors, Lewis Carroll and Charles S. Peirce introduced rules to manipulate diagrams. As such, they opened the way to a formal view of diagrams. However, their motivations seem different, and even opposite: Pierce’s rules are present for the purposes of analysis while Carroll’s rules enable an epistemological strategy to ease calculus.

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References

  1. Bellucci, F., Moktefi, A., Pietarinen, A.-V.: Simplex sigillum veri: Peano, Frege and Peirce on the primitives of logic. Hist. Philos. Logic 39(1), 80–95 (2018)

    Article  MathSciNet  Google Scholar 

  2. Carroll, L.: Symbolic Logic. Macmillan, London (1897)

    Google Scholar 

  3. Moktefi, A.: Beyond syllogisms: Carroll’s (marked) quadriliteral diagram. In: Moktefi, A., Shin, S.-J. (eds.) Visual Reasoning with Diagrams. SUL, pp. 55–71. Birkhäuser, Basel (2013). https://doi.org/10.1007/978-3-0348-0600-8_4

  4. Moktefi, A.: Are other people’s books difficult to read? The logic books in Lewis Carroll’s private library. Acta Baltica Historiae et Philosophiae Scientiarum 5(1), 28–49 (2017)

    Article  Google Scholar 

  5. 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)

    Google Scholar 

  6. 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)

    Google Scholar 

  7. Moktefi, A.: The social shaping of modern logic. In: Gabbay, D., et al. (eds.) Natural Arguments: A Tribute to John Woods, pp. 503–520. College Publications, London (2019)

    Google Scholar 

  8. Morgan, C. (ed.): The Pamphlets of Lewis Carroll: Games, Puzzles & Related Pieces. LCSNA, New York (2015)

    Google Scholar 

  9. Peirce, C.S. (ed.): Studies in Logic. Little, Brown, and Company, Boston (1883)

    Google Scholar 

  10. Peirce, C.S.: On logical graphs. Houghton Library, Harvard University, MS 479 (1903). Peirce Archive (https://rs.cms.hu-berlin.de/peircearchive/)

  11. Peirce, C.S.: Logic of the Future, edited by A.-V. Pietarinen. De Gruyter, Berlin (2020)

    Google Scholar 

  12. 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 (1902)

    Google Scholar 

  13. 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. http://ceur-ws.org/Vol-1132/

  14. Venn, J.: On the diagrammatic and mechanical representation of propositions and reasonings. Philos. Mag. 10, 1–18 (1880)

    Article  Google Scholar 

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Acknowledgement

The first author acknowledges support from TalTech internal grant SSGF21021.

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Correspondence to Amirouche Moktefi .

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Moktefi, A., Bhattacharjee, R. (2021). What Are Rules for? A Carroll-Peirce Comparison. 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_24

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  • DOI: https://doi.org/10.1007/978-3-030-86062-2_24

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  • Print ISBN: 978-3-030-86061-5

  • Online ISBN: 978-3-030-86062-2

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