Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Beyond Syllogisms: Carroll’s (Marked) Quadriliteral Diagram

  • Chapter
Visual Reasoning with Diagrams

Part of the book series: Studies in Universal Logic ((SUL))

Abstract

The logician Lewis Carroll (1832–1898) invented a diagrammatic scheme for syllogisms and described how it could be used for logic problems involving more than 3 terms. Curiously, he never provided in print any diagrammatic solution for such a complex problem. The aim of this paper is to make sense of a manuscript where Carroll attempts to solve a sorite using his quadriliteral diagram. In this problem, three propositions are offered as premises. The purpose is to look for what information can be gathered as to the relation between two given terms involved in the argument. This case study provides some insights about the use of diagrams to solve elimination problems that were highly considered by early symbolist logicians.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abeles, F.F.: Lewis Carroll’s formal logic. Hist. Philos. Logic 26(1), 33–46 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Abeles, F.F.: Lewis Carroll’s visual logic. Hist. Philos. Logic 28(1), 1–17 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Abeles, F.F. (ed.): The Logic Pamphlets of Charles Lutwidge Dodgson and Related Pieces. Lewis Carroll Society of North America, New York (2010)

    MATH  Google Scholar 

  4. Bartley, W.W. III (ed.): Lewis Carroll’s Symbolic Logic. Clarkson N. Potter, New York (1977)

    Google Scholar 

  5. Boole, G.: An Investigation of the Laws of Thought. Walton & Maberly, London (1854)

    Google Scholar 

  6. Carroll, L.: The Game of Logic. Macmillan, London (1887)

    Google Scholar 

  7. Carroll, L.: Fifth Paper on Logic. The Parrish Collection, Princeton University Library, Dodgson 431 (1887)

    Google Scholar 

  8. Carroll, L.: Algebraical Geometry. Notebook. The Parrish Collection, Princeton University Library, box 1, folder 1 (1890?)

    Google Scholar 

  9. Carroll, L.: Two Diagrams. The Parrish Collection, Princeton University Library, Dodgson 224 & 225 (1890?)

    Google Scholar 

  10. Carroll, L.: Notes and Calculations on Problems in Symbolic Logic. The Houghton Collection, Pierpont Morgan Library, New York, AAH545 (1892?)

    Google Scholar 

  11. Carroll, L.: Pillow Problems. Macmillan, London (1893)

    Google Scholar 

  12. Carroll, L.: Symbolic Logic—Part I, 4th edn. Macmillan, London (1897)

    Google Scholar 

  13. Marquand, A.: Logical diagrams for n terms. Philos. Mag. 12, 266–270 (1881)

    Google Scholar 

  14. Moktefi, A.: Lewis Carroll’s logic. In: Gabbay, D.M., Woods, J. (eds.) British Logic in the Nineteenth-Century, pp. 457–505. North-Holland, Amsterdam (2008)

    Chapter  Google Scholar 

  15. Moktefi, A., Edwards, A.W.F.: One more class: Martin Gardner and logic diagrams. In: Burstein, M. (ed.) A Bouquet for the Gardener: Martin Gardner Remembered, pp. 160–174. Lewis Carroll Society of North America, New York (2011)

    Google Scholar 

  16. Moktefi, A., Shin, S.-J.: History of logic diagrams. In: Gabbay, D.M., Pelletier, F.J., Woods, J. (eds.) Logic: A History of Its Central Concepts, pp. 611–682. North-Holland, Amsterdam (2012)

    Chapter  Google Scholar 

  17. Venn, J.: On the various notations adopted for expressing the common propositions of logic. Proc. Camb. Philos. Soc. 4, 36–47 (1880)

    MATH  Google Scholar 

  18. Venn, J.: Symbolic Logic, 2nd edn. Macmillan, London (1894)

    Google Scholar 

  19. Wakeling, E. (ed.): Lewis Carroll’s Diaries, vol. 8. Lewis Carroll Society, Clifford (2004)

    Google Scholar 

Download references

Acknowledgements

This work benefited greatly from conversations with many people, notably Francine Abeles, Anthony Edwards, Mark Richards and Edward Wakeling, to whom I express my gratitude. This paper draws upon work supported by a research grant from The Friends of the University of Princeton Library. Finally, I express grateful acknowledgements to the archivists who helped me to consult the material used in Pierpont Morgan Library (New York) and Princeton University Library.

Author information

Authors and Affiliations

  1. IRIST, Université de Strasbourg, 7 Rue de l’Université, 67000, Strasbourg, France

    Amirouche Moktefi

Authors
  1. Amirouche Moktefi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amirouche Moktefi .

Editor information

Editors and Affiliations

  1. IRIST, Université de Strasbourg, Rue de l'Université 7, Strasbourg, 67000, France

    Amirouche Moktefi

  2. Department of Philosophy, Yale University, Hillhouse Avenue 38, New Haven, 06511, Connecticut, USA

    Sun-Joo Shin

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Basel

About this chapter

Cite this chapter

Moktefi, A. (2013). Beyond Syllogisms: Carroll’s (Marked) Quadriliteral Diagram. 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_4

Download citation

Publish with us

Policies and ethics

Search

Navigation