Skip to main content
SpringerLink
Log in

How Can Numerals Be Iconic? More Varieties of Iconicity

  • Conference paper
  • First Online:
Diagrammatic Representation and Inference (Diagrams 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12909))

Included in the following conference series:

Abstract

The standard notion of iconicity, which is based on degrees of similarity or resemblance, does not provide a satisfactory account of the iconic character of some representations of abstract entities when those entities do not exhibit any imitable internal structure. Individual numbers are paradigmatic examples of such structureless entities. Nevertheless, numerals are frequently described as iconic or symbolic; for example, we say that the number three is represented symbolically by ‘3’, but iconically by ‘\(|||\)’. To address this difficulty, I discuss various alternative notions of iconicity that have been presented in the literature, and I propose two novel accounts.

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

Notes

  1. 1.

    This differs from other conceptions of numbers, e. g., Euclid’s [6, Bk. 7, Def. 2].

  2. 2.

    This view of analogy also underlies the structure-mapping theory of analogy [3].

  3. 3.

    See [5, pp. 52–57] for a general discussion of exemplification in the context of representations.

  4. 4.

    The exact measure of simplicity that is applied here is difficult to make precise, but it might correlate with the notion of naturalness invoked in Sect. 3.1.

  5. 5.

    Note that some of the caveats about the assessment of operational iconicity discussed at the end of Sect. 2 also apply to the notion of systematic iconicity.

References

  1. Chrisomalis, S.: Numerical Notation: A Comparative History. Cambridge University Press, Cambridge (2010)

    Book  Google Scholar 

  2. Gamkrelidze, T.V.: The problem of “l’arbitraire du signe’’. Language 50(1), 102–111 (1974)

    Article  Google Scholar 

  3. Gentner, D.: Structure-mapping: a theoretical framework for analogy. Cogn. Sci. 7(2), 155–170 (1983)

    Article  Google Scholar 

  4. Giardino, V., Greenberg, G.: Introduction: varieties of iconicity. Rev. Philos. Psychol. 6(1), 1–25 (2015)

    Article  Google Scholar 

  5. Goodman, N.: Languages of Art. An Approach to a Theory of Symbols. Bobbs-Merrill Co., Indianapolis (1968)

    Google Scholar 

  6. Heath, T.: The Thirteen Books of Euclid’s Elements. Dover, Chicago (1953)

    Google Scholar 

  7. Hilbert, D., Ackermann, W.: Grundzüge der theoretischen Logik. Springer, Heidelberg (1928)

    MATH  Google Scholar 

  8. Landy, D., Goldstone, R.: How abstract is symbolic thought? J. Exp. Psychol. Learn. Mem. Cogn. 33(4), 720–733 (2007)

    Article  Google Scholar 

  9. Norman, J.: Iconicity and “direct interpretation”. In: Malcolm, G. (ed.) Studies in Multidisciplinarity, Chap. 8, pp. 99–113. Elsevier (2004)

    Google Scholar 

  10. Peirce, C.S.: On an improvement of Boole’s calculus of logic. In: Proceedings of the American Academy of Arts and Sciences, vol. 7, pp. 250–261. Welch, Bigelow, and Co. (1867). Repr. in [13], 3.1–19

    Google Scholar 

  11. Peirce, C.S.: On the algebra of logic: a contribution to the philosophy of notation. Am. J. Math. 7(2–3), 180–202 (1885). Repr. in [13], 3.154–403

    Google Scholar 

  12. Peirce, C.S.: Syllabus. Manuscript (1902). Repr. in [13] 2.274–277, 283–4, 292–4

    Google Scholar 

  13. Peirce, C.S.: Collected Papers. Harvard University Press, Cambridge (1932–1958). Eight volumes. Edited by Charles Hartshorne and Paul Weiss

    Google Scholar 

  14. Resnik, M.D.: Mathematics as a Science of Patterns. Claredon Press, Oxford (1997)

    MATH  Google Scholar 

  15. Russell, B.: Introduction to Mathematical Philosophy. George Allen & Unwin, London (1919). Reprinted by Dover Publications, New York (1993)

    Google Scholar 

  16. Schlimm, D.: Peano on symbolization, design principles for notations, and the dot notation. Philosophia Scientiæ 25(1), 139–170 (2021)

    MathSciNet  Google Scholar 

  17. Shapiro, S.: Philosophy of Mathematics. Structure and Ontology. Oxford University Press, Oxford (1997)

    MATH  Google Scholar 

  18. Stjernfelt, F.: Diagrammatology. An Investigation of the Borderlines of Phenomenology, Ontology, and Semiotics. Springer, Dordrecht (2007). https://doi.org/10.1007/978-1-4020-5652-9

    Book  Google Scholar 

  19. Stjernfelt, F.: On operational and optimal iconicity in Peirce’s diagrammatology. Semiotica 186(1/4), 395–419 (2011)

    Google Scholar 

  20. Wege, T., Batchelor, S., Inglis, M., Mistry, H., Schlimm, D.: Iconicity in mathematical notation: commutativity and symmetry. J. Numer. Cognit. 6(3), 378–392 (2020)

    Article  Google Scholar 

Download references

Acknowledgments

I would like to thank Viviane Fairbank, David Waszek, Jessica Carter, and two anonymous reviewers for fruitful discussions and helpful comments on a draft of this paper. This research was supported by the Social Sciences and Humanities Research Council of Canada.

Author information

Authors and Affiliations

  1. McGill University, Montreal, QC, H3A 2T7, Canada

    Dirk Schlimm

Authors
  1. Dirk Schlimm
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dirk Schlimm .

Editor information

Editors and Affiliations

  1. Jadavpur University, Kolkata, India

    Amrita Basu

  2. University of Cambridge, Cambridge, UK

    Gem Stapleton

  3. Lancaster University in Leipzig, Leipzig, Germany

    Sven Linker

  4. Deakin University, Burwood, VIC, Australia

    Catherine Legg

  5. Kyoto University, Kyoto, Japan

    Emmanuel Manalo

  6. Universidade Federal Fluminense, Niterói, Brazil

    Petrucio Viana

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Schlimm, D. (2021). How Can Numerals Be Iconic? More Varieties of Iconicity. 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_53

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-86062-2_53

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86061-5

  • Online ISBN: 978-3-030-86062-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation