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Introduction to the Semiology of Mathematical Practice

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Handbook of the History and Philosophy of Mathematical Practice
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Abstract

The philosophy and history of mathematical practices have brought the study of mathematical language and signs to the forefront of contemporary mathematical thought. However, despite the fruitfulness of this research trend, a comprehensive and unified account of its various aspects and the diverse approaches taken to explore it remains elusive. Recognizing this gap, we have undertaken the task of editing the present section of the Handbook of the History and Philosophy of Mathematical Practice as a much-needed remedy. Before providing an overview of the various contributions to the section, this introduction provides some context for the subject matter and a few conceptual clarifications.

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Notes

  1. 1.

    For a more comprehensive approach, the reader can consult Barthes (1988); Sebeok (2001); Robering et al. (1996).

  2. 2.

    The fact that semiologies are defined as having “non-scientific” semiotics as objects should not lead us to assume that mathematics cannot be studied as a science from a semiological perspective. For Hjelmslev, a “scientific semiotic” is merely a semiotic organized as a specific analytical procedure. If mathematics were to fall into this category, its study as a sign system would be termed a “meta-(scientific semiotic)” according to Hjelmslev’s view (cf. Hjelmslev 1975, Df. 41,46).

References

  • Barthes R (1988) The semiotic challenge. Basil Blackwell, Oxford

    Google Scholar 

  • Barton B (2008) The language of mathematics: telling mathematical tales. Springer US, Boston

    Google Scholar 

  • Chemla K (2004) History of science, history of text. Kluwer Academic, Boston

    Google Scholar 

  • Chomsky N (1955) Logical syntax and semantics: their linguistic relevance. Language 31(1):36–45

    Google Scholar 

  • CICM (2008–2022) Intelligent computer mathematics. Springer International Publishing, Cham. https://link.springer.com/conference/mkm

  • Herreman A (2000) La topologie et ses signes: éléments pour une histoire sémiotique des mathématiques. L’Harmattan, Paris

    Google Scholar 

  • Hjelmslev L (1975) Résumé of a theory of language. Travaux du Cercle linguistique de Copenhague, Nordisk Sprog-og Kulturforlag, Copenhagen

    Google Scholar 

  • Hjelmslev L, Uldall HJ (1936) Synopsis of an outline of glossematics, Levin og Munksgaard, London

    Google Scholar 

  • Kvasz L (2008) Patterns of change. Birkhäuser, Basel

    Google Scholar 

  • Locke J (2013) An essay concerning human understanding. The Clarendon Edition of the Works of John Locke. Oxford University Press

    Google Scholar 

  • Macbeth D (2005) Frege’s logic. Harvard University Press, Cambridge, MA

    Google Scholar 

  • Netz R (1999) The shaping of deduction in Greek mathematics. Cambridge University Press, Cambridge

    Google Scholar 

  • Robering K, Posner R, Sebeok TA (eds) (1996) Semiotik, no. Bd. 13 in Handbücher zur Sprach- und Kommunikationswissenschaft, W. de Gruyter, Berlin

    Google Scholar 

  • Rotman B (1988) Toward a semiotics of mathematics. Semiotica 72(1–2):1–36

    Google Scholar 

  • Rotman B (2000) Mathematics as sign: writing, imagining, counting. Stanford University Press, Palo Alto

    Google Scholar 

  • Russell B (2010) Principles of mathematics, Routledge classics. Routledge, London

    Google Scholar 

  • Saussure F (1959) Course in general linguistics. McGraw-Hill, New York

    Google Scholar 

  • Sebeok TA (2001) Signs: an introduction to semiotics, Toronto studies in semiotics and communication, 2nd edn. University of Toronto Press, Toronto

    Google Scholar 

  • Serfati M (2005) La révolution symbolique: La constitution de l’écriture symbolique mathéma- tique. Éditions Pétra, Paris

    Google Scholar 

  • Sriraman B (ed) (2020) Handbook of the history and philosophy of mathematical practice. Springer International Publishing, Cham

    Google Scholar 

  • Vandendriessche E (2015) String figures as mathematics?: An anthropological approach to string figure-making in oral tradition societies. Springer, Cham

    Google Scholar 

  • Vinciguerra L (1999) Langage, visibilité, différence: histoire du discours mathématique de l’âge classique au XIXe siècle. J. Vrin, Paris

    Google Scholar 

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Acknowledgments

I want to thank Jeremy Avigad, Karine Chemla, Ladislav Kvasz, Reviel Netz, Anna Kiel Steensen, Lucien Vinciguerra, Roy Wagner and David Waszek for their generosity, patience, and invaluable contribution. I am deeply thankful to all the anonymous reviewers for their careful work, dedication, and constructive advice. Last but not least, I wish to express my gratitude to Bharath Sriraman for his constant support, comprehension and trust.

Funding Information

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 839730

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Correspondence to Juan Luis Gastaldi .

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Gastaldi, J.L. (2024). Introduction to the Semiology of Mathematical Practice. In: Sriraman, B. (eds) Handbook of the History and Philosophy of Mathematical Practice. Springer, Cham. https://doi.org/10.1007/978-3-030-19071-2_130-2

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  • DOI: https://doi.org/10.1007/978-3-030-19071-2_130-2

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Chapter history

  1. Latest

    Introduction to the Semiology of Mathematical Practice
    Published:
    08 February 2024

    DOI: https://doi.org/10.1007/978-3-030-19071-2_130-2

  2. Original

    Introduction to the Semiology of Mathematical Practice
    Published:
    07 October 2023

    DOI: https://doi.org/10.1007/978-3-030-19071-2_130-1