Skip to main content
SpringerLink
Log in

What is a Symbol?

  • Conference paper
  • First Online:
Research in History and Philosophy of Mathematics (CSHPM 2016)

  • 533 Accesses

Abstract

Focusing my discussion on the sixteenth and seventeenth centuries, I argue that the symbolic notation under development at the time reveals connections with rhetorical and poetic aesthetics. In the first section, I show how the mathematical strategies that notation facilitated rely on prudential rhetoric’s sense of the opportune moment, also known as kairos or decorum. In the second, I show how the necessary balance within notation between compression and lucidity similarly relies on an aesthetic judgment that is essentially prudential. In the last section, I show how notation’s ability to accommodate disjunctive values within a general symbol corresponds to similar capabilities in the poetic symbol. Through etymological analysis of the polysemy of its terminology, I demonstrate the philological orientation of early modern algebra.

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Allen, Valerie (2016) “Chaucer and the Poetics of Gold”, in Beatrice Fannon (ed.) New Casebooks: Reading Medieval Literature, London: Palgrave, pp. 144—159.

    Google Scholar 

  • Aquinas, Thomas, St. (1964-1975) Summa Theologiae, ed. and trans. Thomas Gilby, Oxford: Blackfriars.

    Google Scholar 

  • Aristotle (1933, repr. 1989) Metaphysics, Books I—IX, ed. and trans. Hugh Tredennick, Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Aristotle (1995) Poetics, ed. and trans. Stephen Halliwell, Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Baltzell, Jane (April 1967) “Rhetorical ‘Amplification’ and ‘Abbreviation’ and the Structure of Medieval Narrative” Pacific Coast Philology 2, pp. 32—39.

    Google Scholar 

  • Baumlin, James S. (2002) “Ciceronian Decorum and the Temporalities of Renaissance Rhetoric”, in Phillip Sipiora and James S. Baumlin (eds) Rhetoric and Kairos: Essays in History, Theory, and Praxis, Albany: State University of New York Press, pp. 138-164.

    Google Scholar 

  • Bochenski, I.M. (1961) A History of Formal Logic, rev. and trans. Ivo Thomas, Indiana: Notre Dame University Press.

    Google Scholar 

  • Cajori, Florian (1928—1929), A History of Mathematical Notations. 2 vols. Chicago: Open Court, repr. in one vol. (2012) Mineola, NY: Dover.

    Google Scholar 

  • Carroll, Lewis (2013) Alice in Wonderland, ed. Donald J. Gray, 3rd edn, New York and London: Norton.

    Google Scholar 

  • Cifoletti, Giovanna (2006) “Mathematics and Rhetoric. Introduction”, Early Science and Medicine 11.4, 369—389.

    Google Scholar 

  • Faral, Edmond (1924, repr. 1962) Les arts poétiques du XIIe et du XIIIe siècle: recherches et documents sur la technique littéraire du moyen âge, Paris: Champion.

    Google Scholar 

  • Frege, Gottlob (1879) Begriffsschrift eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Halle: Louis Nebert.

    Google Scholar 

  • Frege, Gottlob (1970) Begriffsschrift (English), in Frege and Gödel: Two Fundamental Texts in Mathematical Logic, ed. Jean van Heijenoort, Cambridge MA: Harvard University Press.

    Google Scholar 

  • Harris, William. http://www.orbilat.com/Languages/Latin/Alternative_Grammars/Harris_Grammar/Latin-Harris_17.html

  • Heeffer, Albrecht (2009) “On the Nature and Origin of Algebraic Symbolism”, in Bart van Kerkhove (ed.), New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics, Singapore, World Scientific Publishing, pp. 1—21.

    Google Scholar 

  • Heeffer, Albrecht and Maarten Van Dyck, eds, (2010) Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics, Studies in Logic 26, London: College Publications, King’s College.

    Google Scholar 

  • Heeffer, Albrecht (2015) “On the Historiography of Mathematical Notations”, in Douglas R. Furman and Albrecht Heeffer (eds), Writing the History of Mathematical Notation 1483-1700 by Sister Mark Leontius Schulte, Boston, MA: Docent Press, pp. 3—43.

    Google Scholar 

  • Hobbes, Thomas (1651) Leviathan, or The Matter, Form, and Power of a Common-Wealth Ecclesiastical and Civil, London: printed for Andrew Crooke, at the Green Dragon in St. Paul’s Church-yard.

    Google Scholar 

  • Hobbes, Thomas (1656) Six Lessons to the Professors of the Mathematiques, London: printed by J.M. for Andrew Crook, at the Green-Dragon in Paul’s Church-yard.

    Google Scholar 

  • Kerenyi, C. (1962) The Religion of the Greeks and Romans, trans. Christopher Holme, New York: Dutton.

    Google Scholar 

  • Lanham, Richard A. (1991) A Handlist of Rhetorical Terms, 2nd edn, Berkeley: University of California Press.

    Google Scholar 

  • Lloyd, G.E.R. (1990) Demystifying Mentalities, Cambridge: Cambridge University Press.

    Google Scholar 

  • Middle English Dictionary (2001), University of Michigan http://quod.lib.umich.edu/m/med/

  • Moxon, Joseph (1700) Mathematicks made easie. or, A mathematical dictionary explaining the terms of art and difficult phrases used in arithmetick, geometry, astronomy, astrology, and other mathematical sciences, 3rd edn, London: printed for J. Moxon at the Atlas in Warwick-Lane and Thomas Tuttell at the King’s Arms and Globe at Charing-Cross.

    Google Scholar 

  • Oughtred, William (1647) The Key of the Mathematicks New Forged and Filed: Together with a Treatise of the Resolution of all kinde of Affected Æquations in Numbers, London: printed by Tho. Harper for Rich. Whitaker.

    Google Scholar 

  • Oxford English Dictionary Online (2017), Oxford: Oxford University Press.

    Google Scholar 

  • Puttenham, George (1589) The Arte of English Poesie, London: printed by Richard Field, dwelling in the black-Friers, neere Ludgate.

    Google Scholar 

  • Pycior, Helena M. (1997) Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra through the Commentaries on Newton’s Universal Arithmetick, Cambridge: Cambridge University Press.

    Google Scholar 

  • Recorde, Robert (2010) The Whetstone of Witte, A Facsimile, ed. Thomas Gordon Roberts, Mickleover, Derby: Renascent Books.

    Google Scholar 

  • Rhetorica ad Herennium (1954) ed. and trans. Harry Caplan, Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Rotman, Brian (2000) Mathematics as Sign: Writing, Imagining, Counting, Stanford: Stanford University Press.

    Google Scholar 

  • Royal Astronomical Society (1996-2015) https://www.ras.org.uk/news-and-press/news-archive/ 68-news2009/1641-celebrating-thomas-harriot-the-worlds-first-telescopic-astronomer-ras-pn- 0947

    Google Scholar 

  • Schlimm, Dirk (Published online. 2017) “On Frege’s Begriffsschrift Notation for Propositional Logic: Design Principles and Trade-offs”, History and Philosophy of Logic, 1—34.

    Google Scholar 

  • Serfati, Michel (2010) “Symbolic revolution, scientific revolution: mathematical and philosophical aspects”, in Heeffer and Van Dyck, eds, Philosophical Aspects, pp. 103—22.

    Google Scholar 

  • Sprat, Thomas (1667) The History of the Royal-Society of London for the Improving of Natural Knowledge, London: printed by T.R. for J. Martyn and J. Allestry.

    Google Scholar 

  • Spenser, Edmund (2013) The Faerie Queene, rev. 2nd edn, ed. A.C. Hamilton, Hiroshi Yamashita, and Toshiyuki Suzuki, London and New York: Routledge.

    Google Scholar 

  • Sherry, Richard (1555) A Treatise of the figures of Grammer and Rhetorike, profitable for al that be studious of eloquence, and in especiall for suche as in grammer scholes doe reade moste eloquente poetes and oratours. London: in aedibus Ricardi Totelli.

    Google Scholar 

  • Tanner, R.C.H. (1962 Dec.) “On the Role of Equality and Inequality in the History of Mathematics” British Journal for the History of Science 1.2, pp. 159—69.

    Google Scholar 

  • Tatarkiewicz, Wladyslaw (1970) History of Aesthetics, Vol. II: Medieval Aesthetics, The Hague and Paris: Mouton.

    Google Scholar 

  • Tribble, Evelyn B. (1996) “The Partial Sign: Spenser and the Sixteenth-Century Crisis of Semiotics,” in Douglas F. Rutledge (ed.), Ceremony and Text in the Renaissance (Cranbury, NJ: Associated University Presses), pp. 23—34.

    Google Scholar 

  • Viète, François (2006) The Analytic Art, trans. T. Richard Witmer, Mineola, NY: Dover.

    Google Scholar 

  • Whitehead, Alfred North (1948, repr. 1972) An Introduction to Mathematics, Oxford: Oxford University Press.

    Google Scholar 

  • Wilkins, John (1668) An Essay towards a Real Character, and a Philosophical Language, London: printed for Sa. Gellibrand and John Martyn.

    Google Scholar 

  • Williams, Travis D. (2016) “Mathematical Enargeia: The Rhetoric of Early Modern Mathematical Notation”, Rhetorica 34(2), 163—211.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. John Jay College CUNY, 524 West 59th Street #7.63.04NB, New York, NY, 10019, USA

    Valerie Allen

Authors
  1. Valerie Allen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Valerie Allen .

Editor information

Editors and Affiliations

  1. Mathematical, Information and Computer Sciences, Point Loma Nazarene University, San Diego, California, USA

    Maria Zack

  2. Department of Philosophy, McGill University, Montreal, Quebec, Canada

    Dirk Schlimm

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Allen, V. (2017). What is a Symbol?. In: Zack, M., Schlimm, D. (eds) Research in History and Philosophy of Mathematics. CSHPM 2016. Proceedings of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-64551-3_4

Download citation

Publish with us

Policies and ethics

Search

Navigation