Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-29T01:05:46.304Z Has data issue: false hasContentIssue false
  • English
  • Français

For Some Histories of Greek Mathematics

Published online by Cambridge University Press:  09 November 2009

Roy Wagner
Roy Wagner*
Affiliation:
Tel Aviv University
Get access Rights & Permissions [Opens in a new window]

Argument

This paper argues for the viability of a different philosophical point of view concerning classical Greek geometry. It reviews Reviel Netz's interpretation of classical Greek geometry and offers a Deleuzian, post-structural alternative. Deleuze's notion of haptic vision is imported from its art history context to propose an analysis of Greek geometric practices that serves as counterpoint to their linear modular cognitive narration by Netz. Our interpretation highlights the relation between embodied practices, noisy material constraints, and operational codes. Furthermore, it sheds some new light on the distinctness and clarity of Greek mathematical conceptual divisions.

Type
Research Article
Information
Science in Context , Volume 22 , Issue 4 , December 2009 , pp. 535 - 565
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benjamin, Walter. 1996–2003. Selected Writings (4 vols.). Cambridge, MA and London: Harvard University Press.Google Scholar
Bogue, Ronald. 2003. Deleuze on Music, Painting and the Arts. London and NY: Routledge.Google Scholar
Borges, Jorge L. 1962. Ficciones. Translated by Bonner, Anthony. New York: Grove Press.Google Scholar
Deleuze, Gilles. 1989. Cinema (2 vols.). Translated by Tomlison, Hugh and Galeta, Robert. London: Athlone Press.Google Scholar
Deleuze, Gilles. 1990. Logic of Sense. Translated by Lester, Marc and Stivale, Charles. New York: Columbia University Press.Google Scholar
Deleuze, Gilles. 1994. Difference and Repetition. Translated by Patton, Paul. New York: Columbia University Press.Google Scholar
Deleuze, Gilles. 2003. Francis Bacon: The Logic of Sensation. Translated by Smith, Daniel W.. Minneapolis: University of Minnesota Press.Google Scholar
Deleuze, Gilles and Guattari, Félix. 1987. A Thousand Plateaus. Minneapolis: University of Minnesota Press.Google Scholar
Derrida, Jacques. 1979. Speech and Phenomena. Translated by Allison, David B.. Evanston: Northwestern University Press.Google Scholar
Derrida, Jacques. 1984. Signéponge. Translated by Rand, Richard. New York: Columbia University Press.Google Scholar
Derrida, Jacques. 1988. Limited Inc. Edited by Graff, Gerald. Translated by Weber, Samuel and Mehlman, Jeffrey. Evanston: Northwestern University Press.Google Scholar
Derrida, Jacques. 1989. Edmund Husserl's Origin of Geometry, an Introduction. Translated by Leavy, John P. Jr.Lincoln: University of Nebraska Press.Google Scholar
Duffy, Simon, ed. 2004. Virtual Mathematics. Manchester: Clinamen Press.Google Scholar
Fried, Michael N. and Unguru, Sabetai. 2001. Apollonius of Perga's Conica: Text, Context, Subtext. Leiden: Brill.CrossRefGoogle Scholar
Gadamer, Hans G. 1975. Truth and Method. Translated by Barden, Garrett and Cumming, John. New York: Seabury Press.Google Scholar
Grosholz, Emily R. 2007. Representation and Productive Ambiguity in Mathematics and the Sciences. Oxford: Oxford University Press.CrossRefGoogle Scholar
Hadamard, Jacques. 1973. The Mathematician's Mind. Princeton: Princeton University Press.Google Scholar
Harding, Sandra. 2004. “Rethinking Feminist Standpoint Epistemology: What is ‘Strong Objectivity’?” In The Feminist Standpoint Theory Reader: Intellectual and Political Controversies, edited by Harding, Sandra, 127–140. New York: Routledge.Google Scholar
Heath, Thomas L. 1956. The Thirteen Books of Euclid's Elements. New York: Dover Publications.Google Scholar
Heath, Thomas L. [1949] 1993. Mathematics in Aristotle. Reproduction of the 1949 edition. Bristol: Thoemmes Press.Google Scholar
Joyce, David E. 1988. Euclid's Elements. Last accessed 21 March 2009. <http://aleph0.clarku.edu/djoyce/java/elements/elements.html>Google Scholar
Knorr, Wilbur R. 1975. The Evolution of the Euclidean Elements. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Latour, Bruno. 2008. “The Netz-works of Greek Deductions.” Social Studies of Science 38 (3):441–459.CrossRefGoogle Scholar
Lefebvre, Muriel. 2002. “Construction et déconstruction des diagrammes de Dynkin.” Actes de la recherche en sciences sociales 141–142:121–124.CrossRefGoogle Scholar
Longino, Helen E. 1999. “Feminist Epistemology.” In The Blackwell Guide to Epistemology, edited by Grecco, John and Sosa, Ernest, 327–353. Malden, MA: Blackwell.Google Scholar
Mueller, Ian. 1981. Philosophy of Mathematics and Deductive Structure in Euclid's Elements. Cambridge: MIT Press.Google Scholar
Netz, Reviel. 1998. “Greek Mathematical Diagrams: Their Use and Their Meaning.” For the Learning of Mathematics 18 (3):33–39.Google Scholar
Netz, Reviel. 1999. The Shaping of Deduction in Greek Mathematics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Netz, Reviel. 2004a. “The Limits of Text in Greek Mathematics.” In History of Science, History of Text, edited by Chemla, Karine, 161–176. Dordrecht: Springer.CrossRefGoogle Scholar
Netz, Reviel. 2004b. The Transformation of Mathematics in the Early Mediterranean World: From Problems to Equations. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Parikh, Carol. 1991. The Unreal Life of Oscar Zariski. Boston: Harcourt, Brace Jovanovich.Google Scholar
Radford, Luis. 2006. “Algebraic Thinking and the Generalization of Patterns: A Semiotic Perspective.” In Proceedings of the 28th conference of the international group for psychology of mathematics education, North American chapter, edited by Alatorre, S., Cortina, J., Sáiz, M., and Méndez, A., 1:2–21. Mérida: Universidad Pedagógica Nacional.Google Scholar
Serres, Michel. 1982. The Parasite. Translated by Schehr, Lawrence R.. Baltimore and London: John Hopkins University Press.Google Scholar
Sia, Xin Wei. 2004. “Differential Geometrical Performance and Poiesis.” Configurations 12:133–160.Google Scholar
Starobinski, Jean. 1979. Words upon Words: The Anagrams of Ferdinand de Saussure. Translated by Emmet, Olivia. New Haven: Yale University Press.Google Scholar
Steinbeck, John. 1962. Travels with Charley: In Search of America. New York: Viking Press.Google Scholar
Taisbak, Christian M. 2003. Euclid's Data: The Importance of Being Given. Copenhagen: Museum Tusculanum Press.Google Scholar
Williams, James. 1997. “Deleuze on J. M. W. Turner: Catastrophism in Philosophy?” In Deleuze and Philosophy, the Difference Engineer, edited by Pearson, Keith Ansell, 233–246. London and NY: Routledge.Google Scholar
Unguru, Sabetai. 1975. “On the Need to Rewrite the History of Greek Mathematics.” Archive for the History of Exact Sciences 15:67–114.CrossRefGoogle Scholar
Unguru, Sabetai. 1979. “History of Ancient Mathematics: Some Reflections on the State of the Art.” Isis 70:555–564.CrossRefGoogle Scholar
Unguru, Sabetai and Rowe, David. 1981–1982. “Does the Quadratic Equation Have Greek Roots.” Libertas Mathematics 1 (1981):1–49, 2 (1982):1–62.Google Scholar
Vitrac, Bernard. 1994. Les Eléments, vol. 2: Livres V-IX. Paris: Presses Universitaires de France.Google Scholar
Wagner, Roy. 2009. S(zp, zp): Post-Structural Readings of Gödel's Proof. Milan: Polimetrica.Google Scholar
Wittgenstein, Ludwig. 1975. Lectures on the Foundations of Mathematics. Edited by Diamond, Cora. Chicago: University of Chicago Press.Google Scholar
Zeuthen, Hieronymus G. 1965. Die Lehre von den Kegelschnitten im Altertum. (Photomechnaical reprint of the edition of 1886). Hildesheim: G. Olms.Google Scholar