Abstract
In his famous essay ‘The Origin of Geometry’ Husserl claimed that language is the embodiment (Sprachleib) of geometry. Husserl’s argument for this striking thesis starts from the question as to how the objectivity of geometry is to be understood, given that it is an abstract science dealing with ideal objects. His answer is that the existence of written demonstrations enables people to reactivate the fundamental experiences which formed geometrical practices and share the self-evidence of the ideal truths thereby grasped in a way which vindicates their objectivity. This answer is compared with positions advocated by Russell and Merleau-Ponty. Russell’s work shows that the conception of self-evidence Husserl employs is not tenable; but Russell’s emphasis on the importance of formal proofs in logic and mathematics provides an alternative vindication of the role of language as the embodiment of truth in mathematics and geometry. Merleau-Ponty offers a different approach which draws on the importance of language in upholding the traditions which sustain abstract sciences such as geometry, but since he downgrades the significance of formal proofs it is not clear what the role of language is supposed to be.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
In the talk which I gave in Dublin from which this paper derives I also discussed Derrida’s introduction to his translation of Husserl’s essay (see Derrida 1978). I have decided not to discuss Derrida’s introduction here, interesting though it is, because it raises rather different issues from those which I deal with here, though I plan to return to it on another occasion.
- 3.
Following Husserl’s death in 1938, with the Crisis uncompleted and unpublished, Eugen Fink published an edited version of the essay in the special 1939 edition of the Revue Internationale de philosophie dedicated to Husserl’s memory. Fink modified Husserl’s 1936 text a good deal, perhaps following discussions with Husserl. Almost every sentence in Fink’s version differs from Husserl’s 1936 text. Fink also omitted the first two paragraphs which include the references to Galileo, perhaps in order to make the essay appear self-standing. But Walter Biemel went back to the original 1936 text for his edition of the Crisis, where the essay occurs as ‘Beilage III’ (Husserl 1962, 365–86), and David Carr included a translation of this text as ‘Appendix VI’ in his translation of the Crisis (Husserl 1970a, 353–78, 1970b).
- 4.
For an extended discussion of the early development of geometry in Babylon, Egypt and Greece, see Kline (1972).
- 5.
- 6.
See note 3 above.
- 7.
There is a similar reference to Husserl’s essay at the start of Merleau-Ponty’s essay ‘On the Phenomenology of Language’ (Merleau-Ponty 1964, 85, n. 3).
- 8.
A corrected edition of these notes was translated into English by Leonard Lawlor in Merleau-Ponty (2002b), and I use this for my page references although I have occasionally modified the translations.
- 9.
I am much indebted to Rasmus Jensen for comments on an earlier draft of this paper.
References
Aubrey, J. (1898). In A. Clark (Ed.), Brief lives, 2 vols . Oxford: Clarendon Press.
Derrida, J. (1978) Edmund Husserl’s origin of geometry: An introduction (J. Leavey, Trans.). London: University of Nebraska Press.
Evans, G. (1982). In J. McDowell (Ed.), The varieties of reference. Oxford: Clarendon Press.
Hacking, I. (1973). Leibniz and Descartes: Proof and eternal truths. Proceedings of the British Academy, 59, 175–188.
Hopkins, J. (1973). Visual geometry. Philosophical Review, 82, 3–34.
Hopkins, B. (2011). The origin of the logic of symbolic mathematics: Edmund Husserl and Jacob Klein. Bloomington: Indiana University Press.
Husserl, E. (1962). Die Frage nach dem Ursprung der Geometrie als intentionalhistoriches Problem, Beilage III in ed. W. Biemel, Husserliana VI. (2nd ed., 365–386). The Hague: Martinus Nijhoff.
Husserl, E. (1970a). The origin of geometry, Appendix VI. In The crisis in European sciences and transcendental phenomenology (David Carr of Husserl (1962), Trans., pp. 353–378). Evanston: Northwestern University Press.
Husserl, E. (1970b). Logical investigations. (J. Findlay, Trans., Vol. I). London: Routledge & Kegan Paul.
Klein, J. (1968). Greek mathematical thought and the origin of algebra (E. Brann, Trans.). Cambridge: MIT Press.
Kline, M. (1972). Mathematical thought from ancient to modern times (Vol. I). Oxford: Oxford University Press.
Kuhn, T. (1970). The structure of scientific revolutions (2nd ed.). Chicago: The University of Chicago Press.
Lakatos, I. (1976). Proofs and refutations. Cambridge: Cambridge University Press.
Merleau-Ponty, M. (1964). Signs (R. C. McCleary, Trans.). Evanston: Northwestern University Press.
Merleau-Ponty, M. (1968). The visible and the invisible (A. Lingis, Trans.). Evanston: Northwestern University Press.
Merleau-Ponty, M. (1998). In R. Barbaras (Ed.), Notes de cours sur L’origine de la géometrie de Husserl. Paris: Presses Universitaires de France.
Merleau-Ponty, M. (2002a). Phenomenology of perception (C. Smith, Trans.). London: Routledge.
Merleau-Ponty, M. (2002b). In L. Lawlor with B. Vergo (Ed.), Husserl at the limits of phenomenology. Evanston: Northwestern University Press. (This includes a translation of Merleau-Ponty (1998))
Russell, B. (1992). The theory of logical types, collected papers 6. London: Routledge.
Russell, B. (1993). Recent works on the principles of mathematics, collected papers 3. London: Routledge.
Strawson, P. (1966). The bounds of sense. London: Methuen.
Wittgenstein, L. (1978). Remarks on the foundations of mathematics (3rd ed.). Oxford: Blackwell.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Baldwin, T. (2013). Language as the Embodiment of Geometry. In: Jensen, R., Moran, D. (eds) The Phenomenology of Embodied Subjectivity. Contributions to Phenomenology, vol 71. Springer, Cham. https://doi.org/10.1007/978-3-319-01616-0_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-01616-0_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01615-3
Online ISBN: 978-3-319-01616-0
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)