Skip to main content

Balancing Necessity and Fallibilism: Charles Sanders Peirce on the Status of Mathematics and its Intersection with the Inquiry into Nature

  • Chapter
Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle

Part of the book series: The Western Ontario Series in Philosophy of Science ((WONS,volume 73))

An interest in Charles Sanders Peirce and pragmatist thought in general emerged in the United States in the middle of last century to exert a powerful influence on a generation of American philosophers educated in the 1940s and 1950s, including Abner Shimony, whose thought is the occasion for this paper. Those threads in Peirce's work related to developing a scientifically informed worldview and metaphysics were the natural influences on Abner and this paper will begin by briefly reviewing a number of these threads and their influences in his writings. This sets the scene for the main project of the paper, an earlier historical project on a related aspect of Peirce's thought—his understanding of mathematics and its place in the description of nature. Mathematics was a foundational discipline for Peirce, one with qualities of necessity and certainty, features that stand in interesting contrast and tension to Peirce's view of an evolving nature which is governed by chance and our knowledge of which is always fallible and thus open to revision. Exploring these issues reveals deep background beliefs structuring Peirce's thought. The paper concludes in the contemporary realm with the speculation that due to the scientific developments of the 20th century, aspects of Peirce's work that formed a vision for a scientific metaphysics for earlier generations may be less relevant now. Nevertheless, the naturalistic spirit and orientation of Peirce's work remains compelling and productive.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Peirce, Charles S. (1992). Reasoning and the logic of things: the Cambridge conferences lectures of 1898. Cambridge, MA, Harvard University Press. Edited by Kenneth Laine Ketner; with an introduction by Kenneth Laine Ketner and Hilary Putnam.

    Google Scholar 

  2. Haack, Susan (1996). “Between Scientism and Conversationalism.” Philosophy and Literature 20(2): 455–474.

    Article  Google Scholar 

  3. Buchler (1939), Justus (1939). Charles Peirce's Empiricism. New York: Harcourt Brace and Company.

    Google Scholar 

  4. Nagel, Ernest (1940). “Charles S. Peirce, Pioneer of Modern Empiricism.” Philosophy of Science 7: 69–80.

    Article  Google Scholar 

  5. Kloppenberg, James T. (1996). “Pragmatism: An Old Name for Some New Ways of Thinking?” Journal of American History 83: 100–138.

    Article  Google Scholar 

  6. Rockmore, T. (2004). “On the Structure of Twentieth-Century Philosophy.” Metaphilosophy 35: 466–478.

    Article  Google Scholar 

  7. Bernstein, Richard J. (1992). “The Resurgence of Pragmatism.” Social Research 59: 813–840.

    Google Scholar 

  8. Brent, Joseph (1993). Charles Sanders Peirce: a life. Bloomington, IN, Indiana University Press.

    MATH  Google Scholar 

  9. Peirce, Charles S. (1992). The essential Peirce: selected philosophical writings, Vol. 1. Bloom-ington, IN, Indiana University Press. Edited with an introduction by Nathan Houser and Christian J. W. Kloesel.

    Google Scholar 

  10. Peirce, Charles S. (1998). The essential Peirce: selected philosophical writings, Vol. 2. Bloom-ington, IN, Indiana University Press. Edited by the Peirce Edition Project; with an introduction by Nathan Houser.

    Google Scholar 

  11. Goudge, Thomas A. (1950). The thought of C. S. Peirce. Toronto, University of Toronto Press.

    Google Scholar 

  12. Murphey, Murray G. (1961). The development of Peirce's philosophy. Cambridge, MA, Harvard University Press.

    Google Scholar 

  13. Hookway, Christopher (1985). Pe i rc e. London/Boston, Routledge &Kegan Paul.

    Google Scholar 

  14. Houser, Nathan, Don D. Roberts, and James Van Evra (1997) (eds.). Studies in the logic of Charles Sanders Peirce. Bloomington, IN, Indiana University Press.

    Google Scholar 

  15. Peirce, Charles S. (1931–1958). Collected papers of Charles Sanders Peirce. Vols. 1–8 Cambridge. Originally published: Cambridge, MA, Harvard University Press. Edited by Paul Weiss and Charles Hartshorne and A. W. Burk.

    Google Scholar 

  16. Peirce, Charles S. (1982). Writings of Charles S. Peirce: a chronological edition. Blooming-ton, IN, Indiana University Press. Edited by Max Harold Fisch and Christian J. W. Kloesel.

    Google Scholar 

  17. Gross, Neil (2003). “Richard Rorty's Pragmatism: A Case Study in the Sociology of Ideas.” Theory & Society 32: 93–148.

    Article  Google Scholar 

  18. Shimony, Abner (1993). Search for a naturalistic world view. 2 volumes, Cambridge [England]/New York, NY, Cambridge University Press.

    Google Scholar 

  19. Shimony, Abner (2002). Transcript of oral history interview of Abner Shimony by Joan Bromberg, September 9 and 10, 2002. Niels Bohr Library, American Institute of Physics, 147 pp.

    Google Scholar 

  20. Haack, Susan (2005). “Formal Philosophy? A Plea for Pluralism” in Vincent F. Hendricks and John Symons, eds., Formal Philosophy, Automatic Press, pp. 77–98.

    Google Scholar 

  21. Bernstein, Richard J. (2006). “Pragmatic Reflections on Tolerance.” Available online at http://www.pucp.edu.pe/eventos/congresos/filosofia/programageneral/lunes/plenaria/BernsteinRichard.pdf

  22. Rockmore, T. (2005). “On Classical and Neo-Analytic Forms of Pragmatism.” Metaphiloso-phy 36: 259–271.

    Article  Google Scholar 

  23. Shimony, Abner (1999). “Can the Fundamental Laws of Nature Be the Result of Evolution?” in C. Pagonis and J. Butterfield, eds., From physics to philosophy. Cambridge/New York, Cambridge University Press, pp. 208–223.

    Google Scholar 

  24. Davies, Paul (2007). “The Universe's Weird Bio-Friendliness.” The Chronicle of Higher Education 53(31): B14.

    Google Scholar 

  25. Skrbina, David (2005). Panpsychism in the West. Cambridge, MA, MIT Press.

    Google Scholar 

  26. Shimony, Abner (2002). “Some Intellectual Obligations of Epistemological Naturalism” in D. B. Malement, ed., Reading natural philosophy: essays in the history and philosophy of science and mathematics. Chicago, IL, Open Court, pp. 297–313.

    Google Scholar 

  27. Peirce, Charles S. (1979). The new elements of mathematics. 4 volumes. The Hague, Mouton/ Humanities Press. Edited by Carol Eisele.

    Google Scholar 

  28. Eisele, Carolyn (1979). Studies in the scientific and mathematical philosophy of Charles S. Peirce: essays by Carolyn Eisele. The Hague/New York, Mouton. Edited by R. M. Martin.

    Google Scholar 

  29. Joswick, Hugh (1988). “Peirce's Mathematical Model of Interpretation.” Transactions of the Charles S. Peirce Society 24: 107–121.

    Google Scholar 

  30. Levy, Stephen H. (1997). “Peirce's Theoremic/Corollarial Distinction and the Interconnections between Mathematics and Logic“ in N. Houser, D. D. Roberts, and J. Van Evra, eds., Studies in the logic of Charles Sanders Peirce. Bloomington, IN, Indiana University Press, pp. 85–110.

    Google Scholar 

  31. Cooke, Elizabeth F. (2003). “Peirce, Fallibilism, and the Science of Mathematics.” Philosophia Mathematica 11: 158–175.

    MATH  MathSciNet  Google Scholar 

  32. Campos, Daniel (2007). “Peirce on the Role of Poetic Creation in Mathematical Reasoning.” Transactions of the Charles S. Peirce Society 43: 470–489.

    Google Scholar 

  33. Eisele, Carolyn (1971). “The mathematical foundations of Peirce's Philosophy” in Studies in the scientific and mathematical philosophy of Charles S. Peirce: essays by Carolyn Eisele. The Hague/New York, Mouton. Edited by R. M. Martin.

    Google Scholar 

  34. Hull, Kathleen (1994). “Why Hanker after Logic? Mathematical Imagination, Creativity, and Perception in Peirce's Systematic Philosophy.” Transactions of the Charles S. Peirce Society 30: 271–296.

    Google Scholar 

  35. Dipert, Randall R. (1994). “Peirce's Underestimated Place in the History of Logic: A Response to Quine,” in Kenneth L. Ketner, ed., Peirce and Contemporary Thought: Philosophical Inquiries, New York: Fordham University Press, 32–58.

    Google Scholar 

  36. Whately, Richard (1826). Elements of logic: comprising the substance of the article in the Encyclopedia Metropolitana; with additions, &c. London, J. Mawman.

    Google Scholar 

  37. Peirce, Charles S. and Victoria Welby (2001). Semiotic and significs: the correspondence between Charles S. Peirce and Victoria Lady Welby. Elsah, IL, Arisbe Associates. Edited by Charles S. Harwick and James Cook.

    Google Scholar 

  38. Peirce (1870) Peirce, Benjamin (1881). “Linear Associative Algebra.” American Journal of Mathematics 4: 97–229. This paper is based on a memoir read before the National Academy of Sciences in Washington, 1870. It was published posthumously with notes by Charles S. Peirce.

    Google Scholar 

  39. Seibert, Charles H. (2005). “Charles Peirce's Reading of Richard Whately's ‘Elements of Logic’.” History and Philosophy of Logic 26: 1–31.

    Article  MATH  MathSciNet  Google Scholar 

  40. Boole, George (1847). The mathematical analysis of logic: being an essay towards a calculus of deductive reasoning. Cambridge, England, Macmillan Barclay & Macmillan.

    Google Scholar 

  41. Babbage, Charles and John Herschel (1813). “Preface.” Memoirs of the Analytical Society: i–xxii.

    Google Scholar 

  42. Chrystal, George (1883). “Mathematics”. The ninth edition, Encyclopaedia Britannica. Vol. 15. Edinburgh, Adam & Charles Black.

    Google Scholar 

  43. Peirce, Benjamin (1881). Ideality in the physical sciences. Boston, FL, Little Brown & Co.

    Google Scholar 

  44. Peirce, Benjamin (1880). “The impossible in mathematics”, in Mrs. John T. Sargent, ed., Sketches and reminiscences of the Radical Club of Chestnut St. Boston. Boston, FL, James R. Osgood, pp. 376–379.

    Google Scholar 

  45. Sylvester, James J. (1868). “Presidential Address to the British Association.” reproduced in Sylvester's mathematical papers, vol. 2, p. 654.

    Google Scholar 

  46. Locke, John (1690). An Essay Concerning Human Understanding. London.

    Google Scholar 

  47. Anderson, Ronald and Girish Joshi (1993). “Quaternions and the Heuristic Role of Mathematical Structures in Physics.” Physics Essays 6: 308–319.

    Article  MathSciNet  Google Scholar 

  48. Anderson, Ronald and Girish Joshi (2008), “Interpreting Mathematics in Physics: Charting the Applications of SU(2) in 20th Century Physics.” Chaos, Solitons & Fractals, 36: 397–404.

    Article  MATH  Google Scholar 

  49. Herschel, John F. W. 1831. Preliminary Discourse on the Study of Natural Philosophy. London: Longman, Rees, Orme, Brown, and Green.

    Book  Google Scholar 

  50. Gray, Jeremy J. (2004). “Anxiety and Abstraction in Nineteenth-Century Mathematics.” Science in Context 17: 23–47.

    Article  MATH  MathSciNet  Google Scholar 

  51. Peirce, Charles S. (1975). Charles Sanders Peirce: contributions to the nation. Lubbock, TX, Texas Tech Press. Compiled and annotated by Kenneth Laine Ketner and James Edward Cook.

    Google Scholar 

  52. Haack, Susan (1979). “Fallibilism and Necessity.” Synthese 41: 37–63.

    Article  MathSciNet  Google Scholar 

  53. Bernstein, Richard J. (1989). “Pragmatism, Pluralism and the Healing of Wounds.” Proceedings and Addresses of the American Philosophical Association 63: 5–18.

    Article  Google Scholar 

  54. Mancosu, Paolo (1997). From Brouwer to Hilbert: the debate on the foundations of mathematics in the 1920s. Oxford: Oxford University Press.

    Google Scholar 

  55. Giaquinto, M. (2002). The search for certainty: a philosophical account of foundations of mathematics. Oxford/New York, Clarendon Press/Oxford University Press.

    MATH  Google Scholar 

  56. Thagard, Paul and Beam, Craig (2004). “Epistemological Metaphors and the Nature of Philosophy.” Metaphilosophy 35: 504–516.

    Article  Google Scholar 

  57. Abrams, Jerold J. (2002). “Philosophy After the Mirror of Nature: Rorty, Dewey, and Peirce on Pragmatism and Metaphor.” Metaphor and Symbol 3: 227–242.

    Article  Google Scholar 

  58. Steward, Dugald (1854–1860). The collected works of Dugald Stewart. Edited by Sir W. Hamilton: 11 vols., Edinburgh, T. Constable: Vols. 2–4, Elements of the Philosophy of the Human Mind, vol. II first published 1814.

    Google Scholar 

  59. Chihara, Charles S. (2004). A structural account of mathematics. Oxford/New York, Clarendon/Oxford University Press.

    MATH  Google Scholar 

  60. Bourbaki, Nicolas (1994). Elements of the history of mathematics. Berlin/New York, Springer-Ve r l ag.

    MATH  Google Scholar 

  61. Cooke, Elizabeth F. (2007). “Peirce's General Theory of Inquiry and the Problem of Mathematics” (under review).

    Google Scholar 

  62. Whitehead, Alfred N. (1926). Science and the modern world. Cambridge: Cambridge University Press.

    Google Scholar 

  63. Dewey, John (1938), The later works, 1925–1953, Volume 12, Carbondale and Edwardsville, IL, Southern Illinois University Press, Edited by Jo Ann Boydston.

    Google Scholar 

  64. Campos, Daniel G. (2005). The Discovery of Mathematical Probability Theory: A Case Study in the Logic of Mathematical Inquiry. Ph.D. thesis, Pennsylvania State University, UMI AAT 3202479.

    Google Scholar 

  65. Hacking, Ian (1983). Representing and intervening: introductory topics in the philosophy of natural science. Cambridge/New York, Cambridge University Press.

    Google Scholar 

  66. Peirce, Benjamin (1855). A system of analytic mechanics. Boston, FL, Little Brown & Co.

    Google Scholar 

  67. Walsh, Alison (2000). Relationships Between Logic and Mathematics in the Works of Benjamin and Charles S. Peirce, Ph.D. thesis, Middlesex University.

    Google Scholar 

  68. Peirce, Benjamin (1853). Address of Professor Benjamin Peirce, president of the American Association for the year 1853, on retiring from the duties of president.

    Google Scholar 

  69. Emerson, Edward Waldo (1918). The early years of the Saturday club, 1855–1870. Boston, FL/New York, Houghton Mifflin Co.

    Google Scholar 

  70. Goodman, Nicolas (1991). “Modernizing the Philosophy of Mathematics.” Synthese 88: 119–126.

    Article  MATH  MathSciNet  Google Scholar 

  71. van Kerkhove, Bart (2006). “Mathematical Naturalism: Origins, Guises and Prospects.” Foundations of Science 11: 5–39.

    Article  MATH  MathSciNet  Google Scholar 

  72. Searle, John R. (2006). “Minding the Brain, Review of ‘Seeing Red: A Study in Consciousness’ by Nicholas Humphrey.” The New York Review of Books 53.

    Google Scholar 

  73. Popper, Karl R. (1957). “The Propensity Interpretation of the Calculus of Probability, and the Quantum Theory,” in S. Körner, ed., Observation and Interpretation. London: Butterworths Scientific Publications, pp. 65–70.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media B.V

About this chapter

Cite this chapter

Anderson, R. (2009). Balancing Necessity and Fallibilism: Charles Sanders Peirce on the Status of Mathematics and its Intersection with the Inquiry into Nature. In: Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle. The Western Ontario Series in Philosophy of Science, vol 73. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9107-0_2

Download citation

Publish with us

Policies and ethics