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.
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References
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.
Haack, Susan (1996). “Between Scientism and Conversationalism.” Philosophy and Literature 20(2): 455–474.
Buchler (1939), Justus (1939). Charles Peirce's Empiricism. New York: Harcourt Brace and Company.
Nagel, Ernest (1940). “Charles S. Peirce, Pioneer of Modern Empiricism.” Philosophy of Science 7: 69–80.
Kloppenberg, James T. (1996). “Pragmatism: An Old Name for Some New Ways of Thinking?” Journal of American History 83: 100–138.
Rockmore, T. (2004). “On the Structure of Twentieth-Century Philosophy.” Metaphilosophy 35: 466–478.
Bernstein, Richard J. (1992). “The Resurgence of Pragmatism.” Social Research 59: 813–840.
Brent, Joseph (1993). Charles Sanders Peirce: a life. Bloomington, IN, Indiana University Press.
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.
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.
Goudge, Thomas A. (1950). The thought of C. S. Peirce. Toronto, University of Toronto Press.
Murphey, Murray G. (1961). The development of Peirce's philosophy. Cambridge, MA, Harvard University Press.
Hookway, Christopher (1985). Pe i rc e. London/Boston, Routledge &Kegan Paul.
Houser, Nathan, Don D. Roberts, and James Van Evra (1997) (eds.). Studies in the logic of Charles Sanders Peirce. Bloomington, IN, Indiana University Press.
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.
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.
Gross, Neil (2003). “Richard Rorty's Pragmatism: A Case Study in the Sociology of Ideas.” Theory & Society 32: 93–148.
Shimony, Abner (1993). Search for a naturalistic world view. 2 volumes, Cambridge [England]/New York, NY, Cambridge University Press.
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.
Haack, Susan (2005). “Formal Philosophy? A Plea for Pluralism” in Vincent F. Hendricks and John Symons, eds., Formal Philosophy, Automatic Press, pp. 77–98.
Bernstein, Richard J. (2006). “Pragmatic Reflections on Tolerance.” Available online at http://www.pucp.edu.pe/eventos/congresos/filosofia/programageneral/lunes/plenaria/BernsteinRichard.pdf
Rockmore, T. (2005). “On Classical and Neo-Analytic Forms of Pragmatism.” Metaphiloso-phy 36: 259–271.
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.
Davies, Paul (2007). “The Universe's Weird Bio-Friendliness.” The Chronicle of Higher Education 53(31): B14.
Skrbina, David (2005). Panpsychism in the West. Cambridge, MA, MIT Press.
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.
Peirce, Charles S. (1979). The new elements of mathematics. 4 volumes. The Hague, Mouton/ Humanities Press. Edited by Carol Eisele.
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.
Joswick, Hugh (1988). “Peirce's Mathematical Model of Interpretation.” Transactions of the Charles S. Peirce Society 24: 107–121.
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.
Cooke, Elizabeth F. (2003). “Peirce, Fallibilism, and the Science of Mathematics.” Philosophia Mathematica 11: 158–175.
Campos, Daniel (2007). “Peirce on the Role of Poetic Creation in Mathematical Reasoning.” Transactions of the Charles S. Peirce Society 43: 470–489.
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.
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.
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.
Whately, Richard (1826). Elements of logic: comprising the substance of the article in the Encyclopedia Metropolitana; with additions, &c. London, J. Mawman.
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.
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.
Seibert, Charles H. (2005). “Charles Peirce's Reading of Richard Whately's ‘Elements of Logic’.” History and Philosophy of Logic 26: 1–31.
Boole, George (1847). The mathematical analysis of logic: being an essay towards a calculus of deductive reasoning. Cambridge, England, Macmillan Barclay & Macmillan.
Babbage, Charles and John Herschel (1813). “Preface.” Memoirs of the Analytical Society: i–xxii.
Chrystal, George (1883). “Mathematics”. The ninth edition, Encyclopaedia Britannica. Vol. 15. Edinburgh, Adam & Charles Black.
Peirce, Benjamin (1881). Ideality in the physical sciences. Boston, FL, Little Brown & Co.
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.
Sylvester, James J. (1868). “Presidential Address to the British Association.” reproduced in Sylvester's mathematical papers, vol. 2, p. 654.
Locke, John (1690). An Essay Concerning Human Understanding. London.
Anderson, Ronald and Girish Joshi (1993). “Quaternions and the Heuristic Role of Mathematical Structures in Physics.” Physics Essays 6: 308–319.
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.
Herschel, John F. W. 1831. Preliminary Discourse on the Study of Natural Philosophy. London: Longman, Rees, Orme, Brown, and Green.
Gray, Jeremy J. (2004). “Anxiety and Abstraction in Nineteenth-Century Mathematics.” Science in Context 17: 23–47.
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.
Haack, Susan (1979). “Fallibilism and Necessity.” Synthese 41: 37–63.
Bernstein, Richard J. (1989). “Pragmatism, Pluralism and the Healing of Wounds.” Proceedings and Addresses of the American Philosophical Association 63: 5–18.
Mancosu, Paolo (1997). From Brouwer to Hilbert: the debate on the foundations of mathematics in the 1920s. Oxford: Oxford University Press.
Giaquinto, M. (2002). The search for certainty: a philosophical account of foundations of mathematics. Oxford/New York, Clarendon Press/Oxford University Press.
Thagard, Paul and Beam, Craig (2004). “Epistemological Metaphors and the Nature of Philosophy.” Metaphilosophy 35: 504–516.
Abrams, Jerold J. (2002). “Philosophy After the Mirror of Nature: Rorty, Dewey, and Peirce on Pragmatism and Metaphor.” Metaphor and Symbol 3: 227–242.
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.
Chihara, Charles S. (2004). A structural account of mathematics. Oxford/New York, Clarendon/Oxford University Press.
Bourbaki, Nicolas (1994). Elements of the history of mathematics. Berlin/New York, Springer-Ve r l ag.
Cooke, Elizabeth F. (2007). “Peirce's General Theory of Inquiry and the Problem of Mathematics” (under review).
Whitehead, Alfred N. (1926). Science and the modern world. Cambridge: Cambridge University Press.
Dewey, John (1938), The later works, 1925–1953, Volume 12, Carbondale and Edwardsville, IL, Southern Illinois University Press, Edited by Jo Ann Boydston.
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.
Hacking, Ian (1983). Representing and intervening: introductory topics in the philosophy of natural science. Cambridge/New York, Cambridge University Press.
Peirce, Benjamin (1855). A system of analytic mechanics. Boston, FL, Little Brown & Co.
Walsh, Alison (2000). Relationships Between Logic and Mathematics in the Works of Benjamin and Charles S. Peirce, Ph.D. thesis, Middlesex University.
Peirce, Benjamin (1853). Address of Professor Benjamin Peirce, president of the American Association for the year 1853, on retiring from the duties of president.
Emerson, Edward Waldo (1918). The early years of the Saturday club, 1855–1870. Boston, FL/New York, Houghton Mifflin Co.
Goodman, Nicolas (1991). “Modernizing the Philosophy of Mathematics.” Synthese 88: 119–126.
van Kerkhove, Bart (2006). “Mathematical Naturalism: Origins, Guises and Prospects.” Foundations of Science 11: 5–39.
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.
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.
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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
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