Peirce's Inversions of the Topological and the Logica!. Forgotten Roads for our Contemporary World

Journal title RIVISTA DI STORIA DELLA FILOSOFIA
Author/s Fernando Zalamea
Publishing Year 2017 Issue 2017/3
Language English Pages 20 P. 415-434 File size 22305 KB
DOI 10.3280/SF2017-003004
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We present Peirce’s Existential Graphs as systems of geometric logic, where some inversions are proposed between the logical and the topological, the logos and the topos. Imagination, visualization, abduction and pragmatism can thus be comprehended independently of the linguistic, syntactic, deductive or normative aspects of logic. The shift of perspectives allows a plasticity and a dynamism characteristic of Peirce’s entire architectonics. As a consequence of the inversions, a full, extended reason, capable of comparing and gluing the local and the global, can be applied to the complex, non-linear, ramified spaces of our contemporary World. The paper is divided into the following sections: (1) a synthetic account of Peirce’s Existential Graphs; (2) some inversions of the logos and the topos in the Existential Graphs; (3) some wider topological dialectics along Charles S. Peirce’s architectonics; (4) the "visual turn" of our contemporary World: mathematics, art, and a return to Novalis; (5) category-theory and Peirce’s topo/logical insights one century later.

Keywords: Charles S. Peirce, logic, topology, local/global, obstructions/transits.

  1. Robin 1967: Richard S. Robin, Annotated Catalogue of the Papers of Charles S. Peirce, The University of Massachusetts Press, Amherst 1967. [MS] refers to The Charles S. Peirce Papers, microfilm edition, Harvard University Library, Photographic Service, Cambridge 1966. An entry [MS xyz] refers to manuscript number xyz in Robin 1967.
  2. Robin 1997: Id., Classical Pragmatism and Pragmatism’s Proof, in Jacqueline Brunning, Paul Forster (eds.), The Rule of Reason. The Philosophy of Charles Sanders Peirce, University of Toronto Press, Toronto 1997.
  3. Rodríguez Magda 1998: Rosa María Rodríguez Magda, La sonrisa de Saturno. Hacia una teoría transmoderna, Anthropos, Barcelona 1998.
  4. Rosensohn 1974: William L. Rosensohn, The Phenomenology of Charles S. Peirce, Grüner, Amsterdam 1974.
  5. Thibaud 1975: Pierre Thibaud, La logique de Charles Sanders Peirce: De l’algèbre aux graphes, Université de Provence, Aix-en-Provence 1975.
  6. Thuillier 2003: Jacques Thuillier, Théorie générale de l’histoire de l’art, Odile Jacob, Paris 2003.
  7. Grothendieck 1970-73: Alexander Grothendieck, Séminaire de Géométrie Algébrique du Bois-Marie, 7 vols. (12 parts), Springer, Berlin 1970-1973.
  8. Grothendieck 1985: Id., Récoltes et sémailles, manuscript, 1252 pp. 1985-1986, --available at www.grothendieckcircle.org.
  9. Valéry 1957-1961: Paul Valéry, Cahiers, 29 vols, CNRS, Paris 1957-1961.
  10. Warburg 1924-1929: Aby Warburg, Mnemosyne. L’Atlante delle immagini, Marcello Ghilardi (a cura di), Nino Aragno, Torino 2002.
  11. Zalamea 2012a: Fernando Zalamea, Peirce’s Logic of Continuity, Docent Press, Boston 2012.
  12. Zalamea 2012b: Id., Synthetic Philosophy of Contemporary Mathematics, Collapse-Sequence, Falmouth-New York 2012.
  13. Zalamea 2013: Id., Antinomias de la creación. Las fuentes contradictorias de la invención en Valéry, Warburg, Florenski, Fondo de Cultura Económica, Santiago de Chile 2013.
  14. Zeman 1964: Jay Zeman, The Graphical Logic of C.S. Peirce, Ph.D. Thesis, University of Chicago 1964.
  15. Badiou 1998: Alain Badiou, Court traité d’ontologie transitoire, Seuil, Paris 1998.
  16. Benjamin 2000: Walter Benjamin, I “passages” di Parigi, Rolf Tiedemann, Enrico Ganni (eds.), Einaudi, Torino 2000.
  17. Brady, Trimble 2000: Geraldine Brady, Todd Trimble, A Categorical Interpretation of C. S. Peirce’s Propositional Logic Alpha, «Journal of Pure and Applied Algebra», 149 (2000), pp. 213-239.
  18. Burch 1991: Robert Burch, A Peircean Reduction Thesis. The Foundations of Topological Logic, Texas Tech University Press, Lubbock 1991.
  19. Cantù 1999: Paola Cantù, Giuseppe Veronese e i fondamenti della geometria, Edizioni Unicopli, Milano 1999.
  20. Cassou-Noguès 2008: Pierre Cassou-Noguès, Gödel, Les Belles Lettres, Paris 2008.
  21. Costa da, Béziau 1997: Newton da Costa, Jean-Yves Béziau, Logiques classiques et non-classiques, Masson, Paris 1997.
  22. De Tienne 1996: André De Tienne, L’analytique de la représentation chez Peirce. La genèse de la théorie des catégories, Presses de l’Université de Saint-Louis, Bruxelles 1996.
  23. Esposito 1980: Joseph L. Esposito, Evolutionary Metaphysics: The Development of Peirce’s Theory of Categories, Ohio University Press, Athens 1980.
  24. Fabbrichesi 1986: Rossella Fabbrichesi Leo, Sulle tracce del segno. Semiotica, faneroscopia e cosmologia nel pensiero di C. S. Peirce, La Nuova Italia, Firenze 1986.
  25. Florensky 2014: Pavel Florensky, At the Crossroads of Science & Mysticism, Boris Jakim (ed.), Semantron Press, Kettering 2014.
  26. Francastel 1965: Pierre Francastel, La réalité figurative, in Id., Oeuvres, vol. II, Denoël-Gonthier, Paris 1965.
  27. Hadamard 1943: Jacques Hadamard, Essai sur la psychologie de l’invention dans le domaine mathématique, Albert Blanchard, Paris 1959.
  28. Hanssen 2006: Beatrice Hanssen (ed.), Walter Benjamin and The Arcades Project, Continuum, New York 2006.
  29. Houser 1997: Nathan Houser et al. (eds.), Studies in the Logic of Charles Sanders Peirce, Indiana University Press, Bloomington 1997.
  30. Kassenbrock 2009: Brian W. Kassenbrock, Novalis and the Two Cultures: The Chiasmic Discourse of Mathematics, Philosophy and Poetics, Ph. D. Thesis, New York University, 2009.
  31. Kent 1987: Beverley Kent, Charles S. Peirce. Logic and the Classification of Sciences, McGill-Queen’s University Press, Montreal 1987.
  32. Lautman 2006: Albert Lautman (ed.), Les mathématiques, les idées et le réel physique, Vrin, Paris 2006.
  33. Lautman 2011: Id., Ensayos sobre la dialéctica, estructura y unidad de las matemáticas modernas, Fernando Zalamea (ed.), Universidad Nacional, Bogotá 2011.
  34. Lawvere, Schanuel 1997: William Lawvere, Stephen Schanuel, Conceptual Mathematics, Cambridge University Press, Cambridge 1997.
  35. Mac Lane 1986: Saunders Mac Lane, Mathematics. Form and Function, Springer, New York 1986.
  36. Margantin 1998: Laurent Margantin, Système minéralogique et cosmologique chez Novalis, ou les plis de la terre, L’Harmattan, Paris 1998.
  37. Mayorga 2007: Rosa Mayorga, From Realism to “Realicism”. The Metaphysics of Charles Sanders Peirce, Lexington Books, Lanham 2007.
  38. Murphey 1961: Murray G. Murphey, The Development of Peirce’s Philosophy, Harvard University Press, Cambridge 1961.
  39. Novalis 1993: Novalis, Opera filosofica, Fabrizio Desideri e Giampiero Moretti (a cura di), vol. II, Einaudi, Torino 1993.
  40. Oostra 2010: Arnold Oostra, Los gráficos Alfa de Peirce aplicados a la lógica intuicionista, «Cuadernos de Sistemática Peirceana», 2 (2010), pp. 25-60.
  41. Peirce 1975-1987: Charles Sanders Peirce, Contributions to the Nation, 5 vols., Kenneth L. Ketner, James E. Cook (eds.), Texas Tech University Press, Lubbock 1975-1987.
  42. Peirce 1992: Id., Categorie, Rossella Fabbrichesi Leo (a cura di.), Laterza, Roma-Bari 1992.
  43. Peirce CP followed by volume and paragraph number: Id., Collected Papers, vols. I-VI, Paul Weiss and Charles Hartshorne (eds.), Harvard University Press, Cambridge (MA) 1931-1935; vols. VII-VIII, Arthur W. Burks (ed.), Harvard University Press, Cambridge (MA) 1958.
  44. Peirce NEM followed by volume and page number: Id., The New Elements of Mathematics, 4 vols., Carolyn Eisele (ed.), Mouton, The Hague 1976.
  45. Peirce W followed by volume and page number: Id., Writings (A Chronological Edition), 7 vols., The Peirce Edition Project (eds.), Indiana University Press, Bloomington 1982-2010.
  46. Petitot 2009: Jean Petitot, Per un nuovo illuminismo, Bompiani, Milano 2009.
  47. Poincaré 1908: Henri Poincaré, L’invention mathématique, Institut Général Psychologique, Paris 1908.
  48. Poizat 2000: Bruno Poizat, A Course in Model Theory. An Introduction to Contemporary Logic, Springer, New York 2000.
  49. Quine 1934: Willard V. O. Quine, Review – Collected Papers of Charles Sanders Peirce – Volume IV, «Isis», XXII (1934), pp. 551-553.
  50. Riemann 1851: Bernhard Riemann, Principes fondamentaux pour une théorie générale des fonctions d’une grandeur variable complexe, in Id., Oeuvres mathématiques, Gauthier-Villars, Paris 1898, pp. 1-60.
  51. Roberts 1973: Don Roberts, The Existential Graphs of Charles S. Peirce, Mouton, The Hague 1973.

  • Logical Principles of a Topological Explanation Ľudmila Lacková, Lukáš Zámečník, in Chinese Semiotic Studies /2020 pp.493
    DOI: 10.1515/css-2020-0027

Fernando Zalamea, Peirce's Inversions of the Topological and the Logica!. Forgotten Roads for our Contemporary World in "RIVISTA DI STORIA DELLA FILOSOFIA" 3/2017, pp 415-434, DOI: 10.3280/SF2017-003004