Iconicity in Peirce’s Semiotics

  • Gianluca CaterinaEmail author
  • Rocco Gangle
Part of the Studies in Applied Philosophy, Epistemology and Rational Ethics book series (SAPERE, volume 29)


The hypothesis of the mathematician is always the conception of a system of relations. In order that they may be reasoned about mathematically, these relations must be conceived as embodied in some kind of objects; but the character of the objects, apart from the relations, is utterly immaterial. They are always made as bare, skeleton-like, or diagrammatic as possible. With mathematicians not born blind, they are always visual objects of the simplest kind, such as dots, or lines, or letters, and the like. The mathematician often passes from one mode of embodiment to another. Such a change is no change in the hypothesis but only in the diagrammatic embodiment of the hypothesis. The hypothesis itself consists in the system of relations alone.


Category Theory Mathematical Reasoning Abductive Reasoning Abductive Inference Axiomatic Method 
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  1. 1.
    C.S. Peirce. Ed. Peirce Edition Project. (1998). The Essential Peirce: Selected Philosophical Writings, vol. 2 (1893–1913) (Indiana University Press, Bloomington and Indianapolis)Google Scholar
  2. 2.
    P. Farias, J. Queiroz, On diagrams for Peirce’s 10, 28, and 66 classes of signs. Semiotica 147(1/4), 165–184 (2003)Google Scholar
  3. 3.
    R.W. Burch, Peirce’s 10, 28, and 66 Sign-Types: The Simplest Mathematics. Semiotica 184, 93–98 (2011)Google Scholar
  4. 4.
    R. Gangle, Diagrammatic Immanence: Category Theory and Philosophy (Edinburgh University Press, Edinbergh, 2016)Google Scholar
  5. 5.
    F. Stjernfelt, Diagrammatology: An Investigation on the Borderlines of Phenomenology, Ontology, and Semiotics (Springer, Berlin, 2007)CrossRefGoogle Scholar
  6. 6.
    C.S. Peirce, Collected Papers of Charles Sanders Peirce, vols 1–6 (Belknap Press, Cambridge, 1931–1935)Google Scholar
  7. 7.
    F. Stjernfelt, Natural Propositions: The Actuality of Peirce’s Doctrine of Dicisigns (Docent Press, Boston, 2014)Google Scholar
  8. 8.
    T.L. Short, Peirce’s Theory of Signs (Cambridge University Press, Cambridge, 2007)CrossRefGoogle Scholar
  9. 9.
    P. Farias, J. Queiroz, Images, Diagrams, and Metaphors: Hypoicons in the Context of Peirce’s Sixty-Six-Fold Classification of Signs. Semiotica 162, 287–307 (2006)Google Scholar
  10. 10.
    A. Rodin, Axiomatic Method and Category Theory (Springer, Heidelberg, 2014)CrossRefGoogle Scholar
  11. 11.
    W. Lawvere, Foundations and Applications: axiomatization and education. Bull. Symb. Log. 9(2), 213–224 (2003)CrossRefGoogle Scholar
  12. 12.
    W. Lawvere, Functorial semantics of algebraic theories and some algebraic problems in the context of functorial semantics of algebraic theories. Repr. Theory Appl. Categ. 5, 1–121 (2004)Google Scholar
  13. 13.
    B. Mélès, Pratique mathmatique et lectures de Hegel, de Jean Cavaillès à William Lawvere. Philosophia Scientiae 16(1), 153–182 (2012)CrossRefGoogle Scholar
  14. 14.
    G.W.F. Hegel, Science of Logic (Prometheus Books, Amherst, 1991)Google Scholar
  15. 15.
    C. McClarty, Elementary Categories (Elementary Toposes, Oxford, 1992)Google Scholar
  16. 16.
  17. 17.
    F. Zalamea, Synthetic Philosophy of Contemporary Mathematics (Urbanomic, 2012)Google Scholar
  18. 18.
    S. Mac Lane, Categories for the Working Mathematician (Springer, Heidelberg, 1998)Google Scholar
  19. 19.
    M. Reyes, G. Reyes, H. Zolfaghari, Generic Figures and Their Glueings (Polimetrica, Milan, 2004)Google Scholar
  20. 20.
    F. Zalamea, Peirce’s Logic of Continuity: A Conceptual and Mathematical Approach (Docent Press, Chestnut Hill, 2012)Google Scholar
  21. 21.
    G. Brady, T.H. Trimble, A categorical interpretation of C.S. Peirce’s propositional logic Alpha. J. Pure Appl. Algebr. 49, 213–239 (2000)CrossRefGoogle Scholar
  22. 22.
    G. Caterina, R. Gangle, Iconicity and abduction: a categorical approach to creative hypothesis-formation in Peirce’s existential graphs. Log. J. IGPL 21(6), 1028–1043 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Department of MathematicsEndicott CollegeBeverlyUSA
  2. 2.Department of Humanities and PhilosophyEndicott CollegeBeverlyUSA

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