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The Logic of Picturing: Wittgenstein, Sellars and Peirce’s EG-beta

  • Rocco Gangle
  • Gianluca CaterinaEmail author
  • Fernando Tohmé
Conference paper
Part of the Studies in Applied Philosophy, Epistemology and Rational Ethics book series (SAPERE, volume 49)

Abstract

The semantics of picturing, broadly understood as an isomorphism between relevant relations among parts of a picture and relations constituting a state of affairs in some target domain, are a core feature of Wittgenstein’s Tractarian theory of representation. This theory was subsequently developed by Wilfrid Sellars into a rich theory of language and cognition. In this paper we show that by recasting the positive fragment (without negation) of C.S. Peirce’s beta level of Existential Graphs as a category of presheaves, the iconic coordination of syntax and semantics in the Wittgensteinian-Sellarsian picturing-relation may be represented formally in terms of the natural transformations in this category.

References

  1. 1.
    Bellucci F, Chiffi D, Pietarinen A-V (2018) Assertive graphs. J Appl Non-Classical Logics 28(1):72–91CrossRefGoogle Scholar
  2. 2.
    Brandom R (1994) Making it explicit: reasoning, representing, and discursive commitment. Harvard, CambridgeGoogle Scholar
  3. 3.
    Brandom R (2015) From empiricism to expressivism: brandom reads sellars. Harvard, CambridgeCrossRefGoogle Scholar
  4. 4.
    Brandom R (2009) Reason in philosophy: animating ideas. Harvard, CambridgeCrossRefGoogle Scholar
  5. 5.
    Butz C (1998) Regular categories and regular logic. BRICS LS, AarhusGoogle Scholar
  6. 6.
    Caterina G, Gangle R (2016) Iconicity and abduction. Springer, New YorkCrossRefGoogle Scholar
  7. 7.
    Caterina G, Gangle R (2013) Iconicity and abduction: a categorical approach to creative hypothesis-formation in peirce’s existential graphs. Logic J IGPL 21(6):1028–1043CrossRefGoogle Scholar
  8. 8.
    Dau F (2003) The logic system of concept graphs with negation. Springer-Verlag, BerlinCrossRefGoogle Scholar
  9. 9.
    Fong B, Spivak D (2019) Graphical regular logic. arXiv:1812.05765v2
  10. 10.
    Mac Lane S (2010) Categories for the working mathematician, 2nd edn. Springer, New YorkGoogle Scholar
  11. 11.
    O’Shea JR (2007) Wilfrid sellars: naturalism with a normative turn. Polity, CambridgeGoogle Scholar
  12. 12.
    Pietarinen A-V (2006) Signs of logic: Peircean themes on the philosophy of language, games and communication. Springer, DordrechtGoogle Scholar
  13. 13.
    Roberts D (1973) The existential graphs of Charles S. Peirce. Mouton, The HagueGoogle Scholar
  14. 14.
    Selinger P (2010) A survey of graphical languages for monoidal categories. In: Coecke B (ed) New structures for physics. Springer, HeidelbergGoogle Scholar
  15. 15.
    Sellars W (1996) Naturalism and ontology. Ridgeview, AtascaderoGoogle Scholar
  16. 16.
    Sellars W (1992) Science and metaphysics: variations on Kantian themes. Ridgeview, AtascaderoGoogle Scholar
  17. 17.
    Shin S-J (2002) The iconic logic of Peirce’s graphs. MIT, CambridgeCrossRefGoogle Scholar
  18. 18.
    Wittgenstein L (2000) Tractatus logico-philosophicus. Routledge, London Trans. Ogden CKGoogle Scholar
  19. 19.
    Wittgenstein L (1978) Philosophical investigations. Basil Blackwell, Oxford Trans. Anscombe GEMGoogle Scholar
  20. 20.
    Zalamea F (2012) Peirce’s logic of continuity. Docent, BostonGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Rocco Gangle
    • 1
  • Gianluca Caterina
    • 1
    Email author
  • Fernando Tohmé
    • 2
  1. 1.Endicott CollegeBeverlyUSA
  2. 2.Universidad Nacional del Sur/CONICETBahía BlancaArgentina

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