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

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Model-Based Reasoning in Science and Technology (MBR 2018)

Part of the book series: Studies in Applied Philosophy, Epistemology and Rational Ethics ((SAPERE,volume 49))

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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.

The picture is a model of reality.

L. Wittgenstein, Tractatus

Logico-Philosophicus 2.12

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Notes

  1. 1.

    This example is Sellars’s own as presented and discussed in [16], p. 106.

  2. 2.

    The reader might compare the variant of Peirce’s system detailed in [1] in which the cut as classical negation is also absent but is there replaced with a new type of cut with a non-classical interpretation.

  3. 3.

    Because of our focus on the pictorial character of the graphs and not their strictly logical properties, we do not address the transformation rules of Peirce’s system in this paper.

  4. 4.

    Here the notation \(G(t_n)[G(R_n)]\) represents the action of the “lifted” function \(t_n\) via the functor G as it acts on the “lifted” set \(R_n\) via the same functor G.

  5. 5.

    To organize pictures/states of affairs in a Tarski-style set-theoretical way for instance, given some functor G, one could assign the elements of G(L) to a chosen set M, the elements of each \(T_n\) to a subset of \(M^n\) and each \(R_n\) to an element of \(M^n\) (that is, an n-tuple over M). The functions \(G(r_n^i)\) would then be assigned to the obvious projection maps, and the functions \(G(t_n)\) would be required to send n-tuples \(<a_1,\dots ,a_n>\) to subsets S such that \(<a_1,\dots ,a_n> \in S\).

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Author information

Authors and Affiliations

  1. Endicott College, Beverly, USA

    Rocco Gangle & Gianluca Caterina

  2. Universidad Nacional del Sur/CONICET, Bahía Blanca, Argentina

    Fernando Tohmé

Authors
  1. Rocco Gangle
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  2. Gianluca Caterina
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  3. Fernando Tohmé
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Corresponding author

Correspondence to Gianluca Caterina .

Editor information

Editors and Affiliations

  1. Department of Philosophy, Logic and Philosophy of Science, University of Seville, Seville, Spain

    Ángel Nepomuceno-Fernández

  2. Department of Humanities, Philosophy Section, and Computational Philosophy Laboratory, University of Pavia, Pavia, Italy

    Lorenzo Magnani

  3. Department of Spanish Language, Linguistics and Theory of Literature, University of Seville, Seville, Spain

    Francisco J. Salguero-Lamillar

  4. Department of Philosophy, Logic and Philosophy of Science, University of Seville, Seville, Spain

    Cristina Barés-Gómez

  5. Centre for Philosophy of Science of the University of Lisbon, University of Lisbon, Lisbon, Portugal

    Matthieu Fontaine

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Gangle, R., Caterina, G., Tohmé, F. (2019). The Logic of Picturing: Wittgenstein, Sellars and Peirce’s EG-beta. In: Nepomuceno-Fernández, Á., Magnani, L., Salguero-Lamillar, F., Barés-Gómez, C., Fontaine, M. (eds) Model-Based Reasoning in Science and Technology. MBR 2018. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-030-32722-4_15

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