Rocco Gangle

Endicott College
  •  17
    Native diagrammatic soundness and completeness proofs for Peirce’s Existential Graphs (Alpha)
    with Fernando Tohmé and Gianluca Caterina
    Synthese 200 (6). 2022.
    Peirce’s diagrammatic system of Existential Graphs (EGα)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$EG_{\alpha })$$\end{document} is a logical proof system corresponding to the Propositional Calculus (PL). Most known proofs of soundness and completeness for EGα\documentclass[12pt]{minimal} \usepackage{amsmath} \u…Read more
  •  15
    This article examines types of abductive inference in Hegelian philosophy and machine learning from a formal comparative perspective and argues that Robert Brandom’s recent reconstruction of the logic of recollection in Hegel’s Phenomenology of Spirit may be fruitful for anticipating modes of collaborative abductive inference in human/A.I. interactions. Firstly, the argument consists of showing how Brandom’s reading of Hegelian recollection may be understood as a specific type of abductive infer…Read more
  •  16
    A Generic Figures Reconstruction of Peirce’s Existential Graphs
    with Gianluca Caterina and Fernando Tohme
    Erkenntnis 87 (2): 623-656. 2020.
    We present a category-theoretical analysis, based on the concept of generic figures, of a diagrammatic system for propositional logic ). The straightforward construction of a presheaf category \ of cuts-only Existential Graphs provides a basis for the further construction of the category \ which introduces variables in a reconstructedly generic, or label-free, mode. Morphisms in these categories represent syntactical embeddings or, equivalently but dually, extensions. Through the example of Peir…Read more
  •  7
    A Generic Figures Reconstruction of Peirce’s Existential Graphs (Alpha)
    with Fernando Tohme and Gianluca Caterina
    Erkenntnis 87 (2): 623-656. 2020.
    We present a category-theoretical analysis, based on the concept of generic figures, of a diagrammatic system for propositional logic (Peirce’s Existential Graphs α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}). The straightforward construction of a presheaf category EGα∗\documentclass[12pt]…Read more
  •  14
    Abductive Spaces: Modeling Concept Framework Revision with Category Theory
    with Gianluca Caterina and Fernando Tohmé
    In John R. Shook & Sami Paavola (eds.), Abduction in Cognition and Action: Logical Reasoning, Scientific Inquiry, and Social Practice, Springer Verlag. pp. 49-73. 2021.
    A formal model of abductive inference is provided in which abduction is conceived as expansive and contractive movements through a topological space of theoretical and practical commitments. A pair of presheaves over the space of commitments corresponds to communities sharing commitments on the one hand and possible obstructions to commitments on the other. In this framework, abductive inference is modeled by the dynamics of redistributed communities of commitment made in response to obstructive…Read more
  •  2
    Laruelle and Ordinary Life
    In John Mullarkey & Anthony Paul Smith (eds.), Laruelle and Non-Philosophy, Edinburgh University Press. pp. 60-79. 2012.
  •  29
    A Generic Figures Reconstruction of Peirce’s Existential Graphs
    with Gianluca Caterina and Fernando Tohme
    Erkenntnis 85 1-34. 2020.
    We present a category-theoretical analysis, based on the concept of generic figures, of a diagrammatic system for propositional logic ). The straightforward construction of a presheaf category \ of cuts-only Existential Graphs provides a basis for the further construction of the category \ which introduces variables in a reconstructedly generic, or label-free, mode. Morphisms in these categories represent syntactical embeddings or, equivalently but dually, extensions. Through the example of Peir…Read more
  • The Logic of Picturing: Wittgenstein, Sellars and Peirce’s EG-beta
    with Fernando Tohmé and Gianluca Caterina
    In Matthieu Fontaine, Cristina Barés-Gómez, Francisco Salguero-Lamillar, Lorenzo Magnani & Ángel Nepomuceno-Fernández (eds.), Model-Based Reasoning in Science and Technology: Inferential Models for Logic, Language, Cognition and Computation, Springer Verlag. 2019.
  •  96
    Brandom's method of analyzing pragmatic relations among different practices and vocabularies through meaning-use diagrams is used to specify how Laruelle's nonphilosophical suspension of the Principle of Sufficient Philosophy may be distinguished from the philosophical auto-critiques of such thinkers as Badiou and Derrida. A superposition of diagrams modeling philosophical sufficiency on the one hand and supplementation through the Other on the other provides a schematic representation of the co…Read more
  •  13
    The semiotics of intuition, care, and esotericism in education
    Semiotica 2019 (227): 341-347. 2019.
    A review of Inna Semetsky’s The Edusemiotics of Images: Essays on the Art-Science of Tarot with reference to Peircean semiotics, Deleuze’s philosophy of difference and the feminist ethics of care.
  •  11
    Everything you need to understand both Laruelle's critique of difference and his project of non-philosophyGilles Deleuze described Laruelle's thought as 'one of the most interesting undertakings of contemporary philosophy'. Now, Rocco Gangle - who translated Laruelle's philosophy into English - takes you through Laruelle's trailblazing book Philosophies of Difference, helping you to understand both Laruelle's critique of Difference and his project of non-philosophy, which has become one of the m…Read more
  •  38
    Iconicity and Abduction
    with Gianluca Caterina
    Springer. 2016.
    This book consolidates and extends the authors’ work on the connection between iconicity and abductive inference. It emphasizes a pragmatic, experimental and fallibilist view of knowledge without sacrificing formal rigor. Within this context, the book focuses particularly on scientific knowledge and its prevalent use of mathematics. To find an answer to the question “What kind of experimental activity is the scientific employment of mathematics?” the book addresses the problems involved in forma…Read more
  •  11
    Diagrammatic Immanence: Category Theory and Philosophy
    Edinburgh University Press. 2015.
    Rocco Gangle addresses the methodological questions raised by a commitment to immanence in terms of how diagrams may be used both as tools and as objects of philosophical investigation. Gangle integrates insights from Spinoza, Pierce and Deleuze in conjunction with the formal operations of category theory.
  •  31
    Spinoza for Our Time: Politics and Postmodernity
    with Antonio Negri
    Columbia University Press. 2013.
    Antonio Negri, a leading scholar on Baruch Spinoza (1632–1677) and his contemporary legacy, offers a straightforward explanation of the philosopher’s elaborate arguments and a persuasive case for his ongoing utility.
  •  7
    Superpositions: Laruelle and the Humanities (edited book)
    with Julius Greve
    Rowman & Littlefield International. 2017.
    This book examines the relevance of François Laruelle’s innovative notion of non-standard philosophy to critical and constructive discourses in the humanities, bringing together essays from prominent Anglophone scholars of Laruelle’s work and includes a contribution from Laurelle himself.
  •  30
    Abduction: A categorical characterization
    with Fernando Tohmé and Gianluca Caterina
    Journal of Applied Logic 13 (1): 78-90. 2015.
  •  65
    Laruelle for Levinas
    Philosophy Today 53 (Supplement): 250-256. 2009.
    A comparison and contrast of the notions of subjectivity and otherness in Levinasian phenomenology and Laruelle's non-philosophy.
  •  47
    The sheet of indication: a diagrammatic semantics for Peirce’s EG-alpha
    with Gianluca Caterina
    Synthese 192 (4): 923-940. 2015.
    Following the guiding thread of Peirce’s use of diagrammatic syntax in his system of existential graphs , which depends crucially on the role of the Sheet of Assertion, we introduce the notion of Sheet of Indication as the basis for a general diagrammatic semantics applicable to a wide range of diagrams. We then show how Peirce’s EG-alpha graphs may be understood as instances of SIs and how logically coherent models of the graphs are represented in the SI semantics
  •  29
    Gilles Deleuze and Metaphysics
    with Arnauld Villani, Alberto Anelli, Sjoerd van Tuinen, Joshua Ramey, Daniel Whistler, Adrian Switzer, Gregory Kalyniuk, Thomas Nail, and Mary Beth Mader
    Lexington Books. 2014.
    This collection examines an aspect of Gilles Deleuze’s thought that has largely been neglected; whether or not Deleuze was a metaphysician. Answering this question may reveal the problematic nature of so-called postmodernism and the critique it leveled at the first philosophy, and it may help readers to better understand philosophy’s fate
  •  12
    Laruelle for Levinas
    Philosophy Today 53 (Supplement): 250-256. 2009.
  •  95
    Abstract.Stuart Kauffman's proposal in Investigations to ground a “general biology” in the laws of self‐organization governing systems of autonomous agents runs up against the methodological problem of how to integrate formal mathematical with semantic and semiotic approaches to the study of evolutionary development. Gilles Deleuze's concept of the virtual and C. S. Peirce's system of existential graphs provide a theoretical framework and practical art for answering this problem of method by mod…Read more
  •  233
    Renovating Philosophical Practice through Diagrammatic Reasoning
    Proceedings of the Xxii World Congress of Philosophy 4 47-52. 2008.
    The approach to the question of philosophical practice has been dominated by a subordination of practice to theory corresponding in general to a representational conception of philosophy. Methods of diagrammatic reasoning developed within philosophical semiotics provide a more effective approach. Inparticular, Peirce’s system of existential graphs exemplifies how diagrammatic reasoning is able formally to express the processes through which philosophical dialogue and cooperation actually take pl…Read more