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 formalizing abductive cognition. For this, it implements the concept and (...) method of iconicity, modeling this theoretical framework mathematically through category theory and topoi. Peirce's concept of iconic signs is treated in depth, and it is shown how Peirce's diagrammatic logical notation of Existential Graphs makes use of iconicity and how important features of this iconicity are representable within category theory. Alain Badiou’s set-theoretical model of truth procedures and his relational sheaf-based theory of phenomenology are then integrated within the Peircean logical context. Finally, the book opens the path towards a more naturalist interpretation of the abductive models developed in Peirce and Badiou through an analysis of several recent attempts to reformulate quantum mechanics with categorical methods. Overall, the book offers a comprehensive and rigorous overview of past approaches to iconic semiotics and abduction, and it encompasses new extensions of these methods towards an innovative naturalist interpretation of abductive reasoning. (shrink)

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 inference, one in which the past interpretive failures and errors of a (...) community are explained hypothetically by way of the construction of a narrative that rehabilitates those very errors as means for the ongoing successful development of the community, as in Brandom’s privileged jurisprudential example of Anglo-American case law. Next, this Hegelian abductive dynamic is contrasted with the error-reducing backpropagation algorithms characterizing many current versions of machine learning, which can be understood to perform abductions in a certain sense for various problems but not in the full self-constituting communitarian mode of creative recollection canvassed by Brandom. Finally, it is shown how the two modes of “error correction” may possibly coordinate successfully on certain types of abductive inference problems that are neither fully recollective in the Hegelian sense nor algorithmically optimizable. (shrink)

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.

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 most intriguing avenues in contemporary thought. He explains the context within which (...) Laruelle's thought developed and takes you through the challenging argument and conceptual scaffolding of 'Philosophies of Difference'. (shrink)

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.

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.

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]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {E}}}{{\mathcal {G}}}_{\alpha ^{*}}$$\end{document} of cuts-only Existential Graphs (equivalent to the well-studied category of finite forests) provides a basis for the further construction of the category EGα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} (...) \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {E}}}{{\mathcal {G}}}_\alpha $$\end{document} 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 Peirce’s system, it is shown how the generic figures approach facilitates the formal investigation of relations between syntax and semantics in such diagrammatic systems. (shrink)

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.

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 core duality of what Laruelle calls The-Philosophy. In contrast to this self-implicating and self-reproducing (...) structure, Laruelle's axiomatic method is shown to enable a unilateral usage of the practices and vocabularies of philosophy as mere material that is no longer subject to the presuppositions or ineluctable restitution of philosophy as such. (shrink)

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 place and to link such processes to the methods and practices arising in other disciplines and (...) traditions, including those of science, politics, art, religion and technological production. (shrink)

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} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$EG_{\alpha }$$\end{document} depend upon a translation of Peirce’s diagrammatic syntax into that of a suitable Frege-style system. In this paper, drawing upon standard results but using the native diagrammatic notational framework of the graphs, we present (...) a purely syntactic proof of soundness, and hence consistency, for 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}, along with two separate completeness proofs that are constructive in the sense that we provide an algorithm in each case to construct an 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} formal proof starting from the empty Sheet of Assertion, given any expression that is in fact a tautology according to the standard semantics of the system. (shrink)

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 Peirce’s system, it is shown how the generic figures approach facilitates the (...) formal investigation of relations between syntax and semantics in such diagrammatic systems. (shrink)

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 Peirce’s system, it is shown how the generic figures approach facilitates the (...) formal investigation of relations between syntax and semantics in such diagrammatic systems. (shrink)

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 encounters. This semantic-pragmatic model shows how elementary category (...) theory tools can be used to formalize abductive inference while hewing close to ordinary intuitions about collective agency and reasoning. (shrink)

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 modeling the creative event of collective self‐organization as both represented (...) and practiced in the scientific community. (shrink)

A comparison and contrast of the notions of subjectivity and otherness in Levinasian phenomenology and Laruelle's non-philosophy.

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.

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.