A Conceptual and Mathematical Approach
Author: Fernando Zalamea
Peirce's logic of continuity is explored from a double perspective: (i) Peirce's original understanding of the continuum, alternative to Cantor's analytical Real line, (ii) Peirce's original construction of a topological logic -- the existential graphs -- alternative to the algebraic presentation of propositional and first-order calculi. Peirce's general architectonics, oriented to back-and-forth hierarchical crossings between the global and the local, is reflected with great care both in the continuum and the existential graphs.
Author: Fernando Zalamea
Publisher: Urbanomic/Sequence Press
A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest. A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics. The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830-1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the "real mathematics" of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Châtelet), Zalamea challenges philosophy's self-imposed ignorance of the "making of mathematics." In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd. Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.
Author: Maria Teresa Catena,Felice Masi
This book focuses on various concepts of space and their historical evolution. In particular, it examines the variations that have modified the notions of place, orientation, distance, vacuum, limit, bound and boundary, form and figure, continuity and contingence, in order to show how spatial characteristics are decisive in a range of contexts: in the determination and comprehension of exteriority; in individuation and identification; in defining the meaning of nature and of the natural sciences; in aesthetical formations and representations; in determining the relationship between experience, behavior and environment; and in the construction of mental and social subjectivity. Accordingly, the book offers a comprehensive review of concepts of space as formulated by Kant, Husserl, Heidegger, Einstein, Heisenberg, Penrose and Thorne, subsequently comparing them to notions developed more recently, in the current age, which Foucault dubbed the age of space. The book is divided into four distinct yet deeply interconnected parts, which explore the space of life, the space of experience, the space of science and the space of the arts.
Charles Peirce and the Sign Hypothesis
Author: Anne Freadman
Publisher: Stanford University Press
Category: Language Arts & Disciplines
This radical re-evaluation of some standard debates surrounding Peirce’s theory of signs presents new interpretations of his work by studying his writings genealogically. Freadman uses the term genre to access Peirce’s work, and expands this original theoretical approach by proposing that “genre” interacts with “sign” and that this interaction is central to the study of the semiotic in general.
Author: Kelly A. Parker
Publisher: Vanderbilt University Press
In The Continuity of Peirce's Thought, Kelly Parker shows how the principle of continuity functions in phenomenology and semeiotic, the two most novel and important of Peirce's philosophical sciences, which mediate between mathematics and metaphysics. Parker argues that Peirce's concept of continuity is the central organizing theme of the entire Peircean philosophical corpus. He explains how Peirce's unique conception of the mathematical continuum shapes the broad sweep of his thought, extending from mathematics to metaphysics and in religion. This new book should appeal to all who seek a fuller, unified understanding of the career and overarching contributions of Peirce, one of the key figures in the American philosophical tradition.
Author: Charles S. Peirce
Publisher: Indiana University Press
The philosophy of mathematics plays a vital role in the mature philosophy of Charles S. Peirce. Peirce received rigorous mathematical training from his father and his philosophy carries on in decidedly mathematical and symbolic veins. For Peirce, math was a philosophical tool and many of his most productive ideas rest firmly on the foundation of mathematical principles. This volume collects Peirce's most important writings on the subject, many appearing in print for the first time. Peirce's determination to understand matter, the cosmos, and "the grand design" of the universe remain relevant for contemporary students of science, technology, and symbolic logic.
Dedekind, Cantor, Du Bois-Reymond, and Peirce on Continuity and Infinitesimals
Author: Benjamin Lee Buckley
The topic of this book is the historical struggle to define and defend a real number continuum which could do the work limit theory required of it. These definitions drew heavily on philosophical and foundational assumptions, and each raises numerous philosophical questions of its own. As we shall see, attempts to formulate a non-geometrical mathematical continuity raise questions such as: What is a number? What, in particular, is a real number? What is the true nature of continuity itself? Does a philosophically coherent definition of continuity logically commit us to infinitesimally small quantities? Is the concept of an infinitesimally small quantity even logically coherent? What is the relationship between this real number continuum and other well known continua, such as the geometrical straight line? The main question to be addressed, of course, is whether mathematical continuity exists at all.
Author: Bruce Elwyn Meserve
Publisher: Courier Corporation
Uncommonly interesting introduction illuminates complexities of higher mathematics while offering a thorough understanding of elementary mathematics. Covers development of complex number system and elementary theories of numbers, polynomials and operations, determinants, matrices, constructions and graphical representations. Several exercises — without solutions.
Author: Roberta Kevelson
Publisher: John Benjamins Publishing
In all disciplines there are specifiable basic concepts, our universes of discourse, which define special areas of inquiry. Semiotics is that 'science of sciences' which inquires into all processes of inquiry, and which seeks to discover methods of inquiry. Peirce held that semiotics was to be the method of methods. An account of semiotic method should distinguish between the way the term 'sign' is used in semiotics and the various ways this term was meant in nearly all the traditional disciplines. In this monograph Roberta Kevelson minutely explores Charles S. Peirce's method of methods.
Author: Paul Forster
Publisher: Cambridge University Press
Charles Peirce, the founder of pragmatism, was a thinker of extraordinary depth and range - he wrote on philosophy, mathematics, psychology, physics, logic, phenomenology, semiotics, religion and ethics - but his writings are difficult and fragmentary. This book provides a clear and comprehensive explanation of Peirce's thought. His philosophy is presented as a systematic response to 'nominalism', the philosophy which he most despised and which he regarded as the underpinning of the dominant philosophical worldview of his time. The book explains Peirce's challenge to nominalism as a theory of meaning and shows its implications for his views of knowledge, truth, the nature of reality, and ethics. It will be essential reading both for Peirce scholars and for those new to his work.
A Narrative of Truth and Knowing
Author: Danielle Macbeth
Publisher: OUP Oxford
Realizing Reason pursues three interrelated themes. First, it traces the essential moments in the historical unfolding—from the ancient Greeks, through Descartes, Kant, and developments in the nineteenth century, to the present—that culminates in the realization of pure reason as a power of knowing. Second, it provides a cogent account of mathematical practice as a mode of inquiry into objective truth. And finally, it develops and defends a new conception of our being in the world, one that builds on and transforms the now standard conception according to which our experience of reality arises out of brain activity due, in part, to merely causal impacts on our sense organs. Danielle Macbeth shows that to achieve an adequate understanding of the striving for truth in the exact sciences we must overcome this standard conception and that the way to do that is through a more adequate understanding of the nature of mathematical practice and the profound transformations it has undergone over the course of its history, the history through which reason is first realized as a power of knowing. Because we can understand mathematical practice only if we attend to the systems of written signs within which to do mathematics, Macbeth provides an account of the nature and role of written notations, specifically, of the principal systems that have been developed within which to reason in mathematics: Euclidean diagrams, the symbolic language of arithmetic and algebra, and Frege's concept-script, Begriffsschrift.
Author: Karl Popper
Described by the philosopher A.J. Ayer as a work of 'great originality and power', this book revolutionized contemporary thinking on science and knowledge. Ideas such as the now legendary doctrine of 'falsificationism' electrified the scientific community, influencing even working scientists, as well as post-war philosophy. This astonishing work ranks alongside The Open Society and Its Enemies as one of Popper's most enduring books and contains insights and arguments that demand to be read to this day.
Author: Gianluca Caterina,Rocco Gangle
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.
The Metaphysical Architecture of Charles S. Peirce
Author: Ivo Assad Ibri
This pioneering book presents a reconstitution of Charles Sanders Peirce philosophical system as a coherent architecture of concepts that form a unified theory of reality. Historically, the majority of Peircean scholars adopted a thematic approach to study isolated topics such as semiotics and pragmatism without taking into account the author’s broader philosophical framework, which led to a poor and fragmented understanding of Peirce’s work. In this volume, professor Ivo Assad Ibri, past president of The Charles Sanders Peirce Society and a leading figure in the Brazilian community of Peircean scholars, adopts a systemic approach to Peirce’s thought and presents Peirce’s scientific metaphysics as a deep ontological architecture based on a semiotic logic and on pragmatism as criteria of meaning. Originally published in Portuguese, this book became a classic among Brazilian Peircean scholars by presenting a conceptual matrix capable of providing a clear reference system to ground the thematic studies into the broader Peircean system. Now translated to English, this reviewed, amplified and updated edition aims to make this contributions available to the international community of Peircean scholars and to serve as a tool to understand Peirce’s work in a more systemic way by integrating concepts such as experience, phenomenon, existence and reality, as well as theories such as Chance, Continuity, Objective Idealism, Cosmology and Pragmatism, in a coherent system that reveals Peirce’s complex metaphysical architecture. "As the philosophical reputation of Charles S. Peirce continues to rise to first-tier prominence in the history of American philosophy, Ivo Ibri’s Kósmos Noetós assumes a unique status in both a pioneering and a magisterial work of transcontinental Peirce scholarship. This original work of this internationally renowned scholar and editor, and Professor of Philosophy at the Pontifical Catholic University of San Paulo, penetrates to the heart of Peirce’s architectonic system of phenomenological, metaphysical, and semiotic categories which heuristically characterize our world as “a universe perfused with signs.” Ibri’s own synergistic commentary on the radiating registers of Peirce’s cosmogonically and pragmatistically conceived “one intelligible theory of the universe” also instructively contributes to the illumination of significant nodes of interface with a range of relevant theoretical trends in the contemporary academy; as well, it places Peirce in the company of such thinkers as Plato, Aristotle, Plotinus, Kant, and Schelling who preceded Peirce in providing a legacy of first-tier reasoning on our intelligibly developing world. Kosmos Noetos impresses as Ibri’s pure, lucid, passionately thought-loving, philosophical articulation of his own and as the indispensable prolegomena to all future Peirce studies." David Dilworth, State University of New York at Stone Brook – USA "Ivo Ibri has offered us in this exquisite work a framing of the inner logic of Charles S. Peirce's core metaphysical vision and its existential implications. It is a deep and nuanced exploration of the internal dynamics of Peirce’s central metaphysical categories, developed through rigorous and detailed attention to the evolution of Peirce’s thought on the ‘vitally important topics’ of the appearing, the reality, and the intelligibility of the world. The two-leveled format of the book, an intricate weaving of Peirce’s texts and discursive elaboration and linkage by Ibri, gives it a distinctive feel and is the bedrock of its value. The book is a remarkable combination of presentation and analysis. It is informed by Ibri’s deep philosophical culture and is a gentle and convincing argument for the centrality of metaphysics in understanding Peirce’s thought. It offers in a new way indispensable suggestions for our own attempts to think about our places in an evolving universe with the aid of Peirce and offers threads of thought to be followed up by others." Robert E. Innis, University of Massachusetts Lowell – USA
Author: Charles S. Peirce
First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.
Author: Norma Presmeg,Luis Radford,Wolff-Michael Roth,Gert Kadunz
This volume discusses semiotics in mathematics education as an activity with a formal sign system, in which each sign represents something else. Theories presented by Saussure, Peirce, Vygotsky and other writers on semiotics are summarized in their relevance to the teaching and learning of mathematics. The significance of signs for mathematics education lies in their ubiquitous use in every branch of mathematics. Such use involves seeing the general in the particular, a process that is not always clear to learners. Therefore, in several traditional frameworks, semiotics has the potential to serve as a powerful conceptual lens in investigating diverse topics in mathematics education research. Topics that are implicated include (but are not limited to): the birth of signs; embodiment, gestures and artifacts; segmentation and communicative fields; cultural mediation; social semiotics; linguistic theories; chains of signification; semiotic bundles; relationships among various sign systems; intersubjectivity; diagrammatic and inferential reasoning; and semiotics as the focus of innovative learning and teaching materials.