Phenomenology, Logic, and the Philosophy of Mathematics

Author: Richard L. Tieszen

Publisher: Cambridge University Press

ISBN: 9780521837828

Category: Mathematics

Page: 357

View: 3850

In this 2005 book, logic, mathematical knowledge and objects are explored alongside reason and intuition in the exact sciences.

The New Century

Bergsonism, Phenomenology and Responses to Modern Science

Author: Keith Ansell-Pearson,Alan D. Schrift

Publisher: Routledge

ISBN: 131754692X

Category: Philosophy

Page: 456

View: 3312

This volume covers the period between the 1890s and 1930s, a period that witnessed revolutions in the arts and society which set the agenda for the rest of the century. In philosophy, the period saw the birth of analytic philosophy, the development of new programmes and new modes of inquiry, the emergence of phenomenology as a new rigorous science, the birth of Freudian psychoanalysis, and the maturing of the discipline of sociology. This period saw the most influential work of a remarkable series of thinkers who reviewed, evaluated and transformed 19th-century thought. A generation of thinkers - among them, Henri Bergson, Emile Durkheim, Sigmund Freud, Martin Heidegger, Edmund Husserl, Karl Jaspers, Max Scheler, and Ludwig Wittgenstein - completed the disenchantment of the world and sought a new re-enchantment.

Deduction, Computation, Experiment

Exploring the Effectiveness of Proof

Author: Rossella Lupacchini,Giovanna Corsi

Publisher: Springer Science & Business Media

ISBN: 8847007844

Category: Philosophy

Page: 280

View: 2418

This volume is located in a cross-disciplinary ?eld bringing together mat- matics, logic, natural science and philosophy. Re?ection on the e?ectiveness of proof brings out a number of questions that have always been latent in the informal understanding of the subject. What makes a symbolic constr- tion signi?cant? What makes an assumption reasonable? What makes a proof reliable? G ̈ odel, Church and Turing, in di?erent ways, achieve a deep und- standing of the notion of e?ective calculability involved in the nature of proof. Turing’s work in particular provides a “precise and unquestionably adequate” de?nition of the general notion of a formal system in terms of a machine with a ?nite number of parts. On the other hand, Eugene Wigner refers to the - reasonable e?ectiveness of mathematics in the natural sciences as a miracle. Where should the boundary be traced between mathematical procedures and physical processes? What is the characteristic use of a proof as a com- tation, as opposed to its use as an experiment? What does natural science tell us about the e?ectiveness of proof? What is the role of mathematical proofs in the discovery and validation of empirical theories? The papers collected in this book are intended to search for some answers, to discuss conceptual and logical issues underlying such questions and, perhaps, to call attention to other relevant questions.

Phenomenology and Logic

The Boston College Lectures on Mathematical Logic and Existentialism

Author: Bernard J. F. Lonergan,Frederick E. Crowe,Philip J. McShane,Robert M. Doran,Lonergan Research Institute

Publisher: University of Toronto Press

ISBN: 9780802084484

Category: Mathematics

Page: 419

View: 4640

entirety to contemporary readers." --Book Jacket.

Plato's Problem

An Introduction to Mathematical Platonism

Author: M. Panza,A. Sereni

Publisher: Springer

ISBN: 1137298138

Category: Mathematics

Page: 306

View: 4001

What is mathematics about? And how can we have access to the reality it is supposed to describe? The book tells the story of this problem, first raised by Plato, through the views of Aristotle, Proclus, Kant, Frege, Gödel, Benacerraf, up to the most recent debate on mathematical platonism.


Critical Concepts in Philosophy

Author: Dermot Moran,Lester E. Embree

Publisher: Taylor & Francis

ISBN: 9780415310413

Category: Philosophy

Page: 376

View: 9772

First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.

After Gödel

Platonism and Rationalism in Mathematics and Logic

Author: Richard L. Tieszen

Publisher: Oxford University Press

ISBN: 019960620X

Category: Mathematics

Page: 245

View: 1195

Richard Tieszen analyzes, develops, and defends the writings of Kurt Gödel (1906-1978) on the philosophy and foundations of mathematics and logic. Gödel's relation to the work of Plato, Leibniz, Husserl, and Kant is examined, and a new type of platonic rationalism that requires rational intuition, called 'constituted platonism', is proposed.

In Defense of Intuitions

A New Rationalist Manifesto

Author: A. Chapman,A. Ellis,R. Hanna,T. Hildebrand,H. Pickford

Publisher: Springer

ISBN: 1137347953

Category: Philosophy

Page: 427

View: 4601

A reply to contemporary skepticism about intuitions and a priori knowledge, and a defense of neo-rationalism from a contemporary Kantian standpoint, focusing on the theory of rational intuitions and on solving the two core problems of justifying and explaining them.

Early Writings in the Philosophy of Logic and Mathematics

Author: Edmund Husserl

Publisher: Springer

ISBN: 0792322622

Category: Philosophy

Page: 505

View: 3056

The primary intent of this volume is to give the English reader access to all the philosophical texts published by Husserl between the appearance of his first book, Philosophie der Arithmetik, and that of his second book, Logische Untersuchungen- roughly, from 1890 through 1901. Along with these texts we have included a number of unpublished manuscripts from the same period and dealing with the same or closely related topics. A few of the texts here translated (the review of Pahigyi, the five "report" articles of 1903-1904, the "notes" in Lalande's Vocabulaire, and the brief discussion. article on Marty of 1910) obviously fall outside this time period, so far as their publication dates are concerned; but in content they seem clearly confined to it. The final piece translated, a set of personal notes that date from 1906 through 1908, provides insight into how Husserl experienced his early labors and their results, and into how he saw their relation to work before him: a phenomenological critique of reason in all of its forms. Thus the texts here translated - which obviously are to be read in conjunction with his first two books - cover the progression of Husserl's Problematik from the relatively narrow one of clarifying the epistemic structure of general arithmetic, to the all-encompassing one of establishing in principle, through phenomenological research, the line between legitimate and illegitimate claims to know or to be rational, regardless of the domain concerned.

The Foundation of Phenomenology

Edmund Husserl and the Quest for a Rigorous Science of Philosophy

Author: Marvin Farber

Publisher: SUNY Press

ISBN: 9780873950374

Category: Phenomenology

Page: 585

View: 2807

The Oxford Handbook of the History of Mathematics

Author: Eleanor Robson,Jacqueline Stedall

Publisher: OUP Oxford

ISBN: 0191607444

Category: Mathematics

Page: 926

View: 3870

This Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practise it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textual sources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of the mathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking. Because the history of mathematics should interact constructively with other ways of studying the past, the contributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, philosophy, and literature, as well as history of mathematics more traditionally understood. The thirty-six self-contained, multifaceted chapters, each written by a specialist, are arranged under three main headings: 'Geographies and Cultures', 'Peoples and Practices', and 'Interactions and Interpretations'. Together they deal with the mathematics of 5000 years, but without privileging the past three centuries, and an impressive range of periods and places with many points of cross-reference between chapters. The key mathematical cultures of North America, Europe, the Middle East, India, and China are all represented here as well as areas which are not often treated in mainstream history of mathematics, such as Russia, the Balkans, Vietnam, and South America. A vital reference for graduates and researchers in mathematics, historians of science, and general historians.

The New Yearbook for Phenomenology and Phenomenological Philosophy

Author: Burt Hopkins,Steven Crowell

Publisher: Routledge

ISBN: 1317401484

Category: Philosophy

Page: 396

View: 5202

The New Yearbook for Phenomenology and Phenomenological Philosophy provides an annual international forum for phenomenological research in the spirit of Husserl's groundbreaking work and the extension of this work by such figures as Scheler, Heidegger, Sartre, Levinas, Merleau-Ponty and Gadamer.

Logic and Philosophy of Mathematics in the Early Husserl

Author: Stefania Centrone

Publisher: Springer Science & Business Media

ISBN: 9048132479

Category: Philosophy

Page: 232

View: 9440

Logic and Philosophy of Mathematics in the Early Husserl focuses on the first ten years of Edmund Husserl’s work, from the publication of his Philosophy of Arithmetic (1891) to that of his Logical Investigations (1900/01), and aims to precisely locate his early work in the fields of logic, philosophy of logic and philosophy of mathematics. Unlike most phenomenologists, the author refrains from reading Husserl’s early work as a more or less immature sketch of claims consolidated only in his later phenomenology, and unlike the majority of historians of logic she emphasizes the systematic strength and the originality of Husserl’s logico-mathematical work. The book attempts to reconstruct the discussion between Husserl and those philosophers and mathematicians who contributed to new developments in logic, such as Leibniz, Bolzano, the logical algebraists (especially Boole and Schröder), Frege, and Hilbert and his school. It presents both a comprehensive critical examination of some of the major works produced by Husserl and his antagonists in the last decade of the 19th century and a formal reconstruction of many texts from Husserl’s Nachlaß that have not yet been the object of systematical scrutiny. This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to analytical philosophers and phenomenologists with a background in standard logic.

The Idea of Phenomenology

A Translation of Die Idee der Phänomenologie Husserliana II

Author: Edmund Husserl

Publisher: Springer Science & Business Media

ISBN: 9401573867

Category: Philosophy

Page: 72

View: 1725

3 same lecture he characterizes the phenomenology of knowledge, more specifically, as the "theory of the essence of the pure phenomenon of knowing" (see below, p. 36). Such a phenomenology would advance the "critique of knowledge," in which the problem of knowledge is clearly formulated and the possibility of knowledge rigorously secured. It is important to realize, however, that in these lectures Husserl will not enact, pursue, or develop a phenomenological critique of knowledge, even though he opens with a trenchant statement of the problem of knowledge that such a critique would solve. Rather, he seeks here only to secure the possibility of a phe nomenological critique of knowledge; that is, he attempts to secure the possibility of the knowledge of the possibility of knowledge, not the possibil ity of knowledge in general (see below, pp. 37-39). Thus the work before us is not phenomenological in the straightforward sense, but pre phenomenological: it sets out to identify and satisfy the epistemic require ments of the phenomenological critique of knowledge, not to carry out that critique itself. To keep these two levels of theoretical inquiry distinct, I will call the level that deals with the problem of the possibility of knowledge the "critical level"; the level that deals with the problem of the possibility of the knowledge of the possibility of knowledge the "meta-criticallevel.

Edmund Husserl: The cutting edge : phenomenological method, philosophical logic, ontology, and philosophy of science

Author: Rudolf Bernet,Donn Welton,Gina Zavota

Publisher: Taylor & Francis

ISBN: 9780415289580

Category: Philosophy

Page: 381

View: 6014

This collection makes available, in one place, the very best essays on the founding father of phenomenology, reprinting key writings on Husserl's thought from the past seventy years. It draws together a range of writings, many otherwise inaccessible, that have been recognized as seminal contributions not only to an understanding of this great philosopher but also to the development of his phenomenology. The four volumes are arranged as follows: Volume I Classic essays from Husserl's assistants, students and earlier interlocutors. Including a selection of papers from such figures as Heidegger, Merleau-Ponty, Sartre, Ricoeur and Levinas. Volume II Classic commentaries on Husserl's published works. "Covering the Logical Investigations," " Ideas I," " Phenomenology of Internal Time Consciousness," "" ""and" Formal and Transcendental Logic." Volumes III and IV Papers concentrating on particular aspects of Husserl's theory including: Husserl's account of mathematics and logic, his theory of science, the nature of phenomenological reduction, his account of perception and language, the theory of space and time, his phenomenology of imagination and empathy, the concept of the life-world and his epistemology.

Encyclopedia of Phenomenology

Author: Lester Embree

Publisher: Springer Science & Business Media

ISBN: 9401588813

Category: Philosophy

Page: 765

View: 9746

This encyclopedia presents phenomenological thought and the phenomenological movement within philosophy and within more than a score of other disciplines on a level accessible to professional colleagues of other orientations as well as to advanced undergraduate and graduate students. Entries average 3,000 words. In practically all cases, they include lists of works "For Further Study." The Introduction briefly chronicles the changing phenomenological agenda and compares phenomenology with other 20th Century movements. The 166 entries are a baut matters of seven sorts: ( 1) the faur broad tendencies and periods within the phenomenological movement; (2) twenty-three national traditions ofphenomenology; (3) twenty-two philosophical sub-disciplines, including those referred to with the formula "the philosophy of x"; (4) phenomenological tendencies within twenty-one non-philosophical dis ciplines; (5) forty major phenomenological topics; (6) twenty-eight leading phenomenological figures; and (7) twenty-seven non-phenomenological figures and movements ofinteresting sim ilarities and differences with phenomenology. Conventions Concern ing persons, years ofbirth and death are given upon first mention in an entry ofthe names of deceased non-phenomenologists. The names of persons believed tobe phenomenologists and also, for cross-referencing purposes, the titles of other entries are printed entirely in SMALL CAPITAL letters, also upon first mention. In addition, all words thus occurring in all small capital letters are listed in the index with the numbers of all pages on which they occur. To facilitate indexing, Chinese, Hungarian, and Japanese names have been re-arranged so that the personal name precedes the family name.

The Philosophy of Symbolic Forms: The phenomenology of knowledge

Author: Ernst Cassirer

Publisher: Yale University Press

ISBN: 9780300000399

Category: Philosophy

Page: 528

View: 2651

The Symbolic Forms has long been considered the greatest of Cassirer's works. Into it he poured all the resources of his vast learning about language and myth, religion, art, and science--the various creative symbolizing activities and constructions through which man has expressed himself and given intelligible objective form to this experience. "These three volumes alone (apart from Cassirer's other papers and books) make an outstanding contribution to epistemology and to the human power of abstraction. It is rather as if 'The Golden Bough' had been written in philosophical rather than in historical terms."--F.I.G. Rawlins, Nature

Pluralism and the Pragmatic Turn

The Transformation of Critical Theory, Essays in Honor of Thomas McCarthy

Author: William Rehg,James Bohman

Publisher: MIT Press

ISBN: 9780262264303

Category: Philosophy

Page: 465

View: 2909

The essays in this volume reflect on and expand Frankfurt School critical theory as reformulated after World War II by Karl-Otto Apel, Jürgen Habermas, and others. Frankfurt School critical theory since the pragmatic turn has become a richer source of critical analysis that is at the same time socially and politically more effective. The essays are dedicated to Thomas McCarthy, who has done perhaps more than any other scholar to introduce English-speaking audiences to contemporary German critical theory.The book is organized into three parts. Part one deals with social theory and the rational basis of communication, including basic issues raised by the pragmatic turn. Part two examines conceptions of autonomy and the self. Part three deals with political theory, focusing on problems stemming from sociocultural pluralism. Together, the essays provide an overview of the latest developments in Frankfurt School critical theory as it responds to the challenges of pragmatism and social pluralism.

The Philosophy of Husserl

Author: Burt Hopkins

Publisher: Routledge

ISBN: 131749444X

Category: Philosophy

Page: 290

View: 7610

As the founder of phenomenology, Edmund Husserl has been hugely influential in the development of contemporary continental philosophy. In The Philosophy of Husserl, Burt Hopkins shows that the unity of Husserl’s philosophical enterprise is found in the investigation of the origins of cognition, being, meaning, and ultimately philosophy itself. Hopkins challenges the prevailing view that Husserl’s late turn to history is inconsistent with his earlier attempts to establish phenomenology as a pure science and also the view of Heidegger and Derrida, that the limits of transcendental phenomenology are historically driven by ancient Greek philosophy. Part 1 presents Plato’s written and unwritten theories of eidê and Aristotle’s criticism of both. Part 2 traces Husserl’s early investigations into the formation of mathematical and logical concepts and charts the critical necessity that leads from descriptive psychology to transcendentally pure phenomenology. Part 3 investigates the movement of Husserl’s phenomenology of transcendental consciousness to that of monadological intersubjectivity. Part 4 presents the final stage of the development of Husserl’s thought, which situates monadological intersubjectivity within the context of the historical a priori constitutive of all meaning. Part 5 exposes the unwarranted historical presuppositions that guide Heidegger’s fundamental ontological and Derrida’s deconstructive criticisms of Husserl’s transcendental phenomenology. The Philosophy of Husserl will be required reading for all students of phenomenology.