Phenomenology, Logic, and the Philosophy of Mathematics

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Author: Richard L. Tieszen

Publisher: Cambridge University Press

ISBN: 9780521837828

Category: Mathematics

Page: 357

View: 2173

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

Early Writings in the Philosophy of Logic and Mathematics

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Author: Edmund Husserl

Publisher: Springer

ISBN: 0792322622

Category: Philosophy

Page: 505

View: 4797

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 Along with these texts we have included a number of unpublished manuscripts from the same period and dealing with the same or closely related topics.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.

Introduction to Logic and Theory of Knowledge

Lectures 1906/07

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Author: Edmund Husserl

Publisher: Springer Science & Business Media

ISBN: 1402067275

Category: Philosophy

Page: 479

View: 2722

Claire Ortiz Hill The publication of all but a small, unfound, part of the complete text of the lecture course on logic and theory of knowledge that Edmund Husserl gave at Göttingen during the winter semester of 1906/07 became a reality in 1984 with the publication of Einleitung in die Logik und Erkenntnistheorie, Vorlesungen 1906/07 edited by 1 Ullrich Melle. Published in that volume were also 27 appendices containing material selected to complement the content of the main text in significant ways. They provide valuable insight into the evolution of Husserl’s thought between the Logical Investigations and Ideas I and, therefore, into the origins of phenomenology. That text and all those appendices but one are translated and published in the present volume. Omitted are only the “Personal Notes” dated September 25, 1906, November 4, 1907, and March 6, 1908, which were translated by Dallas Willard and published in his translation of Husserl’s Early 2 Writings in the Philosophy of Logic and Mathematics. Introduction to Logic and Theory of Knowledge, Lectures 1906/07 provides valuable insight into the development of the ideas fun- mental to phenomenology. Besides shedding considerable light on the genesis of phenomenology, it sheds needed light on many other dimensions of Husserl’s thought that have puzzled and challenged scholars.

After Gödel

Platonism and Rationalism in Mathematics and Logic

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Author: Richard Tieszen

Publisher: OUP Oxford

ISBN: 019960620X

Category: Philosophy

Page: 272

View: 3169

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.

Phenomenology and Mathematics

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Author: Mirja Hartimo

Publisher: Springer Science & Business Media

ISBN: 9789048137299

Category: Philosophy

Page: 216

View: 9040

During Edmund Husserl’s lifetime, modern logic and mathematics rapidly developed toward their current outlook and Husserl’s writings can be fruitfully compared and contrasted with both 19th century figures (Boole, Schröder, Weierstrass) as well as the 20th century characters (Heyting, Zermelo, Gödel). Besides the more historical studies, the internal ones on Husserl alone and the external ones attempting to clarify his role in the more general context of the developing mathematics and logic, Husserl’s phenomenology offers also a systematically rich but little researched area of investigation. This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics. It gathers the contributions of the main scholars of this emerging field into one publication for the first time. Combining both historical and systematic studies from various angles, the volume charts answers to the question "What kind of philosophy of mathematics is phenomenology?"

Essays on Husserl's Logic and Philosophy of Mathematics

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Author: Stefania Centrone

Publisher: Springer

ISBN: 9402411321

Category: Philosophy

Page: 526

View: 7573

Essays on Husserl’s Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl’s work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl’s by considering their reception and elaboration by some of his disciples and followers, such as Oskar Becker and Jacob Klein, as well as their influence on some of the most significant logicians and mathematicians of the past century, such as Luitzen E. J. Brouwer, Rudolf Carnap, Kurt Gödel and Hermann Weyl. Most of the papers consider Husserl and another scholar – e.g. Leibniz, Kant, Bolzano, Brentano, Cantor, Frege – and trace out and contextualize lines of influence, points of contact, and points of disagreement. Each essay is written by an expert of the field, and the volume includes contributions both from the analytical tradition and from the phenomenological one.

The Foundation of Phenomenology

Edmund Husserl and the Quest for a Rigorous Science of Philosophy

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Author: Marvin Farber

Publisher: SUNY Press

ISBN: 9780873950374

Category: Phenomenology

Page: 585

View: 9578

Phenomenology and Logic

The Boston College Lectures on Mathematical Logic and Existentialism

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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: 3288

entirety to contemporary readers." --Book Jacket.

The New Century

Bergsonism, Phenomenology and Responses to Modern Science

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Author: Keith Ansell-Pearson,Alan D. Schrift

Publisher: Routledge

ISBN: 131754692X

Category: Philosophy

Page: 456

View: 8725

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.

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

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Author: Rudolf Bernet,Donn Welton,Gina Zavota

Publisher: Taylor & Francis

ISBN: 9780415289580

Category: Philosophy

Page: 381

View: 6881

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.

Phenomenology and the Foundations of the Sciences

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Author: Edmund Husserl

Publisher: Springer Science & Business Media

ISBN: 9781402002564

Category: Philosophy

Page: 130

View: 3135

There is no author's introduction to Phenomenology and the Foundations of the Sciences,! either as published here in the first English translation or in the standard German edition, because its proper introduction is its companion volume: General Introduction to Pure Phenomenology. 2 The latter is the first book of Edmund Husserl's larger work: Ideas Toward a Pure Phenomenology and Phenomenological Philosophy, and is commonly referred to as Ideas I (or Ideen 1). The former is commonly called Ideen III. Between these two parts of the whole stands a third: Phenomeno 3 logical Investigations of Constitution, generally known as Ideen II. In this introduction the Roman numeral designations will be used, as well as the abbreviation PFS for the translation at hand. In many translation projects there is an initial problem of establish ing the text to be translated. That problem confronts translators of the books of Husserl's Ideas in different ways. The Ideas was written in 1912, during Husserl's years in Gottingen (1901-1916). Books I and II were extensively revised over nearly two decades and the changes were incorporated by the editors into the texts of the Husserliana editions of 1950 and 1952 respectively. Manuscripts of the various reworkings of the texts are preserved in the Husserl Archives, but for those unable to work there the only one directly available for Ideen II is the reconstructed one.

The Origin of the Logic of Symbolic Mathematics

Edmund Husserl and Jacob Klein

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Author: Burt C. Hopkins

Publisher: Indiana University Press

ISBN: 0253005272

Category: Philosophy

Page: 592

View: 4448

Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts—especially mathematical concepts and the process of mathematical abstraction that generates them—have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.

Deduction, Computation, Experiment

Exploring the Effectiveness of Proof

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Author: Rossella Lupacchini,Giovanna Corsi

Publisher: Springer Science & Business Media

ISBN: 8847007844

Category: Philosophy

Page: 280

View: 9300

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.

Plato's Problem

An Introduction to Mathematical Platonism

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Author: M. Panza,A. Sereni

Publisher: Springer

ISBN: 1137298138

Category: Mathematics

Page: 306

View: 1942

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.

Husserl and Realism in Logic and Mathematics

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Author: Robert S. Tragesser

Publisher: CUP Archive

ISBN: 9780521285872

Category: Mathematics

Page: 126

View: 9328

Edmund Husserl discusses the question of whether the world is of our making or whether some form of realism is true. In this book Robert Tragesser sets out to determine the conditions under which a realist ontology of mathematics and logic might be justified, taking Husserl as his starting point.

Edmund Husserl: The web of meaning : language, noema, and subjectivity and intersubjectivity

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Author: Rudolf Bernet,Donn Welton,Gina Zavota

Publisher: Taylor & Francis

ISBN: 9780415289603

Category: Philosophy

Page: 377

View: 5374

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.

Phenomenology

Critical Concepts in Philosophy

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Author: Dermot Moran,Lester E. Embree

Publisher: Taylor & Francis

ISBN: 9780415310413

Category: Philosophy

Page: 376

View: 3903

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

In Defense of Intuitions

A New Rationalist Manifesto

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

Publisher: Springer

ISBN: 1137347953

Category: Philosophy

Page: 427

View: 7421

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.

Phenomenology and the Formal Sciences

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Author: Thomas M. Seebohm,Dagfinn Føllesdal,J.N. Mohanty

Publisher: Springer Science & Business Media

ISBN: 9401125805

Category: Philosophy

Page: 263

View: 5668