Phenomenology, Logic, and the Philosophy of Mathematics

Author: Richard L. Tieszen

Publisher: Cambridge University Press

ISBN: 9780521837828

Category: Mathematics

Page: 357

View: 364

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

Author: Edmund Husserl

Publisher: Springer

ISBN: 0792322622

Category: Philosophy

Page: 505

View: 790

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 Along with these texts we have included a number of unpublished manuscripts from the same period and dealing with the same or closely related topics.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

After Gödel

Platonism and Rationalism in Mathematics and Logic

Author: Richard L. Tieszen

Publisher: Oxford University Press

ISBN: 019960620X

Category: Mathematics

Page: 245

View: 4655

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

Author: Mirja Hartimo

Publisher: Springer Science & Business Media

ISBN: 9789048137299

Category: Philosophy

Page: 216

View: 428

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?"

Introduction to Logic and Theory of Knowledge

Lectures 1906/07

Author: Edmund Husserl

Publisher: Springer Science & Business Media

ISBN: 1402067275

Category: Philosophy

Page: 479

View: 6857

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.

Philosophy of Arithmetic

Psychological and Logical Investigations with Supplementary Texts from 1887–1901

Author: Edmund Husserl

Publisher: Springer

ISBN: 1402016034

Category: Mathematics

Page: 515

View: 1005

This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy" so-called. Careful exposition and critique is given to every serious alternative account of number and number relations available at the time.

Essays on Husserl's Logic and Philosophy of Mathematics

Author: Stefania Centrone

Publisher: Springer

ISBN: 9402411321

Category: Philosophy

Page: 526

View: 7610

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

Author: Marvin Farber

Publisher: SUNY Press

ISBN: 9780873950374

Category: Phenomenology

Page: 585

View: 9942

Logic and Philosophy of Mathematics in the Early Husserl

Author: Stefania Centrone

Publisher: Springer Science & Business Media

ISBN: 9789048132461

Category: Philosophy

Page: 232

View: 3615

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.

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: 7271

entirety to contemporary readers." --Book Jacket.

The Origin of the Logic of Symbolic Mathematics

Edmund Husserl and Jacob Klein

Author: Burt C. Hopkins

Publisher: Indiana University Press

ISBN: 0253005272

Category: Philosophy

Page: 592

View: 457

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.

Essays in the Philosophy and History of Logic and Mathematics

Author: Roman Murawski

Publisher: BRILL

ISBN: 9042030917

Category: Philosophy

Page: 344

View: 2751

The book is a collection of the author’s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered. This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields.

The Road Not Taken. on Husserl's Philosophy of Logic and Mathematics

Author: Claire Ortiz Hill,Jairo Jose Da Silva

Publisher: N.A

ISBN: 9781848900998

Category: Mathematics

Page: 456

View: 6021

For different reasons, Husserl's original, thought-provoking ideas on the philosophy of logic and mathematics have been ignored, misunderstood, even despised, by analytic philosophers and phenomenologists alike, who have been content to barricade themselves behind walls of ideological prejudices. Yet, for several decades, Husserl was almost continuously in close professional and personal contact with those who created, reshaped and revolutionized 20th century philosophy of mathematics, logic, science and language in both the analytic and phenomenological schools, people whom those other makers of 20th century philosophy, Russell, Frege, Wittgenstein and their followers, rarely, if ever, met. Independently of them, Husserl offered alternatives to the well-trodden paths of logicism, nominalism, formalism and intuitionism. He presented a well-articulated, thoroughly argued case for logic as an objective science, but was not philosophically naive to the point of not seeing the role of subjectivity in shaping the sense of the reality facing objective science. Given the preeminent role that philosophy of logic and philosophy of mathematics have played in transforming the way philosophy has been done since Husserl's time, and given the depth of his insights and his obvious expertise in those fields, his ideas need to be integrated into present-day, mainstream philosophy. Here, philosopher Claire Ortiz Hill and mathematician-philosopher Jairo da Silva offer a wealth of interesting insights intended to subvert the many mistaken idees recues about the development of Husserl's thought and reestablish broken ties between it and philosophy now.

Mathematics and Mind

Author: Alexander George

Publisher: Oxford University Press on Demand

ISBN: 0195079299

Category: History

Page: 204

View: 3731

The essays in this volume investigate the conceptual foundations of mathematics illuminating the powers of the mind. Contributors include Alexander George, Michael Dummett, George Boolos, W.W. Tait, Wilfried Sieg, Daniel Isaacson, Charles Parsons, and Michael Hallett.

Logic, Truth and the Modalities

From a Phenomenological Perspective

Author: J.N. Mohanty

Publisher: Springer Science & Business Media

ISBN: 9401721130

Category: Philosophy

Page: 238

View: 1956

This volume is a collection of my essays on philosophy of logic from a phenomenological perspective. They deal with the four kinds of logic I have been concerned with: formal logic, transcendental logic, speculative logic and hermeneutic logic. Of these, only one, the essay on Hegel, touches upon 'speculative logic', and two, those on Heidegger and Konig, are concerned with hermeneutic logic. The rest have to do with Husser! and Kant. I have not tried to show that the four logics are compatible. I believe, they are--once they are given a phenomenological underpinning. The original plan of writing an Introduction in which the issues would have to be formulated, developed and brought together, was abandoned in favor of writing an Introductory Essay on the 'origin'- in the phenomenological sense -of logic. J.N.M. Philadelphia INTRODUCTION: THE ORIGIN OF LOGIC The question of the origin of logic may pertain to historical origin (When did it all begin? Who founded the science of logic?), psychological origin (When, in the course of its mental development, does the child learn logical operations?), cultural origin (What cultural - theological, metaphysical and linguisti- conditions make such a discipline as logic possible?), or transcendental constitutive origin (What sorts of acts and/or practices make logic possible?).

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: 8092

Phenomenology and the Foundations of the Sciences

Author: Edmund Husserl

Publisher: Springer Science & Business Media

ISBN: 9781402002564

Category: Philosophy

Page: 130

View: 5335

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.

Merleau-Ponty's Existential Phenomenology and the Realization of Philosophy

Author: Bryan A. Smyth

Publisher: A&C Black

ISBN: 1780937865

Category: Philosophy

Page: 256

View: 2079

Bringing to light the essential philosophical role of Marxism within Merleau-Ponty's reinterpretation of transcendental phenomenology, this book shows that the realization of this project hinges methodologically upon a renewed conception of the proletariat qua universal class-specifically, that it rests upon a humanist myth of incarnation which, substantiated by Merleau-Ponty's notion of 'heroism', locates an objective historical purposiveness in the habituated organism of the modern subject. Foregrounding the phenomenological priority of history over corporeality in this way, Smyth's analysis recovers the 'militant' character of Merleau-Ponty's existential phenomenology. It thus sheds critical new light on his early thought, and challenges some of the main parameters of existing scholarship by disclosing the intrinsic normativity of his basic methodological commitments.

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: 2133

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.

Theories of Judgment

Psychology, Logic, Phenomenology

Author: Wayne Martin

Publisher: Cambridge University Press

ISBN: 1139447742

Category: Philosophy

Page: N.A

View: 3600

The exercise of judgement is an aspect of human endeavour from our most mundane acts to our most momentous decisions. In this book Wayne Martin develops a historical survey of theoretical approaches to judgement, focusing on treatments of judgement in psychology, logic, phenomenology and painting. He traces attempts to develop theories of judgement in British Empiricism, the logical tradition stemming from Kant, nineteenth-century psychologism, experimental neuropsychology and the phenomenological tradition associated with Brentano, Husserl and Heidegger. His reconstruction of vibrant but largely forgotten nineteenth-century debates links Kantian approaches to judgement with twentieth-century phenomenological accounts. He also shows that the psychological, logical and phenomenological dimensions of judgement are not only equally important but fundamentally interlinked in any complete understanding of judgement. His book will interest a wide range of readers in history of philosophy, philosophy of the mind and psychology.