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: 6000

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

After Gödel

Platonism and Rationalism in Mathematics and Logic

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Author: Richard L. Tieszen

Publisher: Oxford University Press

ISBN: 019960620X

Category: Mathematics

Page: 245

View: 6089

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.

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: 1266

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.

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: 9186

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: 5816

entirety to contemporary readers." --Book Jacket.

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: 1123

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.

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: 8992

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 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: 2997

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.

Logic, Truth and the Modalities

From a Phenomenological Perspective

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Author: J.N. Mohanty

Publisher: Springer Science & Business Media

ISBN: 9401721130

Category: Philosophy

Page: 238

View: 1397

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?).

A Logical Journey

From Gödel to Philosophy

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Author: Hao Wang

Publisher: MIT Press

ISBN: 9780262261258

Category: Philosophy

Page: 408

View: 7477

Hao Wang (1921-1995) was one of the few confidants of the great mathematician and logician Kurt Gödel. A Logical Journey is a continuation of Wang's Reflections on Gödel and also elaborates on discussions contained in From Mathematics to Philosophy. A decade in preparation, it contains important and unfamiliar insights into Gödel's views on a wide range of issues, from Platonism and the nature of logic, to minds and machines, the existence of God, and positivism and phenomenology. The impact of Gödel's theorem on twentieth-century thought is on par with that of Einstein's theory of relativity, Heisenberg's uncertainty principle, or Keynesian economics. These previously unpublished intimate and informal conversations, however, bring to light and amplify Gödel's other major contributions to logic and philosophy. They reveal that there is much more in Gödel's philosophy of mathematics than is commonly believed, and more in his philosophy than his philosophy of mathematics. Wang writes that "it is even possible that his quite informal and loosely structured conversations with me, which I am freely using in this book, will turn out to be the fullest existing expression of the diverse components of his inadequately articulated general philosophy." The first two chapters are devoted to Gödel's life and mental development. In the chapters that follow, Wang illustrates the quest for overarching solutions and grand unifications of knowledge and action in Gödel's written speculations on God and an afterlife. He gives the background and a chronological summary of the conversations, considers Gödel's comments on philosophies and philosophers (his support of Husserl's phenomenology and his digressions on Kant and Wittgenstein), and his attempt to demonstrate the superiority of the mind's power over brains and machines. Three chapters are tied together by what Wang perceives to be Gödel's governing ideal of philosophy: an exact theory in which mathematics and Newtonian physics serve as a model for philosophy or metaphysics. Finally, in an epilog Wang sketches his own approach to philosophy in contrast to his interpretation of Gödel's outlook.

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: 947

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 the Foundations of the Sciences

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Author: Edmund Husserl

Publisher: Springer Science & Business Media

ISBN: 9781402002564

Category: Philosophy

Page: 130

View: 5541

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.

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: 8559

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.

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: 6795

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

Mathematical Intuition

Phenomenology and Mathematical Knowledge

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Author: R.L. Tieszen

Publisher: Springer Science & Business Media

ISBN: 9400922930

Category: Philosophy

Page: 210

View: 5331

"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser! there will be a kind of Kantian argument underlying the entire book.

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: 9159

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.

Philosophy of Arithmetic

Psychological and Logical Investigations with Supplementary Texts from 1887–1901

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Author: Edmund Husserl

Publisher: Springer

ISBN: 1402016034

Category: Mathematics

Page: 515

View: 6568

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.

Philosophy of Mathematics

An Introduction to the World of Proofs and Pictures

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Author: James Robert Brown

Publisher: Psychology Press

ISBN: 0415122759

Category: Science

Page: 215

View: 586

Philosophy of Mathematicsis clear and engaging, and student friendly The book discusses the great philosophers and the importance of mathematics to their thought. Among topics discussed in the book are the mathematical image, platonism, picture-proofs, applied mathematics, Hilbert and Godel, knots and notation definitions, picture-proofs and Wittgenstein, computation, proof and conjecture.

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

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Author: Claire Ortiz Hill,Jairo Jose Da Silva

Publisher: N.A

ISBN: 9781848900998

Category: Mathematics

Page: 456

View: 4262

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.