Overview

In his first book, Philosophy of Arithmetic, Edmund Husserl provides a carefully worked out account of number as a categorial or formal feature of the objective world, and of arithmetic as a symbolic technique for mastering the infinite field of numbers for knowledge. It is a realist account of numbers and number relations that interweaves them into the basic structure of the universe and into our knowledge of reality. It provides an answer to the question of how arithmetic applies to reality, and gives an account of how, in general, formalized systems of symbols work in providing access to the world. The ""appendices"" to this book provide some of Husserl's subsequent discussions of how formalisms work, involving David Hilbert's program of completeness for arithmetic. ""Completeness"" is integrated into Husserl's own problematic of the ""imaginary"", and allows him to move beyond the analysis of ""representations"" in his understanding of the logic of mathematics. Husserl's work here provides an alternative model of what ""conceptual analysis"" should be - minus the ""linguistic turn"", but inclusive of language and linguistic meaning. In the process, he provides case after case of ""Phenomenological Analysis"" - fortunately unencumbered by that title - of the convincing type that made Husserl's life and thought a fountainhead of much of the most important philosophical work of the twentieth Century in Europe. Many Husserlian themes to be developed at length in later writings first emerge here: Abstraction, internal time consciousness, polythetic acts, acts of higher order ('founded' acts), Gestalt qualities and their role in knowledge, formalization (as opposed to generalization), essence analysis, and so forth. 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. Husserl's extensive and trenchant criticisms of Gottlob Frege's theory of number and arithmetic reach far beyond those most commonly referred to in the literature on their views.

Full Product Details

Author:   Edmund Husserl ,  Dallas Willard ,  Dallas Willard
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2003 ed.
Volume:   10
Dimensions:   Width: 15.50cm , Height: 3.10cm , Length: 23.50cm
Weight:   1.062kg
ISBN:  

9781402015465

ISBN 10:   1402015461
Pages:   515
Publication Date:   30 September 2003
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
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Table of Contents

First Part: The Authentic Concepts of Multiplicity, Unity and Number.- I: The Origination of the Concept of Multiplicity through that of the Collective Combination.- II: Critical Developments.- III: The Psychological Nature ot the Collective Combination.- IV: Analysis of the Concept of Number in Terms of its Origin and Content.- V: The realations “More” AND “Less”.- VI: The Definition of Number-Equity through the Concept of Reciprocal One-tO- One Correlation.- VII: Definition of Number in Terms of Equivalence.- VIII: Discussions Concerning Unity and Multiplicity.- IX: The Sense of the Statement of Numbers.- Second Part: The Symbolic Number Concepts And The Logical Sources Of Cardinal Arithmetic.- X: Operations on Numbers and the Authentic Number Concepts.- XI: Symbolic Representations of Multiplicities.- XII: The Symbolic Representations of Numbers.- XIII: The Logical Sources of Arithmetic.- Supplementary Texts (1887–1901).- A. Original Version of the Text through Chapter IV: ON the Concept of Number: Psychological Analyses.- B. Essays.

Reviews

From the reviews: This translation is the crowning achievement of Dallas Willard's monumental research into Husserl's early philosophy ... . The volume is hence a good starting point for English-speaking students from freshman to graduate level who wish to familiarise themselves with Husserl's philosophy of mathematics ... . Willard succeeds in creating a very readable English text, maintaining a good balance between correctly rendering difficult and ambiguous German terms and writing in a clear and easy way. (Carlo Ierna, Husserl Studies, Vol. 24, 2008)

From the reviews: <p> The main body of this scholarly edition is formed by the English translation of Edmund Husserla (TM)s first book Philosophie der Arithmetik of 1891 a ] . Several further related research documents and lecture notes are also included. a ] The long a ~Translatora (TM)s introductiona (TM) provides helpful information on the context and history of these texts and also gives an interpretation of the essential lines of argument. (Volker Peckhaus, Zentralblatt MATH, Vol. 1073 (24), 2005) <p> Willard has a ] crafted a fluid and graceful text that is as much a pleasure to read as if Husserl had originally composed it in English. a ] a book that is faithful to Husserla (TM)s purpose and technical distinctions and serves to make the ideas highly accessible to contemporary English readers. a ] Willard does a superb job of guiding the reader through the essentials of Husserla (TM)s philosophy of arithmetic, providing historical context and important sidelines to Husserla (TM)s thought a ] . (Dale Jacquette, Review of Metaphysics, Vol. LIX (2), 2005) <p> This text contains the first English translation of Husserla (TM)s earliest book, Philosophy of Arithmetic 1891. a ] Current discussions on matters such as the nature of number, mathematical intuition, conceptual analysis, computer proofs, rule following, and the division of Anglo-American and Phenomenological philosophy, will gain considerably from an examination of this text. a ] It is also worth noting that the translatora (TM)s introduction is a valuable and substantial piece of scholarship in its own right that effectively makes the text accessible to philosophers of any orientation. (David Kasmier, Journal of theBritish Society of Phenomenology, Vol. 36 (1), 2005)

From the reviews: This translation is the crowning achievement of Dallas Willard's monumental research into Husserl's early philosophy ... . The volume is hence a good starting point for English-speaking students from freshman to graduate level who wish to familiarise themselves with Husserl's philosophy of mathematics ... . Willard succeeds in creating a very readable English text, maintaining a good balance between correctly rendering difficult and ambiguous German terms and writing in a clear and easy way. (Carlo Ierna, Husserl Studies, Vol. 24, 2008)

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