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Philosophy of Arithmetic : Psychological and Logical Investigations with Supplementary Texts from 1887-1901 - Edmund Husserl

Philosophy of Arithmetic

Psychological and Logical Investigations with Supplementary Texts from 1887-1901

By: Edmund Husserl, D. Willard (Translator), Dallas Willard (Editor)

Hardcover Published: 30th September 2003
ISBN: 9781402015465
Number Of Pages: 515

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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.

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"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)

Foreword
First Part: The Authentic Concepts of Multiplicity, Unity and Whole Number 21
The Origination of the Concept of Multiplicity through that of the Collective Combination
The Analysis of the Concept of the Whole Number Presupposes that of the Concept of Multiplicity
The Concrete Bases of the Abstraction Involved
Independence of the Abstraction from the Nature of the Contents Colligated
The Origination of the Concept of the Multiplicity through Reflexion on the Collective Mode of Combination
Critical Developments
The Collective Unification and the Unification of Partial Phenomena in the Total Field of Consciousness at a Given Moment
The Collective "Together" and the Temporal "Simultaneously"
Collection and Temporal Succession
The Collective Synthesis and the Spatial Synthesis
A: F.A. Lange''s Theory. B: Baumann''s Theory
Colligating, Enumerating and Distinguishing
Critical Supplement
The Psychological Nature of the Collective Combination
Review
The Collection as a Special Type of Combination
On the Theory of Relations
Psychological Characterization of the Collective Combination
Analysis of the Concept of Number in Terms of its Origin and Content
Completion of the Analysis of the Concept of Multiplicity. The Concept `Something''
The Cardinal Numbers and the Generic Concept of Number
Relationship between the Concepts `Cardinal Number'' and `Multiplicity''
One and Something. Critical Supplement
The Relations "More" and "Less"
The Psychological Origin of these Relations
Comparison of Arbitrary Multiplicities, as well as of Numbers, in Terms of More and Less
The Segregation of the Number Species Conditioned upon the Knowledge of More and Less
The Definition of Number-Equality through the Concept of Reciprocal One-to-One Correlation
Leibniz''s Definition of the General Concept of Equality
The Definition of Number-Equality. Concerning Definitions of Equality for Special Cases
Application to the Equality of Arbitrary Multiplicities
Comparison of Multiplicities of One Genus
Comparison of Multiplicities with Respect to their Number
The True Sense of the Equality Definition under Discussion
Reciprocal Correlation and Collective Combination
The Independence of Number-Equality from the Type of Linkage
Definitions of Number in Terms of Equivalence
Structure of the Equivalence Theory
Illustrations
Critique
Frege''s Attempt. Kerry''s Attempt
Concluding Remark
Discussions Concerning Unity and Multiplicity
The Definition of Number as a Multiplicity of Units
One as an Abstract, Positive Partial Content
One as Mere Sign
One and Zero as Numbers
The Concept of the Unit and the Concept of the Number One. Further Distinctions Concerning One and Unit
Sameness and Distinctness of the Units
Further Misunderstandings
Equivocations of the Name "Unit"
The Arbitrary Character of the Distinction between Unit and Multiplicity
The Multiplicity Regarded as One Multiplicity, as One Enumerated Unit, as One Whole
Herbartian Arguments
The Sense of the Statement of Number
Contradictory Views
Refutation, and the Position Taken
Appendix to the First Part: The Nominalist Attempts of Helmholtz and Kronecker
The Symbolic Number Concepts and the Logical Sources of Cardinal Arithmetic
Operations on Numbers and the Authentic Number Concepts
The Numbers in Arithmetic are Not Abstracta
The Fundamental Activities on Numbers
Addition
Partition
Arithmetic Does Not Operate with "Authentic" Number Concepts
Symbolic Representations of Multiplicities
Authentic and Symbolic Representations
Sense Perceptible Groups
Attempts at an Explanation of How We Grasp Groups in an Instant
Symbolizations Mediated by the Full Process of Apprehending the Individual Elements
New Attempts at an Explanation of Instantaneous Apprehensions of Groups
Hypotheses
The Figural Moments
The Position Taken
The Psychological Function of the Focus upon Individual Members of
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9781402015465
ISBN-10: 1402015461
Series: Husserliana: Edmund Husserl - Collected Works
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 515
Published: 30th September 2003
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 25.25 x 16.2  x 3.51
Weight (kg): 1.06

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