## Philosophy of Arithmetic: Psychological and Logical Investigations - with Supplementary Texts from 1887-1901In 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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### Índice

THE AUTHENTIC CONCEPTS OF MULTIPLICITY UNITY AND WHOLE NUMBER | 9 |

INTRODUCTION | 11 |

THE ORIGINATION OF THE CONCEPT OF MULTIPLICITY THROUGH THAT OF THE COLLECTIVE COMBINATION The Analysis of the Co... | 15 |

The Concrete Bases of the Abstraction Involved | 16 |

Independence of the Abstraction from the Nature of the Contents Colligated | 17 |

The Origination of the Concept of the Multiplicity through Reflexion on the Collective Mode of Combination | 18 |

CRITICAL DEVELOPMENTS | 23 |

The Collective Together and the Temporal Simultaneously | 25 |

The Figural Moments | 215 |

The Position Taken | 223 |

The Psychological Function of the Focus upon Individual Members of the Group | 225 |

What is It that Guarantees the Completeness of the Traversive Apprehension of the Individuals in a Group? | 226 |

Apprehension of Authentically Representable Groups through Figural Moments | 228 |

MISSING TOC element The Elemental Operations on and Relations between page 229 Infinite Groups | 230 |

THE SYMBOLIC REPRESENTATIONS OF NUMBERS | 235 |

The NonSystematic Symbolizations of Numbers | 236 |

Collection and Temporal Succession | 26 |

The Collective Synthesis and the Spatial Synthesis | 35 |

B Baumanns Theory | 45 |

Colligating Enumerating and Distinguishing | 49 |

Critical Supplement | 61 |

THE PSYCHOLOGICAL NATURE OF THE COLLECTIVE COMBINATION | 67 |

The Collection as a Special Type of Combination | 68 |

On The Theory of Relations | 69 |

Psychological Characterization of the Collective Combination | 74 |

ANALYSIS OF THE CONCEPT OF NUMBER IN TERMS OF ITS ORIGIN AND CONTENT | 81 |

The Concept Something | 84 |

The Cardinal Numbers and the Generic Concept of Number | 85 |

Relationship Between the Concepts Cardinal Number and Multiplicity | 87 |

One and Something | 88 |

Critical Supplement | 89 |

THE RELATIONS MORE AND LESS | 95 |

Comparison of Arbitrary Multiplicities as well as of Numbers in Terms of More and Less | 98 |

The Segregation of the Number Species Conditioned upon the Knowledge of More and Less | 99 |

THE DEFINITION OF NUMBEREQUALITY THROUGH THE CONCEPT OF RECIPROCAL ONETOONE CORRELATION | 101 |

The Definition of NumberEquality | 103 |

Concerning Definitions of Equality for Special Cases | 105 |

Application to the Equality of Arbitrary Multiplicities | 106 |

Comparison of Multiplicities of One Genus | 108 |

The True Sense of the Equality Definition under Discussion | 110 |

Reciprocal Correlation and Collective Combination | 111 |

The Independence of NumberEquality from the Type of Linkage | 114 |

DEFINITIONS OF NUMBER IN TERMS OF EQUIVALENCE | 117 |

Illustrations | 120 |

Critique | 121 |

Freges Attempt | 123 |

MISSING TOC element KERRYS ATTEMPT page 129 Concluding Remark | 131 |

DISCUSSIONS CONCERNING UNITY AND MULTIPLICITY | 133 |

One and Zero as Numbers | 136 |

The Concept of the Unit and the Concept of the Number One | 141 |

Further Distinctions Concerning One and Unit | 143 |

Sameness and Distinctness of the Units | 146 |

Further Misunderstandings | 157 |

Equivocations of the Name Unit | 159 |

The Arbitrary Character of the Distinction between Unit and Multiplicity The Multiplicity Regarded as One Multiplicity as One Enumerated Unit as O... | 162 |

Herbartian Arguments | 164 |

THE SENSE OF THE STATEMENT OF NUMBER | 169 |

Refutation and the Position Taken | 170 |

The Nominalist Attempts of Helmholtz and Kronecker | 179 |

THE SYMBOLIC NUMBER CONCEPTS AND THE LOGICAL SOURCES OF CARDINAL ARITHMETIC | 189 |

OPERATIONS ON NUMBERS AND THE AUTHENTIC NUMBER CONCEPTS | 191 |

MISSING TOC element The Fundamental Activities on Numbers page 192 Addition | 193 |

Partition | 198 |

SYMBOLIC REPRESENTATIONS OF MULTIPLICITIES | 205 |

Sense Perceptible Groups | 207 |

Attempts at an Explanation of How We Grasp Groups in an Instant | 208 |

Symbolizations Mediated by the Full Process of Apprehending the Individual Elements | 210 |

New Attempts at an Explanation of Instantaneous Apprehensions of Groups | 211 |

Hypotheses | 213 |

The Sequence of Natural Numbers | 238 |

The System of Numbers | 241 |

Relationship of the Number System to the Sequence of Natural Numbers | 247 |

MISSING TOC element The Choice of the Base Number page 249 The Systematic of the Number Concepts and the Systematic of the Number Signs | 251 |

The Process of Enumeration via Sense Perceptible Symbols | 253 |

through Sense Perceptible Symbolization | 254 |

Differences between Sense Perceptible Means of Designation | 257 |

The Natural Origination of the Number System | 258 |

Appraisal of Number through Figural Moments | 267 |

Chapter XIII THE LOGICAL SOURCES OF ARITHMETIC | 271 |

The Calculational Methods of Arithmetic and the Number Concepts | 274 |

The Systematic Numbers as Surrogates for the Numbers in Themselves | 275 |

The First Basic Task of Arithmetic | 277 |

Addition | 279 |

Multiplication | 283 |

Subtraction and Division | 284 |

Methods of Calculation with the Abacus and in Columns The Natural Origination of the Indic Numeral Calculation | 288 |

Influence of the Means of Designation upon the Formation of the Methods of Calculation | 290 |

The Higher Operations | 292 |

MISSING TOC element The Indirect Characterization of Numbers by Means of Equations page 296 Mixing of Operations | 294 |

The Logical Sources of General Arithmetic | 298 |

ON THE CONCEPT OF NUMBER PSYCHOLOGICAL ANALYSES | 305 |

Chapter One | 312 |

Critical Exposition of Certain Theories | 318 |

The Analysis of the Concept of Number as to its Origin and Content | 352 |

PSYCHOLOGICAL ANALYSES THESES | 357 |

B ESSAYS | 359 |

II Comparison of Numbers | 364 |

III Addenda | 368 |

2 On the Definition of Number | 369 |

V Remark | 374 |

VI Corrections | 375 |

VII Addenda | 379 |

2 Addendum to p 377 | 380 |

ON THE CONCEPT OF THE OPERATION | 385 |

II Combinations or Operations | 397 |

2 On the Concept of Combination Verknüpfung | 400 |

III Addendum | 405 |

DOUBLE LECTURE ON THE TRANSITION THROUGH THE IMPOSSIBLE IMAGINARY AND THE COMPLETENESS OF AN AXIOM SYSTEM | 409 |

2 Theories Concerning the Imaginary | 413 |

3 The Transition through the Imaginary | 427 |

APPENDIX I | 453 |

APPENDIX II | 459 |

APPENDIX III | 464 |

Husserls Excerpts from an Exchange of Letters between Hilbert and Frege | 468 |

THE DOMAIN OF AN AXIOM SYSTEM AXIOM SYSTEM OPERATION SYSTEM | 475 |

System of Numbers | 477 |

Arithmetizability of a Manifold | 479 |

On the Concept of an Operation System | 482 |

ON THE FORMAL DETERMINATION OF MANIFOLD | 497 |

505 | |

### Otras ediciones - Ver todo

Philosophy of Arithmetic: Psychological and Logical Investigations with ... Edmund Husserl Vista previa restringida - 2012 |

Philosophy of Arithmetic: Psychological and Logical Investigations with ... Edmund Husserl No hay vista previa disponible - 2003 |

### Términos y frases comunes

abstract actual addition already analysis arbitrary authentic axiom system basic basis belongs calculation cardinal number certainly characterized collective combination completely concept of multiplicity concept of number concrete consciousness consider contents correlation corresponding defined definition designation determinate number distinction distinguishing Edmund Husserl elements enumeration equal equinumerous equivalent equivalent transformations essential example expression fact finite number formation Franz Brentano Frege further genus given grasp holds true Husserl identical individual intuition latter Leibniz logical manifold manner mathematical means merely metic mode natural numbers Nominalist number concepts number forms number sequence number series number system objects obviously operation origin Philosophy of Arithmetic possible precisely present presupposes properties propositions psychical act psychological purely question reflexion relations relationship represented result sense signification signs spatial speak symbolic number symbolic representation synthesis systematic numbers temporal theory thing thought tion totality unification units unity univocally whole numbers

### Pasajes populares

Página xxv - Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Página xxxiii - If the number belonging to the concept F is defined as the extension of the concept equinumerous with the concept F, this means to Husserl that what we intend or mean (essentially have before the mind) in thinking of the number belonging to F is: the totality or set of concepts which have extensions that can be correlated one-to-one with the extension ofF. Given this, he says that "Further commentary is surely pointless.

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