Philosophy of Arithmetic

Foreword. First Part: The Authentic Concepts of Multiplicity, Unity and Whole Number. Introduction. I: 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. II: 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. III: 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. IV: 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. V: 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. VI: 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

From the reviews: