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