Numbers in Presence and Absence
A Study of Husserl's Philosophy of Mathematics
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I: The Emergence and Development of Husserl's 'Philosophy of Arithmetic'.- 1. Historical Background: Weierstrass and the Arithmetization of Analysis.- 2. Husserl's First Stage: Analysis as a Science of Number.- 3. Husserl's Second Stage: Analysis as a Formal Technique.- 4. Husserl's Third Stage: Analysis as Manifold Theory.- 5. The Problem of Psychologism in Husserl's Early Writings.- II: Husserl and the Concept of Number.- 1. The Definition of Number.- 2. The Origin of Number as a Phenomenological Problem.- 3. The Origin of Number in Husserl's Eearly Writings.- III: The Presence of Number.- 1...
I: The Emergence and Development of Husserl's 'Philosophy of Arithmetic'.- 1. Historical Background: Weierstrass and the Arithmetization of Analysis.- 2. Husserl's First Stage: Analysis as a Science of Number.- 3. Husserl's Second Stage: Analysis as a Formal Technique.- 4. Husserl's Third Stage: Analysis as Manifold Theory.- 5. The Problem of Psychologism in Husserl's Early Writings.- II: Husserl and the Concept of Number.- 1. The Definition of Number.- 2. The Origin of Number as a Phenomenological Problem.- 3. The Origin of Number in Husserl's Eearly Writings.- III: The Presence of Number.- 1. Sensuous Groups.- 2. Explication.- 3. Comparison.- IV: Numbers as Identities in Presence and Absence.- 1. Intending Numbers in their Absence.- 2. The Unity of Number.- 3. The Unity of Large Numbers.- 4. Sedimented Number Meanings.- V: The Sense of Arithmetic.- 1. Ideal Numbers.- 2. The Formal Character of the Concept of Number.- 3. Arithmetic as Formal Ontology.- VI: The Sense of Analysis.- 1. The Algebraization of Arithmetic.- 2. Theory Forms and Manifolds.- 3. Analysis as Manifold Theory.- 4. Husserl's Attempted Justification of Analysis.- Conclusion.- Note on Abbreviations.
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