The Mathematical Philosophy of Bertrand Russell: Origins and Development

1. Methodological and logicist background.- 1.1. Boole and Peirce.- 1.2. Dedekind and Cantor.- 1.3. Couturat and Whitehead.- 1.4. Bradley and Moore.- 1.5. Foundations of geometry.- 2. The unpublished mathematical philosophy: 1898-1900.- 2.1. The genesis of the 1898-1900 manuscripts.- 2.2. Logic, mathematics and ontology.- 2.3. The evolution of the main concepts.- 2.4. Concepts, axioms, presupposition and implication.- 2.5. The contradiction and the infinite.- 2.6. Relations and the 'principle of abstraction'.- 2.7. The method of definition.- 2.8. The gradual approach to Cantor.- 2.8.1. The first contacts and opinions.- 2.8.2. The reasons for the rejection.- 3. The contribution of Peano and his school.- 3.1. Logic.- 3.1.1. Objective and stages.- 3.1.2. Primitives, logical order and interdefinability.- 3.1.3. Implication, inclusion and membership.- 3.1.4. Classes, propositions and individuals.- 3.1.5. Mathematical propositions and quantification.- 3.1.6. Relations, functions, classes, properties and propositions.- 3.2. Arithmetic.- 3.2.1. The axioms and their interpretation: Dedekind.- 3.2.2. The definability of number.- 3.2.3. Real numbers: construction and definition.- 3.2.4. The 'logicist' arithmetic: Cantor.- 3.3. Geometry.- 3.3.1. The geometric calculus and the principles of geometry.- 3.3.2. The Uogicist' geometry.- 3.4. The method.- 3.4.1. Axiomatics.- 3.4.2. Definitions.- 3.4.3. The definition by abstraction.- 3.4.4. Simplicity, analysis and intuition.- 3.5. Peano's followers and their contributions.- 3.5.1. The various improvements.- 3.5.2. The transformation of definitions by abstraction into nominal ones.- 4. The principles of mathematics.- 4.1. The reaction to the Congress of 1900.- 4.1.1. The notes to the manuscripts: from Moore to Peano.- 4.1.2. The first writings.- 4.1.3. The acceptance of Cantor.- 4.2. Logic.- 4.2.1. The indefinables and the propositional function.- 4.2.2. Relations.- 4.3. Arithmetic.- 4.3.1. The definition of cardinal number.- 4.3.2. Finite and infinite.- 4.3.3. Quantity.- 4.3.4. Order.- 4.3.5. Ordinal numbers.- 4.3.6. Real numbers.- 4.4. Geometry.- 4.5. What Russell learned from Peano.- 5. Philosophical and methodological problems.- 5.1. Origin and evolution of Russell's logicism.- 5.2. The principle of abstraction.- 5.2.1. Origin and evolution.- 5.2.2. Assumptions and implications.- 5.3. The constructive definition.- 5.3.1. Nominal definitions.- 5.3.2. Mathematical and philosophical definitions.- 5.3.3. Analysis and ordinary language.- 5.4. Relational logic and ontology.- B.1. Works by Russell.- B. 1.1. Unpublished manuscripts 224.- B. 1.2. Published or unpublished correspondence 225.- B. 1.3. Published works 225.- B.2. Works by other authors.