Introduction to Mathematical Philosophy
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123
1919
English
- Preface
- The Series of Natural Numbers
- Definition of Number
- Finitude and Mathematical Induction
- The Definition of Order
- Kinds of Relations
- Similarity of Relations
- Rational, Real, and Complex Numbers
- Infinite Cardinal Numbers
- Infintie Series of Ordinals
- Limits and Continuity
- Limits and Continuity of Functions
- Selections and the Multiplicative Axiom
- The Axiom of Infinity and Logical Types
- Incompatibility and the Theory of Deduction
- Propositional Functions
- Descriptions
- Classes
- Mathematics and Logic
Bertrand Russell wrote 'Introduction to Mathematical Philosophy' while imprisoned for protesting Britain's involvement in World War I. Russell summarizes the significance of the momentous work of mathematicians in the late nineteenth-century. He further describes his own philosophy of mathematics, Logicism (the view that all mathematical truths are logical truths), and his earlier, influential work solving the paradoxes that plagued mathematical foundations, which crystallized after ten years of dogged effort into the co-authored (with Alfred North Whitehead), three-volume 'Principia Mathematica'. Russell emphasizes the importance of a doctrine of types, the truth of Logicism, and the clarity brought to the philosophy of mathematics by the method of logical analysis. (summary by Landon D. C. Elkind)
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