Introduction to Mathematical Philosophy cover

Introduction to Mathematical Philosophy

Bertrand Russell (1872-1970)

1. Preface
2. The Series of Natural Numbers
3. Definition of Number
4. Finitude and Mathematical Induction
5. The Definition of Order
6. Kinds of Relations
7. Similarity of Relations
8. Rational, Real, and Complex Numbers
9. Infinite Cardinal Numbers
10. Infintie Series of Ordinals
11. Limits and Continuity
12. Limits and Continuity of Functions
13. Selections and the Multiplicative Axiom
14. The Axiom of Infinity and Logical Types
15. Incompatibility and the Theory of Deduction
16. Propositional Functions
17. Descriptions
18. Classes
19. Mathematics and Logic

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Summary

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.