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From Reducibility to Extensionality The two editions of Principia Mathematica
 

Summary: From Reducibility to Extensionality
The two editions of Principia Mathematica
Jessi Berkelhammer
September 26, 2003
Contents
Overview 3
1 The system of Principia Mathematica's first edition 6
1.1 Basic principles of the logical system . . . . . . . . . . . . . . 6
1.2 The theory of types . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.1 A formal presentation of Russell's type theory . . . . . 15
1.2.2 The axiom of reducibility . . . . . . . . . . . . . . . . . 20
1.3 Identity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4 Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2 The axiom of reducibility and the second edition of Principia
Mathematica 28
2.1 Justification in the first edition for the axiom of reducibility . 28
2.1.1 Introduction to Mathematical Philosophy . . . . . . . . 30
2.2 Reaction to the first edition . . . . . . . . . . . . . . . . . . . 31
2.2.1 Hilbert school . . . . . . . . . . . . . . . . . . . . . . . 31
2.2.2 Weyl . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

  

Source: Avigad, Jeremy - Departments of Mathematical Sciences & Philosophy, Carnegie Mellon University

 

Collections: Multidisciplinary Databases and Resources; Mathematics