Frege's Logic and Foundations for Arithmetic

Complete Table of Contents
With Listing of Subsections

• The Language
• The Logic
• The Rule of Substitution
• The Theory of Concepts

§2: Frege's Theory of Extensions: Basic Law V

• Notation for Courses-of-Values
• Membership in an Extension
• Basic Law V
• First Derivation of the Contradiction
• Second Derivation of the Contradiction
• How the Paradox is Engendered

§3: Frege's Analysis of Cardinal Numbers

• Equinumerosity
• Contextual Definition of ‘The Number of Fs’:
  Hume's Principle
• Explicit Definition of ‘The Number of Fs’
• Derivation of Hume's Principle

§4: Frege's Analysis of Predecessor, Ancestrals, and the Natural Numbers

• Predecessor
• The Ancestral of Relation R
• The Weak Ancestral of R
• The Concept Natural Number

§5: Frege's Theorem

• Zero is a Number
• Zero Isn't the Successor of Any Number
• No Two Numbers Have the Same Successor
• The Principle of Mathematical Induction
• Every Number Has a Successor
• Arithmetic

§6: Philosophical Questions Surrounding Frege's Theorem

• Frege's Goals and Strategy in His Own Words
• The Basic Problem for Frege's Strategy
• The Existence of Concepts
• The Existence of Extensions
• The Existence of Numbers and Truth-Values:
  The Julius Caesar Problem
• Final Observations

Bibliography

Other Internet Resources

Related Entries