## Frege's Logic and Foundations for Arithmetic

### Complete Table of Contents

With Listing of Subsections

§1: Frege's Predicate Calculus and Theory of Concepts
- 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
*F*s’:

Hume's Principle
- Explicit Definition of ‘The Number of
*F*s’
- 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

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