Introduction

Chapter One: A Critique of Minkowski Spacetime

Part I: The Concept of Minkowski Spacetime

Chapter Two Minkowski's "Space and Time"

2.1 Minkowski and Göttingen Science

2.2 "Space and Time," Sections I and II

2.3 "Space and Time," Section III

2.4 "Space and Time," Section IV

Chapter Three Special Relativity and Spacetime

3.1 The Concept of a Continuum

3.2 The "Geometry of Spacetime" Graphs and Images

3.3 The Role of Invariance in Special Relativity

3.3.1 Invariance and Frame-Independence

3.3.2 Invariance and the Clock Paradox

3.4 Transition to Part II: Conceptual Difficulties of Minkowski Spacetime and the Need for a Historical Approach

Part II: The Symbolic-Algebraic Constitution of the Concept of Spacetime

Introduction to Part II The Concept of a Sense-History

Chapter Four The Historical Sense-Structure of Symbolic Algebra

4.1 The Concept of Number in Greek Mathematics

4.1.1 Arithmetical Operations in Euclid

4.1.2 The Concept of Ratio in Euclid

4.1.3 Arithmetic and Geometry in Euclid

4.2 Algebraic Equations in Greek Mathematics: Diophantus of Alexandria

4.2.1 The Concept of Number in Diophantus

4.2.2 Algebraic Calculations with "Species"

3.3 Modern Symbolic Algebra

4.3.1 Vieta's Reinterpretation of Diophantine Species

4.3.2 Vieta's Law of Homogeneity and the Symbolic Concept of Number

4.3.3 Vieta's Algebra as Mathesis Universalis