(Unihedron, 2025) TABLE OF CONTENTS 1. Introduction 2. The Geometric-Arithmetic Divide 3. The Metaphysical Paradox 4. Historical Resonances: The Zenoesque Structure 5. Implications for Real Analysis 6. Toward a Critical Examination 7. Conclusion The essay below will be published on three installments; this, the third and final one, contains sections 6-7. But you can also … [continue reading]
Author Archives: Joseph Wayne Smith and N. Stocks
The Pythagorean Crisis Revisited: A Challenge to the Infinite Decimal Representation of the Reals, #2.
(Unihedron, 2025) TABLE OF CONTENTS 1. Introduction 2. The Geometric-Arithmetic Divide 3. The Metaphysical Paradox 4. Historical Resonances: The Zenoesque Structure 5. Implications for Real Analysis 6. Toward a Critical Examination 7. Conclusion The essay below will be published on three installments; this one, the second, contains sections 4-5. But you can also download and … [continue reading]
The Pythagorean Crisis Revisited: A Challenge to the Infinite Decimal Representation of the Reals, #1.
(Unihedron, 2025) TABLE OF CONTENTS 1. Introduction 2. The Geometric-Arithmetic Divide 3. The Metaphysical Paradox 4. Historical Resonances: The Zenoesque Structure 5. Implications for Real Analysis 6. Toward a Critical Examination 7. Conclusion The essay below will be published on three installments; this one, the first, contains sections 1-3. But you can also download and … [continue reading]
The Limits of Limits: A Skeptical Inquiry into the Foundations of the Calculus, #4.
ε-δ Definition TABLE OF CONTENTS 1. Introduction 2. The Formal Definition of Limits: Weierstrass and the Alleged Achievement of Mathematical Rigor 3. The Triumph of Rigor? 4. Objections to the Standard Theory of Limits 5. The Circularity Objection: A Fundamental Challenge to Epsilon-Delta Logic 6. The Structure of the Circularity 7. Applications Under Threat 8. … [continue reading]
The Limits of Limits: A Skeptical Inquiry into the Foundations of the Calculus, #3.
ε-δ Definition TABLE OF CONTENTS 1. Introduction 2. The Formal Definition of Limits: Weierstrass and the Alleged Achievement of Mathematical Rigor 3. The Triumph of Rigor? 4. Objections to the Standard Theory of Limits 5. The Circularity Objection: A Fundamental Challenge to Epsilon-Delta Logic 6. The Structure of the Circularity 7. Applications Under Threat 8. … [continue reading]
The Limits of Limits: A Skeptical Inquiry into the Foundations of the Calculus, #2.
ε-δ Definition TABLE OF CONTENTS 1. Introduction 2. The Formal Definition of Limits: Weierstrass and the Alleged Achievement of Mathematical Rigor 3. The Triumph of Rigor? 4. Objections to the Standard Theory of Limits 5. The Circularity Objection: A Fundamental Challenge to Epsilon-Delta Logic 6. The Structure of the Circularity 7. Applications Under Threat 8. … [continue reading]
The Limits of Limits: A Skeptical Inquiry into the Foundations of the Calculus, #1.
ε-δ Definition TABLE OF CONTENTS 1. Introduction 2. The Formal Definition of Limits: Weierstrass and the Alleged Achievement of Mathematical Rigor 3. The Triumph of Rigor? 4. Objections to the Standard Theory of Limits 5. The Circularity Objection: A Fundamental Challenge to Epsilon-Delta Logic 6. The Structure of the Circularity 7. Applications Under Threat 8. … [continue reading]
The Algebraic Shadow of Change: On the Philosophical Failure of Distribution Theory, #2.
(Robinson, 2014) TABLE OF CONTENTS 1. Introduction 2. Distribution Theory 3. The Distributional Derivative: A Formal Trick 4. Pathologies and the Limits of Generalization 5. Constructivist and Finitist Concerns 6. Conclusion The essay below is being published in two installments; this one, the second and final installment, contains sections 4-6. But you can also download … [continue reading]
The Algebraic Shadow of Change: On the Philosophical Failure of Distribution Theory, #1.
(Robinson, 2014) TABLE OF CONTENTS 1. Introduction 2. Distribution Theory 3. The Distributional Derivative: A Formal Trick 4. Pathologies and the Limits of Generalization 5. Constructivist and Finitist Concerns 6. Conclusion The essay below will be published in two installments; this one, the first, contains sections 1-3. But you can also download and read or … [continue reading]
The Falling Dominoes of the Principle of Proof by Mathematical Induction, #3.
(Wikipedia, 2025) TABLE OF CONTENTS 1. Introduction 2. The Definition of Mathematical Induction 3. Wang’s Paradox and the Predicate “Small” 4. Edward Nelson’s Critique of Mathematical Induction 5. Mathematical Induction Meets Gödel’s Incompleteness Theorems 6. Omega-Consistency and Its Role in Gödel’s Theorems 7. A Foundational Skepticism about Mathematical Induction 8. A Foundational Skepticism about Mathematical … [continue reading]