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]
Author Archives: Joseph Wayne Smith and N. Stocks
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]
The Falling Dominoes of the Principle of Proof by Mathematical Induction, #2.
(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]
The Falling Dominoes of the Principle of Proof by Mathematical Induction, #1.
(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]
The Fermi Delusion: Why Aliens Haven’t Called and Probably Never Will.
(SETI Institute, 2025) You can also download and read or share a .pdf of the complete text of this essay by scrolling down to the bottom of this post and clicking on the Download tab. The Fermi Delusion: Why Aliens Haven’t Called and Probably Never Will 1. Introduction The Fermi Paradox—why do we see no … [continue reading]