(FreePik, 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. Intractability in Cognitive Science: Further Problems for Mechanism 1. Introduction In an earlier essay, we explored and critically exposed the inherent … [continue reading]
Author Archives: Joseph Wayne Smith and N. Stocks
The Pythagorean Crisis Revisited: A Challenge to the Infinite Decimal Representation of the Reals, #3.
(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]
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]