(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]
Author Archives: Joseph Wayne Smith and N. Stocks
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]
Mathematical Skepticism: Infinity and Real Numbers, #4.
(Scientific American, 2023) TABLE OF CONTENTS 1. Introduction 2. Chaitin and Borel 3. B.H. Slater 4. N.J. Wildberger 5. A Benacerraf-Inspired Critique of Real Numbers 6. Critique of Other Accounts of Real Numbers 7. Infinite Decimals and a Contradiction The following essay has been published in four installments; this installment, the fourth and final one, … [continue reading]
Mathematical Skepticism: Infinity and Real Numbers, #3.
(Scientific American, 2023) TABLE OF CONTENTS 1. Introduction 2. Chaitin and Borel 3. B.H. Slater 4. N.J. Wildberger 5. A Benacerraf-Inspired Critique of Real Numbers 6. Critique of Other Accounts of Real Numbers 7. Infinite Decimals and a Contradiction The following essay will be published in four installments; this installment, the third, contains sections 5 … [continue reading]
Mathematical Skepticism: Infinity and Real Numbers, #2.
(Scientific American, 2023) TABLE OF CONTENTS 1. Introduction 2. Chaitin and Borel 3. B.H. Slater 4. N.J. Wildberger 5. A Benacerraf-Inspired Critique of Real Numbers 6. Critique of Other Accounts of Real Numbers 7. Infinite Decimals and a Contradiction The following essay will be published in four installments; this installment, the second, contains section 4. … [continue reading]
Mathematical Skepticism: Infinity and Real Numbers, #1.
(Scientific American, 2023) TABLE OF CONTENTS 1. Introduction 2. Chaitin and Borel 3. B.H. Slater 4. N.J. Wildberger 5. A Benacerraf-Inspired Critique of Real Numbers 6. Critique of Other Accounts of Real Numbers 7. Infinite Decimals and a Contradiction The following essay will be published in four installments; this installment, the first, contains sections 1-3. … [continue reading]
Mathematics, Metaphysics, and Mystery, #4.
(Montessori Schools, 2018) TABLE OF CONTENTS 1. Introduction: From Mind to Mathematics 2. The Nature of Mathematical Entities: Nothing Works 3. Set Theory: Should One Believe? 4. Metaphysics and Ontology 5. Mathematical Fictionalism 6. Mathematical Realism 7. Hanna’s Neo-Intuitionism as a Way Out of the Impasse? 8. Conclusion: From Mathematics to Mind This essay will … [continue reading]
Mathematics, Metaphysics, and Mystery, #3.
(Montessori Schools, 2018) TABLE OF CONTENTS 1. Introduction: From Mind to Mathematics 2. The Nature of Mathematical Entities: Nothing Works 3. Set Theory: Should One Believe? 4. Metaphysics and Ontology 5. Mathematical Fictionalism 6. Mathematical Realism 7. Hanna’s Neo-Intuitionism as a Way Out of the Impasse? 8. Conclusion: From Mathematics to Mind This essay will … [continue reading]
Mathematics, Metaphysics, and Mystery, #2.
(Montessori Schools, 2018) TABLE OF CONTENTS 1. Introduction: From Mind to Mathematics 2. The Nature of Mathematical Entities: Nothing Works 3. Set Theory: Should One Believe? 4. Metaphysics and Ontology 5. Mathematical Fictionalism 6. Mathematical Realism 7. Hanna’s Neo-Intuitionism as a Way Out of the Impasse? 8. Conclusion: From Mathematics to Mind This essay will … [continue reading]