(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]
Author Archives: Joseph Wayne Smith and N. Stocks
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]
Mathematics, Metaphysics, and Mystery, #1.
(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]
The Limits of Statistical Methodology: Why A “Statistically Significant” Number of Published Scientific Research Findings are False, #4.
(Ioannidis, 2005a) TABLE OF CONTENTS 1. Introduction 2. Troubles in Statistical Paradise 3. A Critique of Bayesianism 4. The Limits of Probability Theory 5. Conclusion The essay that follows below will be published in four installments; this is the fourth and final installment. But you can also download and read or share a .pdf of … [continue reading]
The Limits of Statistical Methodology: Why A “Statistically Significant” Number of Published Scientific Research Findings are False, #3.
(Ioannidis, 2005a) TABLE OF CONTENTS 1. Introduction 2. Troubles in Statistical Paradise 3. A Critique of Bayesianism 4. The Limits of Probability Theory 5. Conclusion The essay that follows below will be published in four installments; this is the third. But you can also download and read or share a .pdf of the complete text … [continue reading]