This book explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians into thinking about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge.
This book explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians into thinking about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge.
Ahmet Çevik is Associate Professor of logic and foundations of mathematics, working in both mathematical and philosophical domains. He holds a Ph.D. from the University of Leeds, UK. Ahmet was postdoctoral visitor in the Department of Mathematics at the University of California, Berkeley. He has lectured at Middle East Technical University and is affiliated with the Gendarmerie and Coast Guard Academy, in Ankara, Turkey. His research interests are mathematical logic, recursion theory, theoretical computer science, and philosophy of mathematics.
Inhaltsangabe
1. Introduction 2. Mathematical Preliminaries 3. Platonism 4. Intuitionism 5. Logicism 6. Formalism 7. Gödel's Incompleteness Theorem and Computability 8. The Church-Turing Thesis 9. Infinity 10. Supertasks 11. Models, Completeness, and Skolem's Paradox 12. Axiom of Choice 13. Naturalism 14. Structuralism 15. Yablo's Paradox 16. Mathematical Pluralism 17. Does Mathematics Need More Axioms? 18. Mathematical Nominalism
