The philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge.
With this new approach, the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones, including subjects which are more engaged with mathematical logic.
Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice, and no concern on giving crucial mathematical results and their philosophical relevance, consequences, reasons, etc. This book fills this gap.
The book can be used as a textbook for a one-semester or even one-year course on philosophy of mathematics.
"Other textbooks on the philosophy of mathematics are aimed at philosophers. This book is aimed at mathematicians. Since the author is a mathematician, it is a valuable addition to the literature."
- Mark Balaguer, California State University, Los Angeles
"There are not many such texts available for mathematics students. I applaud efforts to foster the dialogue between mathematics and philosophy."
- Michele Friend, George Washington University and CNRS, Lille, France
Table of Contents
2. Mathematical Preliminaries
7. Gödel’s Incompleteness Theorem and Computability
8. The Church-Turing Thesis
11. Models, Completeness, and Skolem’s Paradox
12. Axiom of Choice
15. Yablo’s Paradox
16. Mathematical Pluralism
17. Does Mathematics Need More Axioms?
18. Mathematical Nominalism
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.