Philosophy of Mathematics: Classic and Contemporary Studies

ISBN-13: 9781032022680 / Angielski / Miękka / 2021 / 338 str.

Ahmet Cevik

Opis

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.

Recenzje

"The philosophically minded mathematician will find every penny and every second engaged with this book well spent." - Firdous Ahmad Mala, The Mathematical Intelligencer

Spis treści

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

O autorze

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.