واقع گرایی ریاضی توماس آکویناس [کتاب انگلیسی] | کتابخانه مجازی الفبا

Table of contents :
Preface
Contents
Chapter 1: Introduction
Bibliography
Part I: Mathematical Realism in Plato and Aristotle
Chapter 2: Plato on Mathematics and the Mathematicals
Platonism as Mathematical Realism
The Justification for, and Place of, Plato’s Mathematicals
Why Is Platonism Attractive to Some Philosophies of Mathematics?
Bibliography
Chapter 3: Aristotle on the Objects of Mathematics
Where Do the Mathematicals Exist?
Idealizing the Mathematicals
How Do the Mathematicals Exist Materially?
Realist or Non-Realist?
Bibliography
Chapter 4: Aristotle on the Speculative and Middle Sciences
The Practical and Speculative Sciences
Necessary and Sufficient Conditions for Episteme
Pure Mathematics Is Episteme
The Middle Sciences
The Pure Sciences Are Prior to the Applied
Bibliography
Chapter 5: Aristotle on Abstraction and Intelligible Matter
Formal Abstraction: A Middle Way Between Platonism and Nominalism
Intelligible Matter
Intelligible Matter and the Reality of Mathematicals
Intelligible Matter and Access
Bibliography
Part II: Mathematical Realism in Aquinas
Chapter 6: Objects, Freedom, and Art
Mathematics and Existence
Mathematical Ideals
Mathematical Freedom
Mathematical Legitimacy
Mathematical Illegitimacy
The Art of the Fiction
Bibliography
Chapter 7: To Be Virtually
Virtual Reality
Intuitionism and the Excluded Middle
Remote and Proximate Objects
Bibliography
Chapter 8: Mathematics and the Liberal Arts
Episteme and Art
The Mathematical Arts
Bibliography
Chapter 9: The Place of the Imagination
Imagination: A Thomistic Development
What About Mathematics?
Aristotelian Hints
The Representative and Creative Imagination
Imagination and the Truth
Bibliography
Part III: Modern Philosophies of Mathematics
Chapter 10: Going Beyond
Numerical Extensions
Geometrical Extensions
Non-Euclidean Geometries
Bibliography
Chapter 11: Cantor, Finitism, and Twentieth-Century Controversies
Finitism and Infinitism
The Big Three
Bibliography
Chapter 12: Mathematical Realism and Anti-Realism
The Controversy
Anti-Realisms
Realisms
Bibliography
Chapter 13: Modern Aristotelian and Thomistic Accounts
The Aristotelians
The Thomists
Bibliography
Part IV: Conclusion
Chapter 14: Mathematics Is a Mixed Bag
Bibliography
Index