ENGLISH

Thomas Aquinas’ Mathematical Realism

By Jean W. Rioux

Book information

Publisher
Palgrave Macmillan
Year
2023
ISBN
3031331273, 9783031331275
Language
english
Format
PDF
Filesize
6 MB (6566665 bytes)
Pages
279\280
Time added
2023-07-01 11:10:15

Description

In this book, philosopher Jean W. Rioux extends accounts of the Aristotelian philosophy of mathematics to what Thomas Aquinas was able to import from Aristotle’s notions of pure and applied mathematics, accompanied by his own original contributions to them. Rioux sets these accounts side-by-side modern and contemporary ones, comparing their strengths and weaknesses. 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

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