Mathematical Knowledge, Objects and Applications: Essays in Memory of Mark Steiner

ISBN-13: 9783031216541 / Angielski / Twarda / 2023 / 360 str.

Carl Posy; Yemima Ben-Menahem

Opis

This book provides a survey of a number of the major issues in the philosophy of mathematics, such as ontological questions regarding the nature of mathematical objects, epistemic questions about the acquisition of mathematical knowledge, and the intriguing riddle of the applicability of mathematics to the physical world. Some of these issues go back to the nascent years of mathematics itself, others are just beginning to draw the attention of scholars. In addressing these questions, some of the papers in this volume wrestle with them directly, while others use the writings of philosophers such as Hume and Wittgenstein to approach their problems by way of interpretation and critique. The contributors include prominent philosophers of science and mathematics as well as promising younger scholars. The volume seeks to share the concerns of philosophers of mathematics with a wider audience and will be of interest to historians, mathematicians and philosophers alike.

Spis treści

1. Yemima Ben Menahem and Carl Posy: Introduction:  

2. Andrew Arana:  “Purity and Explanation:  Essentially Linked?”

3. Yemima Ben Menahem:   “Rules, Conventions, and Regularities”

4. Mark Colyvan:  ” On  Mathematical Explanation”

5. Juliet Floyd: “Steiner’s Wittgenstein”

6. Curtis Franks:  "Logic Discovered and Imposed"

7. Guy Hetzroni  “Mathematical Analogies and Applicability in Physics”

8. Aviv Keren: “Learning Cardinals and Ordinals”

9. Saul Kripke:  “Buck Stopping and  Identification of Numbers”

10. Charles Parsons, TBA (in the philosophy of set theory)

11. Carl Posy:  “Platonism and the Proto-Ontology of Mathematics”

12. Stewart Shapiro and Øystein Linnebo: “Potential infinity, Mathematical Explanation and de re Reference to Mathematical Objects”

13. Gila Sher, “Mathematics and Physical Discovery”

14. Orly Shenker:  “Observer Dependent Naturalism”

15. Ruth Weintraub:  “David Hume’s Treatise View  of Geometry” 

O autorze

Carl Posy has published widely in the philosophy of mathematics and in the history of philosophy.   He is the author of Mathematical Intuitionism (Cambridge 2020), and the editor of Kant’s Philosophy of Mathematics: Modern Essays (Kluwer, 1992). He co-edited (with Jack Copeland and Oron Shagrir) Computability: Turing, Gödel, Church and Beyond (MIT, 2013), and (with Ofra Rechter) Kant’s Philosophy of Mathematics, Volume I:  The Critical Philosophy and Its Roots (Cambridge, 2020); and Kant’s Philosophy of Mathematics, Volume II:  Reception and Influence (Cambridge, Forthcoming)

Yemima Ben-Menahem is a philosopher of science, specializing in the philosophy of physics. She is author of Conventionalism (Cambridge University Press, 2006) and Causation in Science (Princeton University Press, 2018. She edited Hilary Putnam (Cambridge University Press 2005) and coedited (with Meir Hemmo) Probability in Physics (Springer, 2012)

Blurb

This book provides a survey of a number of the major issues in the philosophy of mathematics, such as ontological questions regarding the nature of mathematical objects, epistemological questions about the acquisition of mathematical knowledge, and the intriguing riddle of the applicability of mathematics to the physical world.  Some of these issues go back to the nascent years of mathematics itself, others are just beginning to draw the attention of scholars.  In addressing these question, some of the papers in this volume wrestle with them directly, while others use the writings of philosophers such as Hume and Wittgenstein to approach their problems by way of interpretation and critique.  These issues and these approaches lay at the heart of Mark Steiner’s work throughout his career.  They are addressed in the present volume by prominent philosophers of science and of mathematics as well as promising younger scholars.   The volume seeks to share the concerns of philosophers of mathematics and of science with a wider audience and will be of interest to historians, mathematicians and philosophers alike.