Synopses & Reviews
What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem.
Synopsis
What is mathematics about? And how can we have access to the reality it is supposed to describe? The book tells the story of this problem, first raised by Plato, through the views of Aristotle, Proclus, Kant, Frege, Godel, Benacerraf, up to the most recent debate on mathematical platonism."
About the Author
MARCO PANZA is research Professor at the CNRS. He is the author and editor of several books and papers in the domains of history and philosophy of mathematics. Including
Analysis and sinthesis in Mathematics (ed., with M. Otte), 1997;
Isaac Newton, 2003;
Newton et l'origine de l'analyse, 1664-1666, 2005;
Nombres. Eléments de mathématiques pour philosophes, 2007.
ANDREA SERENI is Lecturer at San Raffaele University, Milan. He has been a visiting scholar at Arché Centre at the University of St. Andrews. He has taught courses at the Universities of Modena and Reggio Emilia, Parma, and Bologna. His teaching, research and publications cover philosophy of mathematics, epistemology, and philosophy of language.
Table of Contents
Preface
Terminological Conventions
Introduction
The Origins
From Frege to Gödel (through Hilbert)
Benacerraf's Arguments
Non-conservative Responses to Benacerraf's Dilemma
Conservative Responses to Benacerraf's Dilemma
The Indispensability Argument: Structure and Basic Notions
The Indispensability Argument: The Debate
Conclusion
Notes
References
Index