Introduction
1: The mathematical practice of definitions by abstraction from
Euclid to Frege (and beyond)
2: The logical and philosophical reflection on definitions by
abstraction: From Frege to the Peano school and Russell
3: Measuring the size of infnite collections of natural numbers:
Was Cantor's theory of infinite number inevitable?
4: In good company? On Hume's Principle and the assignment of
numbers to infinite concepts
Paolo Mancosu is Willis S. and Marion Slusser Professor of
Philosophy at the University of California at Berkeley. He is the
author of numerous articles and books in logic and philosophy of
mathematics. He is also the author of Inside the Zhivago Storm: The
editorial adventures of Pasternak's masterpiece (Feltrinelli,
Milan, 2013). During his career he has taught at Stanford, Oxford,
and Yale. He has been a fellow of the Humboldt Stiftung, the
Wissenschaftskolleg zu Berlin, the Institute for Advanced Study in
Princeton, and the Institut d'Études Avancées in Paris. He has
received grants from the Guggenheim Foundation, the NSF, and the
CNRS.
Mancosu's book is packed with new ideas, novel perspectives, and
important insights, offering the reader a thorough and exciting
examination.... The book should be required reading for anyone
interested in the history and foundations of mathematics.
*Ray T. Cook and Michael Calasso, Philosophia Mathematica*
'I highly recommend Mancosu's book to philosophers and
mathematicians interested in the philosophy or the history of
mathematics and logic. It is rich in historical commentary and
philosophical ideas. Mancosu not only proves to be one of the great
detectives of the history of mathematical practice, but shows us
how an historical approach to mathematical practice can, and in
this case, does successfully move forward our current debates in
the philosophy of mathematics.'
*Philip A. Ebert, Notre Dame Philosophical Reviews*
'It is an absolutely first-rate piece of work, both of scholarship
and philosophy, which no one seriously interested in definition by
abstraction, in Frege's work on the foundations of arithmetic, or
in the neo-Fregean project, can afford not to study.'
*Bob Hale, Journal of Philosophy*
'Mancosu's book is packed with new ideas, novel perspectives, and
important insights, offering the reader a thorough and exciting
examination of abstraction as a methodology that is not limited to
a contemporary position in the philosophy of mathematics, but
instead has been, and continues to be, a central component of
mathematical methodology.'
*Roy Cook & Michael Calasso, Philosophia Mathematica*
'The book is a pleasure to read.'
*Roman Kossak, Mathematical Intelligencer*
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