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
Mancosu's book is valuable for its original insights into abstraction principles and its exceptionally ... Read morescholarly presentation of the history of both abstraction and infinity. His facility with the history of mathematics is unparalleled and this work is rich in sources, often in original translations of German, Latin, or Italian that are otherwise unavailable in English.
Paolo Mancosu, MathSciNet
Paolo Mancosu's Abstraction and Infinity expertly straddles the history and philosophy of mathematics. ... Mancosu's work is well written and has been well received by those involved with neo-logicism. But it also offers readers not engaged in such debates an opportunity to reflect on the fact that of two intuitively true principles for comparing finite collections (one-to-one correspondence and part-whole inclusion), the historic choice of equinumerosity by Cantor for investigating infinite collections was and is not as cut-and-dried as some believe. And, of course, the book provides a valuable scholarly account of the history of definition by abstraction, the use of equivalence relations, and notions of infinity.
Calvin Jongsma, Mathematical Association of America Reviews
This is a very rich and rewarding book. It provides not merely a much-needed, detailed account of the history of so called definitions by abstraction or abstraction principles, but also advances the current philosophical debate about the foundational status of such principles. These themes are presented in a beautifully clear prose which makes this book, quite simply, a joy to read
not something that is easily accomplished by a book in the history and philosophy of mathematics ... I highly recommend Mancosu's book to philosophers and mathematicians interested in the philosophy or the history of mathematics and logic. ... 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.
Notre Dame Philosophical Reviews
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