Mancosu offers an original investigation of key notions in mathematics: abstraction and infinity, and their interaction. He gives a historical analysis of the theorizing of definitions by abstraction, and explores a novel approach to measuring the size of infinite sets, showing how this leads to deep mathematical and philosophical problems.

• 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.