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Abstraction and Infinity

Format: Academic Paperback
Media: Paperback
PublisherCode: 9780198822684
Publisher: OUP Oxford

Paolo Mancosu provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. A familiar way of introducing concepts in mathematics rests on so-called definitions by abstraction. Hume's Principle introduces the concept of number by stating that two concepts have the same number if and only if the objects falling under each one of them can be put in one-one correspondence. This principle is at the core of neo-logicism. In the first two chapters of the book, Mancosu provides a historical analysis of the mathematical uses and foundational discussion of definitions by abstraction up to Frege, Peano, and Russell. In the second part of the book, Mancosu shows that unconventional assignments of numbers to infinite sets offer alternatives to Hume's Principle and can be exploited to provide surprisingly novel perspectives on neo-logicism.

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