Free Delivery Over $100
|
|
|||
|
||||
OverviewIf numbers were objects, how could there be human knowledge of number? Numbers are not physical objects: must we conclude that we have a mysterious power of perceiving the abstract realm? Or should we instead conclude that numbers are fictions? This book argues that numbers are not objects: they are magnitude properties. Properties are not fictions and we certainly have scientific knowledge of them. Much is already known about magnitude properties such as inertial mass and electric charge, and much continues to be discovered. The book says the same is true of numbers. In the theory of magnitudes, the categorial distinction between quantity and individual is of central importance, for magnitudes are properties of quantities, not properties of individuals. Quantity entails divisibility, so the logic of quantity needs mereology, the a priori logic of part and whole. The three species of quantity are pluralities, continua and series, and the book presents three variants of mereology, one for each species of quantity. Given Euclid’s axioms of equality, it is possible without the use of set theory to deduce the axioms of the natural, real and ordinal numbers from the respective mereologies of pluralities, continua and series. Knowledge and the Philosophy of Number carries out these deductions, arriving at a metaphysics of number that makes room for our a priori knowledge of mathematical reality. Full Product DetailsAuthor: Dr Keith Hossack (Birkbeck College, University of London, UK)Publisher: Bloomsbury Publishing PLC Imprint: Bloomsbury Academic Weight: 0.485kg ISBN: 9781350102903ISBN 10: 1350102903 Pages: 216 Publication Date: 20 February 2020 Audience: College/higher education , Tertiary & Higher Education Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsPreface Introduction 1. Properties 2. Frege's Theory of Concepts 3. The Logic of Quantity 4. Mereology 5. The Homomorphism Theorem 6. The Natural Numbers 7. Multiplication 8. Ratio 9. Geometry 10. The Ordinals Notes References IndexReviewsHossack's book revives the ancient view that numbers are magnitudes and thus a special kind of property, which are instantiated in the physical world. This view receives a powerful mathematical and philosophical development and defense. The book is highly recommended to anyone with an interest in metaphysics or the philosophy of mathematics. * Oystein Linnebo, Professor of Philosophy, University of Oslo, Norway * Recommended. Upper-division undergraduates, graduate students, and faculty. * CHOICE * Hossack's book revives the ancient view that numbers are magnitudes and thus a special kind of property, which are instantiated in the physical world. This view receives a powerful mathematical and philosophical development and defense. The book is highly recommended to anyone with an interest in metaphysics or the philosophy of mathematics. * Oystein Linnebo, Professor of Philosophy, University of Oslo, Norway * Author InformationKeith Hossack is Reader in Philosophy, Birkbeck College, University of London, UK. Tab Content 6Author Website:Countries AvailableAll regions |
||||
