Knowledge and the Philosophy of Number: What Numbers Are and How They Are Known

Description: Knowledge and the Philosophy of Number by Dr Keith Hossack If 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 Euclids 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Author Biography Keith Hossack is Reader in Philosophy, Birkbeck College, University of London, UK. Table of Contents PrefaceIntroduction1. Properties2. Freges Theory of Concepts3. The Logic of Quantity4. Mereology5. The Homomorphism Theorem6. The Natural Numbers7. Multiplication8. Ratio9. Geometry10. The OrdinalsNotesReferencesIndex Review Recommended. Upper-division undergraduates, graduate students, and faculty. * CHOICE *Hossacks 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. * Øystein Linnebo, Professor of Philosophy, University of Oslo, Norway * Promotional Argues that numbers are properties, not objects, and are therefore knowable. Review Quote "Recommended. Upper-division undergraduates, graduate students, and faculty." - CHOICE "Hossacks 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." -- Promotional "Headline" Argues that numbers are properties, not objects, and are therefore knowable. Feature Nearly half the chapters include an appendix offer further explanation of a topic and relevant theorems. Details ISBN1350102903 Year 2020 ISBN-10 1350102903 ISBN-13 9781350102903 Format Hardcover Publication Date 2020-02-20 Pages 216 Imprint Bloomsbury Academic Place of Publication London Country of Publication United Kingdom DEWEY 512.7 Short Title Knowledge and the Philosophy of Number Language English Author Dr Keith Hossack UK Release Date 2020-02-20 NZ Release Date 2020-02-20 Subtitle What Numbers Are and How They Are Known Publisher Bloomsbury Publishing PLC Series Mind, Meaning and Metaphysics Audience Tertiary & Higher Education AU Release Date 2020-02-19 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:140207361;

Price: 351.54 AUD

Location: Melbourne

End Time: 2024-11-25T03:07:17.000Z

Shipping Cost: 0 AUD