Knowledge and the Philosophy of Number: What Numbers Are and How They Are Known (Mind, Meaning and Metaphysics) - Hardcover
Synopsis
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 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.
"synopsis" may belong to another edition of this title.
About the Authors
Keith Hossack is Reader in Philosophy, Birkbeck College, University of London, UK.
Max Kölbel is ICREA Research Professor at the University of Barcelona, Spain.
"About this title" may belong to another edition of this title.
Other Popular Editions of the Same Title
Search results for Knowledge and the Philosophy of Number: What Numbers...
Stock Image
Knowledge and the Philosophy of Number What Numbers Are and How They Are Known
Seller: Michener & Rutledge Booksellers, Inc., Baldwin City, KS, U.S.A.
Seller rating 5 out of 5 stars
Hardcover. Condition: As New. Text clean and tight; no dust jacket; Mind, Meaning And Metaphysics; 8vo 8" - 9" tall; 216 pages. Seller Inventory # 234479
Stock Image
Knowledge and the Philosophy of Number
Published by
Bloomsbury Publishing (UK), 2020
ISBN 10: 1350102903
ISBN 13: 9781350102903
New
Hardcover
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
Seller rating 5 out of 5 stars
HRD. Condition: New. New Book. Shipped from UK. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Seller Inventory # L1-9781350102903
Stock Image
Knowledge and the Philosophy of Number
Published by
Bloomsbury Publishing (UK), 2020
ISBN 10: 1350102903
ISBN 13: 9781350102903
New
Hardcover
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
Seller rating 5 out of 5 stars
HRD. Condition: New. New Book. Delivered from our UK warehouse in 4 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Seller Inventory # L1-9781350102903
Buy New
US$ 146.02
Shipping:
US$ 6.58
From United Kingdom to U.S.A.
Quantity: Over 20 available
Stock Image
Knowledge and the Philosophy of Number: What Numbers Are and How They Are Known (Mind, Meaning and Metaphysics)
Seller: Ria Christie Collections, Uxbridge, United Kingdom
Seller rating 5 out of 5 stars
Condition: New. In. Seller Inventory # ria9781350102903_new
Buy New
US$ 140.57
Shipping:
US$ 15.70
From United Kingdom to U.S.A.
Quantity: Over 20 available
Seller Image
Knowledge and the Philosophy of Number (Hardcover)
Published by
Bloomsbury Publishing PLC, London, 2020
ISBN 10: 1350102903
ISBN 13: 9781350102903
New
Hardcover
Seller: Grand Eagle Retail, Bensenville, IL, U.S.A.
Seller rating 5 out of 5 stars
Hardcover. Condition: new. Hardcover. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9781350102903
Stock Image
Knowledge and the Philosophy of Number: What Numbers Are and How They Are Known
Published by
Bloomsbury Publishing PLC, 2020
ISBN 10: 1350102903
ISBN 13: 9781350102903
New
Hardcover
Seller: THE SAINT BOOKSTORE, Southport, United Kingdom
Seller rating 5 out of 5 stars
Hardback. Condition: New. This item is printed on demand. New copy - Usually dispatched within 5-9 working days 485. Seller Inventory # C9781350102903
Buy New
US$ 171.07
Shipping:
US$ 20.44
From United Kingdom to U.S.A.
Quantity: Over 20 available
Stock Image
Knowledge and the Philosophy of Number (Hardcover)
Published by
Bloomsbury Publishing PLC, London, 2020
ISBN 10: 1350102903
ISBN 13: 9781350102903
New
Hardcover
Seller: CitiRetail, Stevenage, United Kingdom
Seller rating 5 out of 5 stars
Hardcover. Condition: new. Hardcover. 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. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Seller Inventory # 9781350102903
Buy New
US$ 155.22
Shipping:
US$ 48.49
From United Kingdom to U.S.A.
Quantity: 1 available
Seller Image
Knowledge and the Philosophy of Number: What Numbers Are and How They Are Known
Print on DemandSeller: moluna, Greven, Germany
Seller rating 4 out of 5 stars
Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Seller Inventory # 291226206
Buy New
US$ 170.73
Shipping:
US$ 56.44
From Germany to U.S.A.
Quantity: Over 20 available
Stock Image
Knowledge and the Philosophy of Number: What Numbers Are and How They Are Known
Seller: Revaluation Books, Exeter, United Kingdom
Seller rating 5 out of 5 stars
Hardcover. Condition: Brand New. 256 pages. 9.25x6.25x1.00 inches. In Stock. Seller Inventory # x-1350102903
Buy New
US$ 240.57
Shipping:
US$ 13.11
From United Kingdom to U.S.A.
Quantity: 2 available
Seller Image
Knowledge and the Philosophy of Number | What Numbers Are and How They Are Known
Print on DemandSeller: preigu, Osnabrück, Germany
Seller rating 5 out of 5 stars
Buch. Condition: Neu. Knowledge and the Philosophy of Number | What Numbers Are and How They Are Known | Keith Hossack | Buch | Gebunden | Englisch | 2020 | Bloomsbury 3PL | EAN 9781350102903 | Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, 36244 Bad Hersfeld, gpsr[at]libri[dot]de | Anbieter: preigu Print on Demand. Seller Inventory # 129707787