Description: Knowledge and the Philosophy of Number : What Numbers Are and How They Are Known, Paperback by Hossack, Keith, ISBN 1350277967, ISBN-13 9781350277960, Brand New, Free shipping in the US 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. Th 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 th 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.
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Book Title: Knowledge and the Philosophy of Number : What Numbers Are and How
Number of Pages: 216 Pages
Publication Name: Knowledge and the Philosophy of Number : What Numbers Are and How They Are Known
Language: English
Publisher: Bloomsbury Publishing
Publication Year: 2021
Item Height: 0.5 in
Subject: History & Philosophy, General, Number Theory, Logic
Type: Textbook
Item Weight: 11.1 Oz
Author: Keith Hossack
Subject Area: Mathematics, Philosophy
Item Length: 9.2 in
Item Width: 6.1 in
Series: Mind, Meaning and Metaphysics Ser.
Format: Trade Paperback
