{"product_id":"9781350277960","title":"Knowledge and the Philosophy of Number What Numbers Are and How They Are Known","description":"\u003ch3\u003eMind, Meaning and Metaphysics\u003c\/h3\u003e\u003ch1\u003eKnowledge and the Philosophy of Number\u003c\/h1\u003e\u003ch2\u003eWhat Numbers Are and How They Are Known\u003c\/h2\u003e\u003ch3\u003eKeith Hossack | Johannes L. Brandl | Christopher Gauker | Max Kölbel | Mark Textor\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eMathematics \/ History \u0026amp; Philosophy\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\u003cp\u003e\u003cb\u003eIf numbers were objects, how could there be human knowledge of number? \u003c\/b\u003eNumbers 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?\u003cbr\u003e\u003cbr\u003eThis 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.\u003cbr\u003e\u003cbr\u003eIn 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 \u003ci\u003ea priori\u003c\/i\u003e 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. \u003cbr\u003e\u003cbr\u003eGiven 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. \u003ci\u003eKnowledge and the Philosophy of Number\u003c\/i\u003e carries out these deductions, arriving at a metaphysics of number that makes room for our \u003ci\u003ea priori\u003c\/i\u003e knowledge of mathematical reality.\u003c\/p\u003e\u003c\/div\u003e\u003cdiv\u003e\n\u003cb\u003eKeith Hossack\u003c\/b\u003e is Reader in Philosophy, Birkbeck College, University of London, UK.\u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e26 August 2021\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003eBloomsbury Academic\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eBloomsbury Academic\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9781350277960\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003ePaperback softback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePage Count: \u003c\/td\u003e\n\u003ctd\u003e216\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eWeight (oz): \u003c\/td\u003e\n\u003ctd\u003e11.04\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Bloomsbury Academic","offers":[{"title":"Default Title","offer_id":51515326922892,"sku":"9781350277960","price":40.5,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/getimage_aecaa0ea-5d31-44ae-a2b5-44fbbb993dff.jpg?v=1784692226","url":"https:\/\/lateknightbooks.com\/products\/9781350277960","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}