{"product_id":"the-arche-papers-on-the-mathematics-of-abstraction-9789048170906","title":"The Arché Papers on the Mathematics of Abstraction","description":"\u003cp\u003e • Author(s): Roy T. Cook\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Philosophy \u0026amp; Social Aspects\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eGottlob Frege's original logicist project was, in effect, refuted by Russell's paradox. Crispin Wright has recently revived Frege's enterprise, however, providing a philosophical and technical framework within which a reconstruction of arithmetic is possible. While the Neo-Fregean project has recieved extensive attention and discussion, the present volume is unique in presenting a thorough going examination of the mathematical aspects of the neo-logicist project (and the particular philosophical issues arising from these technical concerns). Attention is focused on extending the Neo-Fregean treatment to all of mathematics, with the reconstruction of real analysis from various cut - or cauchy-sequence-related abstraction principles and the reconstruction of set theory from various restricted versions of Basic Law V as case studies. As a result, the volume provides a test of the scope and limits of the neo-logicist project, detailing what has been accomplished and outlining the desiderata still outstanding.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eAll papers in the anthology have their origins in presentations at Arché events, thus providing a volume that is both a survey of the cutting edge in research on the technical aspects of abstraction and a catalogue of the work in this area that has been supported in various ways by Arché. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45277099557015,"sku":"9789048170906","price":13221.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9789048170906.webp?v=1769287498","url":"https:\/\/atlanticbooks.com\/products\/the-arche-papers-on-the-mathematics-of-abstraction-9789048170906","provider":"Atlantic Books","version":"1.0","type":"link"}