Book Details

The Arché Papers on the Mathematics of Abstraction

Publication year: 2007

ISBN: 978-1-4020-4265-2

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This 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. 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.


Subject: Humanities, Social Science and Law, Abstraction, Arithmetic, Gottlob Frege, Philosophy of mathematics, Real Analysis, formal logic, logic, philosophy of science, set theory, symbolic logic