Table of contents
The Philosophy and Mathematics of Hume’s Principle
The Logic of Abstraction
Abstraction and the Continuum
Basic Law V and Set Theory
About this book
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.
Gottlob 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.
All 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.
- DOI https://doi.org/10.1007/978-1-4020-4265-2
- Copyright Information Springer Science+Business Media B.V. 2007
- Publisher Name Springer, Dordrecht
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-1-4020-4264-5
- Online ISBN 978-1-4020-4265-2
- Series Print ISSN 1566-659X
- Buy this book on publisher's site