The Arché Papers on the Mathematics of Abstraction

• Corporate Author: SpringerLink (Online service)
• Other Authors: Cook, Roy T. (Editor)
• Format: Electronic eBook
• Language: English
• Published: Dordrecht : Springer Netherlands, 2007.
• Series: The Western Ontario Series in Philosophy of Science, 71
• Subjects: Mathematics.; Logic.; Philosophy and science.; Mathematical logic.; Mathematics, general.; Philosophy of Science.; Mathematical Logic and Foundations.

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...

Table of Contents:

• The Philosophy and Mathematics of Hume’s Principle
• Is Hume’s Principle Analytic?
• Is Hume’s Principle Analytic?
• Frege, Neo-Logicism and Applied Mathematics
• Finitude and Hume’s Principle
• On Finite Hume
• Could Nothing Matter?
• On the Philosophical Interest of Frege Arithmetic
• The Logic of Abstraction
• “Neo-Logicist” Logic is not Epistemically Innocent
• Aristotelian Logic, Axioms, and Abstraction
• Frege’s Unofficial Arithmetic
• Abstraction and the Continuum
• Reals by Abstraction
• The State of the Economy: Neo-Logicism and Inflation
• Frege Meets Dedekind: A Neo-Logicist Treatment of Real Analysis
• Neo-Fregean Foundations for Real Analysis: Some Reflections on Frege’s Constraint
• Basic Law V and Set Theory
• New V, ZF, and Abstraction
• Well- and Non-Well-Founded Fregean Extensions
• Abstraction & Set Theory
• Prolegomenon to Any Future Neo-Logicist Set Theory: Abstraction and Indefinite Extensibility
• Neo-Fregeanism: An Embarrassment of Riches
• Iteration one More Time.