rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    non sort: The
    title: Arché Papers on the Mathematics of Abstraction
  name:
    name part: Cook, Roy T.
    role:
      role term: editor.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: ne
    date issued: 2007
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXXVIII, 454 p. online resource.
  abstract: 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.
  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.
  note: edited by Roy T. Cook.
  subject:
    topic: Mathematics
  subject:
    topic: Logic
  subject:
    topic: Philosophy and science
  subject:
    topic: Mathematical logic
  subject:
    topic: Mathematics
  subject:
    topic: Mathematics, general
  subject:
    topic: Philosophy of Science
  subject:
    topic: Logic
  subject:
    topic: Mathematical Logic and Foundations
  classification: QA1-939
  classification: 510
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: The Western Ontario Series in Philosophy of Science, 71
  identifier: 9781402042652
  identifier: http://dx.doi.org/10.1007/978-1-4020-4265-2
  record info:
    record creation date: 100301
    record change date: 20151204150022.0
    record identifier: 978-1-4020-4265-2