Skip Navigation


The British Journal for the Philosophy of Science Advance Access originally published online on February 5, 2009
The British Journal for the Philosophy of Science 2009 60(2):239-252; doi:10.1093/bjps/axp001
This Article
Right arrow Full Text
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
60/2/239    most recent
axp001v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Linnebo, O.
Right arrow Articles by Uzquiano, G.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author (2009). Published by Oxford University Press. For Permissions, please email: journals.permissions@oxfordjournals.org

Which Abstraction Principles are Acceptable? Some Limitative Results

Øystein Linnebo

Department of Philosophy, University of Bristol, 9 Woodland Rd. Bristol, BS8 1TB, UK Oystein.Linnebo{at}bristol.ac.uk

Gabriel Uzquiano

Pembroke College, University of Oxford, Oxford OX1 1DW, UK gabriel.uzquiano{at}philosophy.ox.ac.uk


  Abstract

Neo-Fregean logicism attempts to base mathematics on abstraction principles. Since not all abstraction principles are acceptable, the neo-Fregeans need an account of which ones are. One of the most promising accounts is in terms of the notion of stability; roughly, that an abstraction principle is acceptable just in case it is satisfiable in all domains of sufficiently large cardinality. We present two counterexamples to stability as a sufficient condition for acceptability and argue that these counterexamples can be avoided only by major departures from the existing neo-Fregean programme.

  1. Introduction
  2. A Simple Counterexample
  3. A Fregean Counterexample
  4. The Argument
    4.1 Defending step 1
    4.2 Defending step 2
    4.3 Defending step 3
    4.4 Defending step 4

  5. Concluding Remarks


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.