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The British Journal for the Philosophy of Science Advance Access published online on February 5, 2009
The British Journal for the Philosophy of Science, doi:10.1093/bjps/axp001
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© 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 and Gabriel Uzquiano

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


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