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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