Journal Article

Which Abstraction Principles are Acceptable? Some Limitative Results

Øystein Linnebo and Gabriel Uzquiano

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 60, issue 2, pages 239-252
Published in print June 2009 | ISSN: 0007-0882
Published online February 2009 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/axp001
Which Abstraction Principles are Acceptable? Some Limitative Results

More Like This

Show all results sharing these subjects:

  • Philosophy of Science
  • Science and Mathematics

GO

Show Summary Details

Preview

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.

Introduction

A Simple Counterexample

A Fregean Counterexample

The Argument 4.1

Defending step 1

4.2

Defending step 2

4.3

Defending step 3

4.4

Defending step 4

Concluding Remarks

Journal Article.  5485 words.  Illustrated.

Subjects: Philosophy of Science ; Science and Mathematics

Full text: subscription required

How to subscribe Recommend to my Librarian

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.