Philosophical Studies

, Volume 158, Issue 3, pp 377–400 | Cite as

Arbitrary reference

  • Wylie Breckenridge
  • Ofra Magidor


Two fundamental rules of reasoning are Universal Generalisation and Existential Instantiation. Applications of these rules involve stipulations (even if only implicitly) such as ‘Let n be an arbitrary number’ or ‘Let John be an arbitrary Frenchman’. Yet the semantics underlying such stipulations are far from clear. What, for example, does ‘n’ refer to following the stipulation that n be an arbitrary number? In this paper, we argue that ‘n’ refers to a number—an ordinary, particular number such as 58 or 2,345,043. Which one? We do not and cannot know, because the reference of ‘n’ is fixed arbitrarily. Underlying this proposal is a more general thesis:

Arbitrary Reference (AR): It is possible to fix the reference of an expression arbitrarily. When we do so, the expression receives its ordinary kind of semantic-value, though we do not and cannot know which value in particular it receives.

Our aim in this paper is defend AR. In particular, we argue that AR can be used to provide an account of instantial reasoning (one that is better than the prominent alternatives), and we suggest that AR can also figure in offering new solutions to a range of difficult philosophical puzzles.


Reference Arbitrary Arbitrary reference Arbitrary objects Instantial reasoning Universal generalisation Existential instantiation Natural deduction Vagueness Indiscernible Structuralism Random Indefinite 



We are grateful to audiences at Cornell University, CSMN Oslo, Macquarie University, and the University of Oxford, as well as to Ross Cameron, John Hawthorne, Stephen Kearns, Jeff King, Vann McGee, Moritz Schulz, Stewart Shapiro, Nick Smith, and Robbie Williams for helpful discussions.


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Balliol CollegeUniversity of OxfordOxfordUK
  2. 2.School of Humanities and Social SciencesCharles Sturt UniversityWagga WaggaAustralia

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