Arbitrary reference

John Breckenridge, O. Magidor

    Research output: Contribution to journalArticlepeer-review

    40 Citations (Scopus)
    5 Downloads (Pure)


    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.
    Original languageEnglish
    Pages (from-to)377-400
    Number of pages24
    JournalPhilosophical Studies
    Issue number3
    Publication statusPublished - Apr 2012


    Dive into the research topics of 'Arbitrary reference'. Together they form a unique fingerprint.

    Cite this