Arbitrary reference

Philosophical Studies 158 (3):377-400 (2012)
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Abstract

Two fundamental rules of reasoning are Universal Generalisation and Existential Instantiation. Applications of these rules involve stipulations 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 : 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, and we suggest that AR can also figure in offering new solutions to a range of difficult philosophical puzzles

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Author Profiles

Ofra Magidor
Oxford University
Wylie Breckenridge
Charles Sturt University

Citations of this work

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Vagueness.Timothy Williamson - 1996 - New York: Routledge.
Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
The reference book.John Hawthorne & David Manley - 2012 - Oxford: Oxford University Press. Edited by David Manley.
What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Précis of Vagueness.Timothy Williamson - 1997 - Philosophy and Phenomenological Research 57 (4):921-928.

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