Arbitrary reference

Philosophical Studies 158 (3):377-400 (2012)
Abstract
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.
Keywords Reference  Arbitrary  Arbitrary reference  Arbitrary objects  Instantial reasoning  Universal generalisation  Existential instantiation  Natural deduction  Vagueness  Indiscernible  Structuralism  Random  Indefinite
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References found in this work BETA
Paul Benacerraf (1965). What Numbers Could Not Be. Philosophical Review 74 (1):47-73.
Kit Fine (1985). Natural Deduction and Arbitrary Objects. Journal of Philosophical Logic 14 (1):57 - 107.

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Citations of this work BETA
Emanuel Viebahn (2013). Counting Stages. Australasian Journal of Philosophy 91 (2):311-324.
Francesca Boccuni (2013). Plural Logicism. Erkenntnis 78 (5):1051-1067.
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