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Published online by Cambridge University Press: 24 May 2019
In this chapter I introduce the notion of arbitrary object and give an initial discussion of it. I take puzzles surrounding the notion of arbitrary object as key questions that should motivate and inspire the construction of a metaphysical theory of arbitrary objects. The theory that I propose bears resemblance to Kit Fine's theory of arbitrary objects. Moreover, key elements of the theory of arbitrary objects can already be found in the theory of variables in Russell's \emph{Principles of Mathematics}.
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