Russell and Fine on variable objects

In the first half of the 1980s, British philosopher Kit Fine developed a metaphysical theory of arbitrary objects in his book entitled ‘Reasoning with arbitrary objects’ (1985). In Section 29.2 of the article under consideration, Horsten and Ito provide a concise overview of this theory. The core thesis of Fine’s theory of arbitrary objects, the authors tell us, is that alongside specific objects, there are arbitrary objects. Arbitrary objects differ metaphysically from specific objects. Each arbitrary object is associated with a value range. There is a sense in which an arbitrary object can take specific objects as its value. Fine refers to this principle as the principle of generic attribution. The primary aim of this article is to compare Fine’s theory of arbitrary objects with the theory of variables that Russell formulated in his ‘Principles of Mathematics’ (1903). The authors argue that Russell’s early theory of variables can be seen as anticipating Fine’s theory of arbitrary objects.