Russell’s Leibnizian Concept of Vagueness

The account of vagueness Bertrand Russell provided in his 1923 paper, entitled simply “Vagueness” (see Russell [1923]1997), has been thought by some to be inconsistent. One main objection, raised by Timothy Williamson (1994), is that Russell’s attempt early in the paper to distinguish vagueness from generality is at odds with the definition of vagueness he presents later in the same paper. It is as if, as Williamson puts it, Russell “backslides” from his previous distinction (1994, 60), resulting in a conflation of generality and vagueness that is at best problematic for a rigorous account of the phenomenon of vagueness. In this paper, I will defend Russell from this particular objection. While his 1923 paper may not be as clear at various points as one might hope, I do believe it is possible to construct a single theory of vagueness that can be applied equally well to his earlier and later discussions. Thus, Russell’s view is not ultimately inconsistent. In this paper, I will first present the interpretation of Russell’s concept of vagueness that falls prey to the charge of conflating vagueness and generality. Once the problem is clear, I will present an alternative interpretation, one that arises from certain reflections on G. W. Leibniz’s theory of perception. This Leibnizian interpretation of Russell, I will argue, resolves the apparent contradiction in Russell’s account of vagueness.