Abstract

The present chapter is organised as follows. First, the unity problem will be presented as it struck Bertrand Russell in 1903. Russell’s articulation of the problem is a useful and traditional starting place. Second, it will be argued that there are in fact two unity problems. The first is what I call the _interpretive problem,_ which bears on how we can compositionally describe what a given unity means. This problem presupposes that there are unities around; the problem is how to specify their content in the appropriate way. Although historically deep, the basic problem here is resolvable in a fairly straightforward way. The second unity problem I call the _combinatorial problem_. This problem does not presuppose that there are unities, but asks how there can be unities at all, or, as it is often put, what’s the difference between a sentence and a list. The remainder of the present chapter and the next one will argue that none of a range of entertained solutions to the combinatorial problem is satisfactory. The arguments to be presented will be based upon three desiderata on an adequate solution. Chapter 5 will attempt something like a solution that meets the three desiderata, and chapters 6 and 7 will clarify and defend the solution.