In this lecture and the next, I will discuss some approaches to plurality, in particular, the approaches by Remko Scha, Godehard Link, and myself. (Other proposals, like Craige Roberts’, will be discussed in later lectures.) For reasons of comparison (and simplicity), I will reformulate the set theoretic proposals of Scha and myself in terms of lattice structures. I will start, then, by defining the plurality structures that I will use in formulating these proposals. I will be rather succinct here. Extensive exposition of these structures can be found in Landman 1991.