There are a number of frameworks for modelling argumentation in logic. They incorporate formal representation of individual arguments and techniques for comparing conflicting arguments. In these frameworks, if there are a number of arguments for and against a particular conclusion, an aggregation function determines whether the conclusion is taken to hold. We propose a generalization of these frameworks. In particular, this new framework makes it possible to define aggregation functions that are sensitive to the number of arguments for or against (in most other frameworks, aggregation functions just consider the existence of arguments for and against). In this paper, we explore this framework (based on classical logic) in which an argument is a pair where the first item in the pair is a minimal consistent set of formulae that proves the second item (which is a formula).