Abstract
In this paper I argue that to explain and resolve some kinds of disagreement we need to go beyond what logic alone can provide. In particular, following Perelman, I argue that we need to consider how arguments are ascribed different strengths by different audiences, according to how accepting these arguments promotes values favoured by the audience to which they are addressed. I show how we can extend the standard framework for modelling argumentation systems to allow different audiences to be represented. I also show how this formalism can explain how some disputes can be resolved while in others the parties can only agree to differ. I illustrate this by consideration of a legal example. Finally, I make some suggestions as to where these values come from, and how they can be used to explain differences across jurisdictions, and changes in views over time