Domain dependence is an issue that most researchers in corpus-based computational linguistics have faced at one time or another. With this paper we describe a method to perform sentiment polarity classification across domains that utilises Argumentation. We train standard supervised classifiers on a corpus and then attempt to classify instances from a separate corpus, whose contents are concerned with different domains (e.g. sentences from film reviews vs. Tweets). As expected the classifiers perform poorly and we improve upon the use of a simple classifier for out-of-domain classification by taking class labels suggested by classifiers and arguing about their validity. Whenever we can find enough arguments suggesting a mistake has been made by the classifier we change the class label according to what the arguments tell us. By arguing about class labels we are able to improve F1 measures by as much as 14 points, with an average improvement of F1 = 7.33 across all experiments.