A key area in the research agenda of modelling argumentation is to accurately model argumentation on the social web. In this paper we propose additional extensions to our ontology for argumentation on the social web (which integrates elements of the Argument Interchange Format and the Semantically Interlinked Online Communities project) for the purposes of modelling social and rhetorical tactics used in eristic or irrational arguments. We then present a review of these extensions from a panel of experts in the fields of argumentation modelling, web science, philosophy and open and linked data and discuss the value of modelling social argument, the challenges faced to create usable and accurate models and the completeness, clarity and consistency of our proposed additions.