The main goal of argumentation mining is to analyze argumentative structures within an argument-rich document, and reason about their composition. Recently, there is also interest in the task of simply detecting claims (sometimes called conclusion) in general documents. In this work we ask how this set of detected claims can be augmented further, by adding to it the negation of each detected claim. This presents two NLP problems: how to automatically negate a claim, and when such a negated claim can plausibly be used. We present first steps into solving both these problems, using a rule-based approach for the former and a statistical one towards the latter.