Should a health campaign emphasise the potential gains from compliance (e.g., "If you quit smoking, you'll reduce your risk of lung cancer") or the potential losses from non-compliance (e.g., "If you don't quit smoking, you won't reduce your risk of lung cancer")? A large literature on so-called goal framing, or message framing, assumes that such messages are equivalent, but their persuasiveness may vary, for instance, depending on the perceived risk associated with the recommended behaviour. As no existing hypothesis received conclusive empirical support, we propose a novel theoretical approach. We argue that goal frames must be analysed as arguments interpreted in context. We report an experiment showing the effect of the participants' background beliefs about disabling conditions and alternative causes on the persuasiveness of positive and negative frames recommending detection behaviour.