The idea that smallpox could be eradicated was not necessarily the ultimate aim when inoculation was introduced in Europe in the 1720s. This potentiality was not clearly articulated as an aim until the end of the eighteenth century. This article argues that during most of the eighteenth century, the main aim of inoculation was to lead people as safely as possible through what was regarded as an unavoidable disease. Inoculation became safer, simpler and less expensive from the 1760s, but the changing ideas about its potentiality had more complex roots. A new understanding was produced through an interaction between inoculation practice, more general medical theory and developments within probabilistic thinking and political arithmetic. The first part of the article explores how smallpox inoculation was incorporated into existing medical thinking based on traditional humoral pathology. Inoculation was a new technology, but as it was perceived in the early eighteenth century, the innovation did not first and foremost concern the medical principles of the treatment. The second part of the article investigates arguments about why and when to inoculate: what kind of remedy was inoculation for eighteenth-century agents? The article concludes with a discussion on changes emerging towards the end of the century, and relates them to developments during the preceding decades rather than seeing them as inspired precursors of events and ideas to come.