This paper introduces a new kind of explanation that we describe as ‘purely theoretical’. We first present an example, E, of what we take to be a case of purely theoretical explanation. We then show that the explanation we have in mind does not fit neatly into any of the existing categories of explanation. We take this to give us prima facie motivation for thinking that purely theoretical explanation is a distinctive kind of explanation. We then argue that it can (...) earn its keep via application to two existing literatures: the literature on how we explain the truth of true negative existential propositions and the literature on how we explain the truth of true propositions about the past. We reply to some possible concerns regarding the introduction of purely theoretical explanations. We conclude that there is nothing obviously wrong with them and explore the ramifications for particular debates in metaphysics. (shrink)