An agent trained within a closed system can master any desired capability, as long as the following three conditions hold: (a) it receives sufficiently informative and aligned feedback, (b) its coverage of experience/data is broad enough, and (c) it has sufficient capacity and resource. We justify these conditions and consider what limitations arise from (a) and (b) in closed systems, when assuming that (c) is not a bottleneck. Considering the special case of homoiconic agents with matching input and output spaces (namely, language), we argue that such pure recursive self-improvement, dubbed "Socratic learning", can boost performance vastly beyond what is present in its initial data or initial knowledge, and is only limited by time, as well as gradual misalignment concerns. Furthermore, we propose a constructive framework to implement it, based the notion of language games.