In recent years, a trend in AI research has started to pursue human-level, general artificial intelli-gence (AGI). Although the AGI framework is characterised by different viewpoints on what intelligence is and how to implement it in artificial systems, it conceptualises intelligence as flexible, general-purposed, and capable of self-adapting to different contexts and tasks. Two important ques-tions remain open: a) should AGI projects simu-late the biological, neural, and cognitive mecha-nisms realising the human intelligent behaviour? and b) what is the relationship, if any, between the concept of general intelligence adopted by AGI and that adopted by psychometricians, i.e., the g factor? In this paper, we address these ques-tions and invite researchers in AI to open a dis-cussion on the theoretical conceptions and practi-cal purposes of the AGI approach