This paper introduces a new approach to the study of Paleolithic minds. It is developed on the basis of the phenomenological concept of intentionality: the mind's central characteristic of being about or directed at something. In phenomenology, the world is considered not qua fact, but qua appearance, as a correlate of the mind's intentional activity. Both world-appearance and the mind's directedness are further considered from a first-person viewpoint, and in a scaffolding fashion, with more complex acts disclosing new types of objects or aspects of them. This paper develops a framework for applying intentional analysis to minds of the past. This way, the subjective “world-having” of past subjects can be systematically reconstructed in a manner consistent with the empirical data available. This discloses a new field of inquiry that thus far has not been clearly grasped, even though the questions belonging to it are everywhere recognized as being of the greatest importance to the discipline. The intentional analysis of the scaffolding of acts and what they disclose can help to clarify essential concepts in cognitive archaeological debates, and to better understand the evolution of the hominin mind.