ABSTRACT
This conclusion presents some closing thoughts on the concepts covered in the preceding chapters of this book. The book shows that, in order to establish a more general representational system of the kind required by Euclidean geometry, the inherent limits of the core systems should be overcome through the kind of individual cognitive development that is facilitated by using language involving spatial expressions and other cultural inventions by children. It also shows that elucidating the problem requires recursion not only to everyday, natural language, but also to the more specific geometric cognitive artifacts that shaped these epistemic virtues in ancient Greece. The book argues that the uniquely human form of geometric cognition that brought about Euclidean geometry emerged within a specific cognitive niche that enhanced our “hardwired” cognitive capacities. Compared to the neural foundations of number processing, knowledge about the “geometric brain” is still relatively scarce.
