ABSTRACTWe discuss the thesis of universality of geometric notions and offer critical reflections on the concept of “natural geometry” employed by Spelke and others. Promoting interdisciplinary wor...

We argue against the claim that the employment of diagrams in Euclidean geometry gives rise to gaps in the proofs. First, we argue that it is a mistake to evaluate its merits through the lenses of Hilbert’s formal reconstruction. Second, we elucidate the abilities employed in diagram-based inferences in the Elements and show that diagrams are mathematically reputable tools. Finally, we complement our analysis with a review of recent experimental results purporting to show that, not only is the Euclidean diagram-based (...) practice strictly regimented, it is rooted in cognitive abilities that are universally shared. (shrink)

Review of: José Ferreirós. 2016. Mathematical knowledge and the interplay of practices. Princeton: Princeton University Press.