Introduction
Educational reflections on the epistemology of mathematics have contributed to clarify several aspects of the conceptual density of mathematical knowledge (Barbin, 2009 ; Bkouche, 1997; Fried, 2009). However, educational reflections have shown limited interest in tackling the ontological question of the nature of knowledge in general, and mathematical knowledge in particular (notable exceptions are Otte [2003] and Freitas et al. [2017]). This limited interest could be attributed to the philosophies that have influenced, often implicitly, reflections on the teaching and learning of mathematics. In fact, the predominant philosophies in our research field have been, usually implicitly, empiricism and rationalism. While the former tends to regard knowledge as a subjective entity, as American constructivism in all its variants does (see, for example, von Glasersfeld, 1995), the latter considers knowledge as teleologically driven by a universal inner reason (Husserl, 1972). Ul...