ABSTRACT
This chapter faces a difficult task: that of showing the relationship between subjective and objective knowledge of mathematics in social constructivism. The task is difficult for a number of reasons. It skirts the edge of psychologism, and it needs to conjoin two different languages, theories and modes of thought that apply to two different realms, the subjective and the objective. Beyond this, the epistemology underpinning social constructivism is quite slippery to grasp, since it is claimed that there is no realm where a determinate entity ‘knowledge’ basks in tranquillity. Knowledge, perhaps analogous to consciousness, is seen as an immensely complex and ultimately irreducible process of humankind dependent on the contributions of a myriad of centres of activity, but also transcending them. Science fiction authors (Stapledon, 1937) and mystical philosophers (Chardin, 1966) have groped for a vision of how the consciousnesses of individual human beings can meld into a greater whole. But these provide too simplistic a vision to account for knowledge and culture as dynamic, cooperative dances uniting millions of thinking and acting but separate human beings. The seduction of idealism is great: to say that knowledge exists somewhere in an ultimate form, possibly growing and changing, but that all our representations of knowledge are but imperfect reflections. The pull to view human knowledge attempts as parts of a convergent sequence that tends to a limit in another realm, is almost irresistible.
