D. The Divisions of Knowledge
A key tenet of social constructivism, following Lakatos, is that mathematical
knowledge is quasi-empirical. This leads to the rejection of the categorical
distinction between a priori knowledge of mathematics, and empirical knowledge.
Other philosophers have also rejected this distinction, most notably Duhem and
Quine (1951), who hold that because the assertions of mathematics and science are
all part of a continuous body of knowledge, the distinction between them is one of
degree, and not of kind or category. White (1950) and Wittgenstein (1953) also reject
the absoluteness of this distinction, and a growing number of other philosophers also
reject the water-tight division between knowledge and its empirical applications
(Ryle, 1949; Sneed, 1971; Jahnke).