This provides the basis for a social constructivist philosophy of mathematics. However, if the theory is accepted tentatively, it is possible to indicate how it addresses the two problems described above. One problem is to account for 'the unreasonable effectiveness of mathematics' in describing the world via the theories of science. First of all, the concepts of mathematics are derived by abstraction from direct experience of the physical world, from the generalisation and reflective abstraction of previously constructed concepts, by negotiating meanings with others during discourse, or by some combination of these means. Thus mathematics is a branch of knowledge which is indissolubly connected with other knowledge, through the web of language.
Language enables the formulation of theories about social situations and physical reality.
Dialogue with other persons and interactions with the physical world play a key role in refining these theories, which consequently are continually being revised to improve their 'fit'. As a part of the web of language, mathematics thus maintains contact with the theories describing social and physical reality, and hence indirectly, with the physical world. The 'fit' of mathematical structures in areas beyond mathematics is continuously being tested, and mathematics is evolving to provide the patterns and solve the tensions that arise from this modelling enterprise. Thus, 'the unreasonable effectiveness of mathematics' is no miracle of coincidence. It is built in.