ABSTRACT
This chapter expounds and criticizes the dominant epistemological perspective of mathematics. This is the absolutist view that mathematical truth is absolutely certain, that mathematics is the one and perhaps the only realm of certain, unquestionable and objective knowledge. Much is made of the absolutist-fallibilist distinction because, as is shown subsequently, the choice of which of these two philosophical perspectives is adopted is perhaps the most important epistemological factor underlying the teaching of mathematics. Intuitionism represents the most fully formulated constructivist philosophy of mathematics. Two separable claims of intuitionism can be distinguished, which Dummett terms the positive and the negative theses. The absolutist view of mathematical knowledge has been subject to a severe, and in view, irrefutable criticism. Its rejection leads to the acceptance of the opposing fallibilist view of mathematical knowledge. In Quantum Theory, Heisenberg’s Uncertainty Principle means that the notions of precisely determined measurements of position and momentum for particles also has had to be given up.
