Chapter 5: The Analytic/Synthetic Distinction in Kant and Bolzano

No education, no mathematics education in particular without a philosophy and an epistemology. Philosophical reflection, when taken in its broader concerns, rather than as the activities of a specialized group of academics, is essentially concerned with the universality of human being and; therefore, with the relation between the particular and the universal. Plato had been the first to state this in clear terms and he had used mathematics to illustrate the issue epistemologically. As the ideal and essential can only be itself, rather than its opposite, differently from what happens in case of the particular and concrete, we can build up consistent knowledge about the universal, but not about the empirically concrete, which the Sophists have shown to remain always ambiguous. This provides mathematics with a privileged role. Mathematics gives us an example of how to answer a given question by building up a consistent theory (see for example Phaedo).