Main Questions

Epistemology is concerned with one main question: What is knowledge?

From this question, many other questions can be derived: How is knowledge acquired? What are the parts played by action, by perception, by language and symbolism in the development and the functioning of knowledge? What is the relationship between routinized knowledge and problem solving? And so forth.

There are also epistemological questions that are specific to mathematics: What kind of objects is mathematics all about? Are there different kinds? What is the relationship of mathematics to other sciences and to other fields of human experience? In what sense is mathematics both a set of tools and a set of objects?

To many researchers such questions appear philosophical, nonempirical, and possibly useless. But it is easy to trace implicit epistemologies in researchers' work and in the way teachers teach. Therefore it is wise to try to clarify, as much as possible, the main epistemological issues that can be raised and state explicitly our own standpoints. For instance, some teachers think that mathematics is timeless truths, waiting to be discovered like an unknown country; others think that mathematics can be completely reinvented by students. An important epistemological debate concerns the part of ordinary experience and the part of physics and other disciplines in the meaning of mathematical concepts; another concerns the part of symbolism and formalism.