Husserl began to publish on problems in the philosophy of mathematics and logic soon after he received his doctoral degree in mathematics in 1883 and he continued to publish on them throughout his lifetime. Although much has happened in the foundations of mathematics since the beginning of the twentieth century, many of Husserl's ideas are still relevant to recent issues in the philosophy of mathematics. In this chapter I argue that a number of the views on mathematics that are part of Husserl's transcendental phenomenology are more compelling than current alternative views in the philosophy of mathematics. In particular, I provide an overview of how Husserl's ideas can be used to solve some basic problems in the philosophy of mathematics that arise for (naive) platonism, nominalism, fictionalism, Hilbertian formalism, pragmatism, and conventionalism.

A Précis of Problems in the Philosophy of Mathematics

Many of the basic problems in the philosophy of mathematics center around the positions just mentioned. It will not be possible to discuss these problems in any detail here, but at least some general indications can be given.

A major difficulty for platonism has been to explain how it is possible to have knowledge of immutable, acausal, abstract entities such as numbers, sets, and functions. Once it is argued that these entities are abstract and mind independent there seems to be no way to establish an epistemic link with them that does not involve mysticism.