ABSTRACT
This chapter offers an overview of phenomenological reflections on the foundations of formal mathematics during the 1920s, and of the philosophical discussions these reflections triggered. Among the main protagonists of these discussions, some were mathematicians that were interested in phenomenology such as Hermann Weyl. Mathematics, as Husserl conceives it, is an a priori science, not an empirical science; for mathematical propositions are not about either facts or factual beings. The chapter considers Hilbert’s axiomatic method as it was presented at the Copenhagen and Hamburg 1921 conferences that were published in 1922 under the title Neubegrundung der Mathematik. In his article “From Husserl to Hilbert”, whose purpose is to introduce readers with a science background to phenomenology and to its method, starting with the example of the phenomenological analysis of axiomatized arithmetic, Dietrich Mahnke endeavors to elucidate, from the point of view of the theory of knowledge, the meaning of the axiomatic method and of its objects.
