Abstract: There exist multiple intellectual affinities between Husserl and Gödel, among which the often-neglected one is their consensus regarding the problem of searching for new axioms for formal systems. Husserl’s manifold theory offers a deep and stratified discussion of the completeness of axiomatic systems by means of the concept of definiteness, including extensional dimensions (syntactic and semantic definiteness) as well as intensional dimensions (objectual and axiomatical definiteness). A comprehensive understanding of Husserl’s manifold theory requires situating it within the framework of his formal ontology. Meanwhile, Gödel’s standpoint on the continuum problem is a mathematized philosophical claim. He shares with Husserl the same modern Platonist worldview of mathematics, an intuition-based constitutive theory of knowledge, and a view of the definite expansion of axiomatic systems. Gödel’s philosophical position permeates mathematical theory by shaping mathematical practice. From the perspective of transcendental phenomenology, Gödel’s program can receive a more complete clarification and justification along the dual dimensions of constitution and construction.

Key Words: Manifold; Definiteness; Continuum hypothesis; New axioms