Mathematized Phenomenology and the Science of Consciousness

In this contribution, we emphasize the relevance of mathematical approaches to the first-person perspective. We briefly discuss why this is necessary and why mathematics plays a special role when it comes to integrating scientific (empirical) and philosophical (theoretical) projects. We also sketch some potential ways that mathematics could be used in phenomenology, based on a selection of four ``phenomenological primitives'' that characterize constitution: intentionality, minimal subjectivity, lifeworld, and time consciousness. We also spell out a minimal topological toymodel and refer to some contemporary approaches using modern mathematics (e.g. category theory). We then discuss how this could be usefully applied to the (neuro)scientific study of consciousness and throughout stress the need to highlight (and formalize) phenomenology's transcendental character.