The limits of the mathematization of the living and the idea of formal morphology of the living world following Husserlian phenomenology.

Through a presentation and a commentary of Husserl's little-known analyses of mathematization in the life sciences and on morphology, this article proposes three goals. First, it aims at establishing the real meaning and results of the critical analyses of the mathematization in natural sciences and of exactness put forth as a standard of scientific knowledge that we read in the Krisis. As a result, it will appear that these analyses belong to the perspective of a project of a formal morphology, understood as an extension of mathesis. It is then to explain why this project only makes sense in the larger framework of the description of the “correlational a priori,” i.e., the theory of constituting subjectivity, experiencing these morphologies, and engaging, theoretically, by induction, in the typification and categorial elaboration of possible explanatory models. After presenting the contours of this project and its achievements, we will conclude with some conjectural proposals concerning the profile of plausible mathematical structures likely to satisfy the minimal algebraic formal conditions for a model of stability and plasticity of the living and allowing to understand and express the dynamic stratification of morphological levels and the various forms of morphogenesis.