Mathesis Universalis and Husserl’s Phenomenology

Axiomathes - The paper’s central theme is the link between phenomenology and the notion of the mathesis universalis, a link articulated by Husserl in the third volume of the Ideas: “My...     

Derrida and Cavaillès: Mathematics and the Limits of Phenomenology

Abstract

This paper examines Derrida’s interpretation of Jean Cavaillès’s critique of phenomenology in On Logic and the Theory of Science. Derrida’s main claim is that Cavaillès’s arguments, especially the argument based on Gödel’s incompleteness theorems, need not lead to a total rejection of Husserl’s phenomenology, but only its static version. Genetic phenomenology, on the other hand, not only is not undermined by Cavaillès’s critique, but can even serve as a philosophical framework for Cavaillès’s own position. I will argue that Derrida’s approach to Cavaillès is fruitful, facilitating the exposition of some central Cavaillèsian ideas, including the notion of dialectics. Nevertheless, it is important to evaluate Derrida’s own arguments against static phenomenology. I undertake such an assessment in the last section of the paper, showing that Gödel’s theorems do not in themselves warrant rejection of static phenomenology. I base this conclusion in part on Gödel’s own understanding of phenomenology as a philosophical basis for mathematics.