This paper examines Derrida's interpretation of Jean Cavailles's critique of phenomenology in On Logic and the Theory of Science. Derrida's main claim is that Cavailles's arguments, especially the argument based on Godel'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 Cavailles's critique, but can even serve as a philosophical framework for Cavailles's own position. I will argue that Derrida's approach to Cavailles is fruitful, facilitating the exposition of some central Cavaillesian 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 Godel's theorems do not in themselves warrant rejection of static phenomenology. I base this conclusion in part on Godel's own understanding of phenomenology as a philosophical basis for mathematics.