Our aim in this article is to take the full measure of the formula cited as an epigraph and, through it, to reflect on the problem of the relation between philosophy and mathematics in the work of Jean Cavaillès. In particular, the question will be how to interpret the phrase “by means of mathematics” that appears in this formula. Does this mean that mathematics properly constitutes, for Cavaillès, the framework of expression of thought, or, as we will argue here, that it provides a privileged expression of thought—more “speaking,” though not exclusive?

To approach this problem, we bring to light a double danger: either the philosophical is effaced within the mathematical, or, conversely, the mathematical is subjected to external philosophical norms. The difficulty then consists in situating a theory of science that belongs to the scientific movement while remaining distinct from it. Cavaillès proposes to understand such a theory as an “auto-illumination” of the scientific movement, through which it reveals its own necessity. Mathematics thus appears as an autonomous becoming, governed by necessary sequences, irreducible to any constitutive dependence on the real. It does not coincide with thought, but constitutes its most privileged expression.

Against Ludwig Wittgenstein, Cavaillès maintains the possibility of a theoretical discourse capable of revealing the structure of science. This structure manifests itself in processes of paradigm and thematization, which express the internal dynamics of these sequences. The reference to Baruch Spinoza allows one to conceive this autonomy as a necessary order of ideas. Philosophy thus follows the mathematical movement in order to bring out its necessity, without ever substituting itself for it.