This paper discusses the origins of two key notions in Foucault's work up to and including The Archaeology of Knowledge. The first of these notions is the notion of "archaeology" itself, a form of historical investigation of knowledge that is distinguished from the mere history of ideas in part by its unearthing what Foucault calls "historical a prioris". Both notions, I argue, are derived from Husserlian phenomenology. But both are modified by Foucault in the light of Jean Cavaillès's critique of Husserl's theory of science. On Husserl's view, we demand that propositions holding of scientific objects be intersubjective and invariant, but this demand conflicts with our immediate experience, which is essentially bound to a subject's perspective. Thus the mathematical and physical sciences must utilise formal languages to fix these truths independently of the thoughts of a particular subject. This necessary procedure leads to the sedimentation of these formal systems: we forget their source in the concrete experiences of individuals, and use them as purely technical means. The technique of reactivating the intentional acts in which sedimented formal systems originated is thus, in Fink's terminology, an archaeological method. Foucault and Cavaillès retain the general outlines of this archaeology of the sciences, but they reject its appeal to conscious acts of meaning, to what Cavaillès calls "the philosophy of consciousness". I conclude by discussing the implicit difficulties in the "linguistic transcendentalism" proposed as an alternative by these French critics of Husserl.