Here’s a great talk by philosopher of cognitive science Mike Wheeler entitled Science Friction: Phenomenology, Naturalism and Cognitive Science.
Wheeler’s basic claim (if I understand him) is that we can reconcile Heidegger’s historicized transcendental with naturalism by employing a McDowellian distinction between constitutive and enabling explanations. Phenomenology and philosophy give us constitutive explanations that describe the structural conditions of possibility of phenomena. Science can provide enabling accounts of the mechanisms required to generate these phenomena.
However, yoking these together within a naturalistic cognitive science requires a twist in the notion of the transcendental. Wheeler argues that even if science has transcendental preconditions these are not and need not be explicitly referred to in the regional ontologies of theories in the special sciences. This anti-foundationalist position receives its imprimatur in Division 1 of Being and Time where Heidegger discusses the relationship between fundamental ontology and the social sciences:
Since the positive science neither ‘can’ nor should wait for the ontological labours of philosophy to be done, the further course of research will not take the form of an ‘advance’ but will be accomplished by recapitulating what has already been ontically discovered, and by purifying it in a way that is ontologically more transparent (Heidegger 1962, p. 76)
The standard assumption made by all anti-naturalists is that because science presupposes transcendental X (substitute your preferred transcendental invariant here), X must be science-proof because any naturalistic explanation of X will have to presuppose X. Thus X will always precede any scientific theory in the order of justification.
However, the disconnect between the local ontologies of special sciences and their transcendental conditions means scientific progress does not require correlative progress in fundamental ontology or other transcendental enterprises. So enabling explanations of putative transcendental X’s don’t presuppose X’s in the way that the anti-naturalist argument requires
By the same token, although science does not directly provide constitutive explanation of transcendental foundations it can provide ground for revising philosophical theories about them. Both phenomenology and transcendental philosophy answer to naturalistic epistemological constraints. Thus, claims Wheeler, we can have our transcendental cake and naturalize it.
Heidegger, Martin (1962), Being and Time, John Macquarrie and Edward Robinson (trans.), New York and Evanston: Harper and Row.