McDowell (in the essay cited here) claims that Rorty ignores an important distinction between an assertion that “validity claims” are raised within a context (which is by definition a particular context) and a different assertion that justification is reducible to the particular context. Habermas explains the same point (and he makes this point in his discussion of Rorty as well) in the following way:
“. . . the validity claimed for propositions and norms transcends space and times, but in each case the claim is raised here and now, in a specific context, and accepted or rejected with real implications for social interactions.” (PT: 139).
Habermas’ assertion that the validity of a proposition ‘transcends space and times,” might be misleading in the way it stands but what he really means is that when we raise claims (necessarily within a particular context) we implicitly (undertake) to defend in all possible contexts.
It is interesting to note that Habermas presents that above formulation as his way of rendering of Putnam’s following remarks:
“Reason is, in this sense, both immanent (not to be found outside of concrete language games and institutions) and transcendent (a regulative idea that we use to criticize the conduct of all activities and institutions).” [Putnam, “Why Reason Can’t be Naturalized,” Synthese 52 (1982)].
Habermas quotes Putnam’s above remarks with his own equivalent of it (quoted above) in order to substantiate his assertion that:
“From the possibility of reaching understanding linguistically, we can read off a concept of situated reason that is given voice in validity claims that are both context-dependent and transcendent.” (PT: 139).
A situated reason is context dependent but provides the basis of transcendence which is a situated transcendence and hence “transcendence from within.”
Addendum: “. . . with the validity claims factually raised and recognized within an action coordinating role, an element of unconditionality enters into every day communicative practice. Criticizable validity claims have two faces: as claims, at least from the viewpoint of the participants, they transcend all merely local agreements and base themselves on a subversive, continually flexible potential of disputable reasons. Yet they must be raised here and now within specific contexts and with coverage provided by an unquestioned cultural background and accepted (or rejected) with a view to non-reversible action sequence. The social reality of the lifeworld consists of such action sequence as are interlinked via criticizable validity claims.” (Habermas, "A reply" in Communicative action : essays on Jurgen Habermas's The theory of communicative action , pp. 214-264, here p. 243).