It may still be objected, of course (see e.g. Adams & Aizawa 2001; Rupert 2004) that even if material culture sets the scene for new ways of thinking, the thinkings themselves are always fully internal, and brain-bound just as tradition has it. Two quick closing comments on this popular compromise.Now, A&A and Rupert, all agree that there is a reading of " there is no obvious reason why, when the right external stuff is present, it should not play an active role as part of the physical substrate of thinking" that is true. The idea is that one can combine some form of functionalism about cognition with some appropriate interpretation of qualifier "when the right external stuff is present," then get extended cognition.
First, there is no obvious reason why, when the right external stuff is present, it should not play an active role as part of the physical substrate of thinking. As Hurley (1998) notes, the skull is not a magical membrane beyond which physical stuff obtains some special property that makes it Gust then and not a moment before) capable of implementing thought and reason. Instead, if we are broadly speaking functionalists about the role of physical organizations in supporting thought, it must be at least possible that the relevant functional wholes should sometimes extend beyond the ancient confines of skin and skull, and include inextricable tangles of feedback, feed-forward and feed-around loops that promiscuously criss-cross the boundaries of brain, body and world. Something of this ilk may indeed occur, it seems to me, in the case of the musical cognizer mentioned above. (Clark, 2010, p. 17)
But, this seems to me just to go back to the idea that extended cognition is possible, which we have agreed to as early as Adams & Aizawa, 2001, p. 47.