In some ways, extended mind and collective intentionality are highly distinct positions: the extended mind is always some one person’s mind, where collective intentionality always involves a group. But:
What if X and Y work in the same lab. X works days and Y works nights, and they’ve working on the same project. They share a lab notebook. Each morning X reads Y’s entries, and at night Y reads X’s. On Clark’s extended mind hypothesis, it seems that X and Y share a mind-part. While X has a mind separate from Y and Y from X, they also have overlapping minds in that the notebook is part of both of their minds. Further, since Y and X both input into the notebook, they intrude upon each other’s minds and partly constitute the others mental content.
Since they are working on the same project, they could be said to have collective intentionality, in Searle’s sense, even though they do not act at the same time. They coordinate their activity partly through the mediation of the notebook, but they also maintain a part of their shared mental content in the notebook. Further, they clearly are working towards the same end (the research project) and their individual actions (checking a reading, adjusting an instrument, etc.) are best described as intentionally directed towards the shared project. X only adjusts the instrument because he intends to do the research project.
Of course, at some point, Clark’s extended mind thesis starts to implicate large groups of people, perhaps everyone, in one shared extended mind, via institutions like the science of chemistry with its shared journals, research facilities, results, their propagation through newspapers and the internet. This would also include collectively held content, like child-rearing techniques that are well-known by some members of the community who are then consulted when necessary, and the consultees then become more aware of these techniques. There are large networks of experts–doctors, DIY handbook writers, on-line software FAQ writers, who can be consulted as needed when an individual mind seeks to expand its capacity to deal with some particular situation (illness, building a house, fixing a glitch in a web browser.)
But these don’t necessarily imply collective intentionality in the way that the notebook does, and it and cases like it provide a strong example of not just extended mind, but overlapping mind in shared intention.
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