 On the naturalist version of the Individual Ownership Thesis, any (primary) intentional state is a higher order feature of a brain. It is not the case that in collective intentionality, individual brains are integrated in a Borg-like manner to form a collective super-brain. Therefore, it seems that collective intentionality reduces to an aggregate, or combination, of individual brain states. According to an internalist version, all the intentionality an individual has is structurally independent of the existence or non-existence of anything outside the individual mind. The question of whether or not an individual’s intentional states are collective is therefore settled by internal features of individual minds. A third version, that might seem attractive to non-naturalists and externalists, emphasizes that intentional states are, or involve, commitments. It seems, however, that only an individual agent’s own intentional states can commit them to a particular course of action, or to inferences. Other individuals’ intentional states may provide an agent with a reason only on the base of what they themselves believe or desire. Thus, it seems that the commitments involved in collective intentional states are the individual commitments of each of the participants.