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Distributive / Collective / Shared

distributive

vs

collective commitment (or intention)

vs

shared (or joint) intention (or commitment)

Ayesha and Beatrice played the horse in our pantomime.

Case 1-individual: actors who perform a role distributively (different theatres, each performs the role) vs Case 1-collective: actors who perform a role collectively (one plays the back of the horse, the other plays the front of the horse)
Case 1-individual: actors who perform a role distributively (different theatres, each performs the role)
vs
Case 1-shared: actors who share a role: one plays the character as a child, the other plays the character as an adult. (Compare Bratman on shared intention: Bratman)
Case 1-collective: actors who perform a role collectively (one plays the back of the horse, the other plays the front of the horse) vs Case 1-shared: actors who share a role: one plays the character as a child, the other plays the character as an adult.
Could give blame as a second example.
You have two minutes to think of another three-way contrast.
Think of Bratman on shared intention. According to Bratman, a shared intention is something that we share in the same sense that Ayesha and Beatrice share the role of pantomime horse when one plays the young horse and the other the old horse. The shared intention comprises intentions and knowledge states some of which are mine and some of which are yours.
By contrast, a collective commitment or intention would be one that we collectively have. It’s analogous to the case where Ayesha and Beatrice join their bodies to play the horse. (That is, we would be its plural subject.)
What Gilbert has in mind is not a shared commitment, where the bits are distributed across people, but ...
... a collective commitment, something that is yours and mine, so that we are the plural subjects of that commitment.
Logically, you can see that there are these alternative possibilities. We will explore the idea of collective mental states (plural subjects) later.