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Three Strategies: Plural, Aggregate and Reductive

Assume we do need a theory of shared intention in order to solve The Problem of Joint Action. In selecting a theory of shared intention, we must answer two main questions. First, can intentions have not only individual subjects but also plural subjects? Second, are there aggregate subjects and can such subjects have intentions? The answers to these two questions determine which of three broad strategies are viable.

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Three Strategies for Constructing an Theory of Shared Intention

Plural Subject Strategy

Can intentions have plural subjects?

If intentions can have plural subjects, then our theory of shared intention is trivial: a shared intention is just an intention with a plurality of subjects (that is, with two or more subjects).

Aggregate Subject Strategy

Are there aggregate subjects and, if so, can they have intentions?

Theories of team reasoning require that teams can have preferences. To have a preference is to be a subject (of the preference), so teams are aggregate subjects.

If aggregate subjects can have not just preferences but also intentions, then it is possible that to have a shared intention is to be a part of an aggregate subject which has an intention.

Reductive Strategy

On a view like Bratman (2014)’s, for us to have a shared intention is just for us each to have certain intentions and for this to be common knowledge among us.

This is a reductive strategy: nothing other than ordinary individual subjects need have intentions.

Background: Collective vs distributive interpretations

Consider these sentences:

  1. The tiny leaves fell from the tree.
  2. The tiny leaves blocked the drain.

The first sentence is naturally read distributively; that is, as specifying something that each leaf did individually. Perhaps first one leaf fell, then another fell. But the second sentence is naturally read collectively. No one leaf blocked the drain; rather the blocking was something that the leaves accomplished together. For the sentence to be true on this collective reading, the tiny leaves' blocking the drain cannot be, or cannot only be, a matter of each leaf blocking the drain.[see-linnebo]

[see-linnebo]: This informal contrast between collective and distributive readings is linked to a debate about the logic of plural quantification; see Linnebo (2005) for an overview of that debate.

Background: Distinguishing Plural Subjects from Aggregate Subjects

When we have plural subjects, there is nothing distinct from the subjects which is the subject of the predication. But when we have aggregate subjects, there is something distinct.

For an uncontroversial illustration, consider:

‘The tiny leaves formed an impenetrable barrier.’

The forming is something the leaves do collectively; they are the plural subject of the forming. But in talking about the impenterable barrier we are talking about an aggregate entity which, although composed entirely of the leaves, is distinct from them.

To see that this distinction is significant, note that in ‘The tiny leaves formed an impenetrable barrier’ is true only if the leaves you are referring to did this, whereas the impenetrable barrier can exist although some leaves fall off and new ones join. So there really is a distinction between plural subjects and aggregate subjects.

Not everything true of an aggregate subject is true of a plural subject. For example, an aggregate animal, the Portuguese man o' war (Physalia physalis), stings and eats but the animals (polyps) that compose it do not collectively sting or eat.[1] Conversely, the animals that comprise an aggregate animal do collectively comprise an aggregate animal; but the aggregate animal itself does not comprise an aggregate animal.

So even where there is a plural subject and an aggregate subject and the componets of the aggregate subject are the plural subject, still different things can be true of the aggregate subject and of the plural subject! The man o’ war is nothing but the polyps, but the man o’ war can surive the loss of one polyp and the addition of another whereas the polyps can’t (they aren’t these polyps anymore if there is one missing or one addded).

Background: Terminology

Why aggregate? From biology (an aggregate or colonial organism): Wikipedia: ‘the Portuguese man o' war is a colony of four different types of polyp or related forms’

Theories of group agency are theories of aggregate subjects.

Aside: Ontological Innocence

Assumption: the right theory about the semantics of sentences that have a collective interpretation (and so involve plural quantification) exemplifies Ontological Innocence. That is, it is a theory on which a sentence being true on a collective interpretation

‘introduces no new ontological commitments to sets or any other kind of “set-like” entities over and above the individual objects that compose the pluralities in question’ (Linnebo, 2005).

Compare Boolos:

‘It is haywire to think that when you have some Cheerios, you are eating a set---what you're doing is: eating THE CHEERIOS’ (Boolos quoted in Oliver & Smiley, 2001, p. 295).

For more on plural quantification, read Linnebo (2005).

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aggregate subject : A subject whose proper parts are themselves subjects. A paradigm example would be a Portuguese man o' war (Physalia physalis), which is an animal that can swim and eat and whose swimming and eating is not simply a matter of the swimming or eating of its constituent animals. Distinct from, but sometimes confused with, a plural subject.
plural subject : Some subjects who are collectively the subject of an intention or other attitude. If there is one token intention that is both my intention and your intention and no one else’s intention, then we are the plural subject of that intention. (The intention is therefore shared in the same sense that, if we were siblings, we would share a parent.) Distinct from, but sometimes confused with, an aggregate subject.
shared intention : An attitude that stands to joint action as ordinary, individual intention stands to ordinary, individual action. It is hard to find consensus on what shared intention is, but most agree that it is neither shared nor intention. (Variously called ‘collective’, ‘we-’ and ‘joint’ intention.)
The Problem of Joint Action : What distinguishes doing something jointly with another person from acting in parallel with them but merely side by side?


Bacharach, M. (2006). Beyond individual choice. Princeton: Princeton University Press. Retrieved from
Bratman, M. E. (2014). Shared agency: A planning theory of acting together. Oxford: Oxford University Press. Retrieved from
Dixit, A., Skeath, S., & Reiley, D. (2014). Games of strategy. New York: W. W. Norton; Company.
Gold, N., & Sugden, R. (2007). Collective intentions and team agency. Journal of Philosophy, 104(3), 109–137.
Helm, B. W. (2008). Plural agents. Nous, 42(1), 17–49.
Linnebo, Ø. (2005). Plural quantification. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy (spring 2005 edition). Stanford, CA: Metaphysics Research Lab, Stanford University.
Ludwig, K. (2016). From Individual to Plural Agency: Collective Action. Oxford University Press.
Oliver, A., & Smiley, T. (2001). Strategies for a logic of plurals. Philosophical Quarterly, 51(204), 289–306.
Sugden, R. (2000). Team preferences. Economics and Philosophy, 16, 175–204.


  1. ‘Contractile cells in each tentacle drag the prey into range of the digestive polyps, the gastrozooids, which surround and digest the food by secreting enzymes that break down proteins, carbohydrates, and fats, while the gonozooids are responsible for reproduction’ (Wikipedia). ↩︎