After winning a championship, each individual team member can truthfully say 'I won the championship.' Does this show that 'the team won the championship' is a distributive property?
AYes — if the property is true of every individual member, it must be distributive by definition
BNo — a property is distributive only if the group-predication is logically equivalent to member-predication; here members win derivatively because the team won, not independently
CNo — championship-winning is always collective because only groups can participate in team sports
DYes — the fact that each member can claim victory shows the property distributes to individuals
The key test for distributiveness is logical equivalence, not mere coincidental truth. Even if it happens to be true that each member won, the question is whether 'the team won' is logically equivalent to 'each member won independently.' Winning is achieved collectively — it is the team's coordinated performance that constitutes victory. Individual members win because the team won, not the other way around. A property can hold for every member while still being genuinely collective in its logical structure.
Question 2 Multiple Choice
Which of the following is the most reliable philosophical test for whether a property is genuinely collective rather than distributive?
AWhether the property is true of every member of the group
BWhether the group has more than two members
CWhether predicating the property of the group is logically equivalent to predicating it of each member individually
DWhether the property requires physical interaction among members
The logical equivalence test is the correct criterion: a distributive property is one where 'The Xs are F' is logically equivalent to 'Each X is F.' A collective property resists this equivalence — 'The Xs are F' may be true while 'each X is F' is false. For example, 'the soldiers surrounded the building' is true; 'each soldier surrounded the building' is false. The test is logical, not empirical — it's about what must follow, not what happens to be true.
Question 3 True / False
'The students surrounded the building' expresses a collective property — no individual student surrounded the building; only the group as a coordinated whole did.
TTrue
FFalse
Answer: True
This is a paradigm example of a genuine collective property. 'Surrounding' requires positions distributed around a perimeter — something only a coordinated group can achieve. If you try to distribute the predicate: 'each student surrounded the building' — this is false. The property cannot be predicated of the parts without loss of truth, which is the hallmark of a genuine collective property.
Question 4 True / False
A property is distributive if and only if it happens to be true of most individual member of the group.
TTrue
FFalse
Answer: False
This conflates the logical structure of a predicate with its coincidental truth. A property is distributive if it is logically equivalent to predication of each member — not merely if it happens to be true of each. Consider 'the soldiers marched in formation': each soldier was walking forward (so 'walking forward' happens to be true of each), but 'marching in formation' is a relational, collective property constituted by the arrangement among soldiers. Even if a collective property coincidentally holds for all members, it is still collective if the group-predication is not logically equivalent to member-predication.
Question 5 Short Answer
What is the philosophical test for whether a property is genuinely collective? Explain why 'the soldiers marched in formation' illustrates this test even though each soldier was individually walking forward.
Think about your answer, then reveal below.
Model answer: The test is logical equivalence: a distributive property is one where 'the group is F' is logically equivalent to 'each member is F.' A collective property is one where this equivalence fails — the group-predication is true but the member-predication is false or meaningless. 'The soldiers marched in formation' illustrates this because formation is a relational property constituted by the spatial arrangement and coordination among soldiers. Even though each soldier was walking forward, no individual soldier was 'in formation' — formation requires multiple bodies coordinated relative to each other. The property belongs to the group as an organized whole, not to any member taken individually, making it genuinely collective despite the presence of an individual correlate.
The key insight is that collective properties are not reducible to member properties even when those member properties are present. The formation is an emergent relational structure; walking is an individual act. Students who miss this conflate 'happens to be true of members' with 'logically equivalent to member-predication.'