Contribution
It sets out criteria a theory of groups (teams, committees, clubs, courts) must meet, shows that the four theories then on offer each fail at least one, and proposes a structuralist alternative that meets all six. The criteria and the comparison tables are the lasting part. The positive view is introduced, not developed.
Key insight
What distinguishes a group from its members is its structure. The chess club and the nature club can have exactly the same members and still be two clubs, because the members stand in different functional relations in each. Any theory that identifies a group by its members alone (plurality, fusion, aggregate, set) collapses them.
Assumptions
- Groups exist. Supposed, not argued (p. 2).
- The six criteria hold of all groups. Each is supported by one ordinary example (p. 2), and Coincidence by the claim that a student “is in two clubs” (p. 3). The paper rejects the Wiggins “truism” that two things cannot be in one place at one time, for groups (n. 4).
- Many members is not a criterion. The Senate reduced to one senator, then refilled, is “quite natural” to call one shrinking and growing body (p. 3).
- Intentions are optional. Social groups differ from tables in that members (or authorities, as when a president creates a committee by fiat) have group-forming intentions; such a condition “might be added to any of the views” (p. 4). It is not part of the view proposed.
- Substantive answers beat sui generis ones. Uzquiano’s view that groups are sui generis is set aside for space; a substantive answer is “a mark in favor” (n. 1).
- Structures as in mathematical structuralism (Shapiro, Resnik, Hellman, Putnam; n. 9), with node-occupation in a plural logic (Boolos; n. 12).
Key results
- The six criteria (p. 3). (1) Members–Times; (2) Members–Worlds; (3) Existence–Times; (4) Existence–Worlds; (5) Space; (6) Coincidence: groups of the same basic kind can be extensionally coincident and non-identical. Only (6) is said to mark groups off from tables and trees, which have coincident non-identicals only across sorts, as in Fine’s tree and wood (p. 4).
- Non-singular pluralities (§2). Fail (1) and (2), since some people are not identical to more or other people; meet (3)–(5); meet (6) only if arrangements are added, which may reify arrangements and abandon the pluralist’s nominalism (pp. 5–6).
- Fusions (§3, Sider). Meet (1) by time-relative parthood and (2) with counterpart theory, and (3)–(5); fail (6), since fusion identity is extensional. The Supreme Court and a committee of exactly the Justices, with the same members at every time, would be one group (p. 7). Counterparts “qua” a sortal give one fusion several modal properties, not two groups (p. 8).
- Aggregates (§4, Burge). Fail (1) for member-components, meet (2) only with counterparts, fail (6) when the member-components are the same (pp. 9–10; n. 8 allows distinct aggregates with different member-components).
- Sets (§5, Effingham). A group as a set of world-indexed sets of time-indexed member sets meets (1) and (2); fails (5) unless some sets are concrete; captures (6) only “in spirit” (possibly, not necessarily, coincident groups differ); meets (3)–(4) only by an ad hoc stipulation; and faces a Benacerraf problem, since the choice of set construction is arbitrary (pp. 10–12).
- Groups as realizations of structures (§6). A structure has nodes joined by functional relations (pitch-ball-to, return-ball-to), some hierarchical, all nodes connected to all others (p. 12). Grain is left open: weighted edges, a vague class of structures, or vague reference of “a group” (p. 13). Nodes may take one occupier (Chief Justice) or several (treasurer). Some things jointly realize S iff each occupies a node and every node is occupied; occupying a node is standing in the relations it requires (p. 14). Membership at t and w: x occupies a node of S and is functionally related as S requires to the other occupiers (p. 14). Identity at t and w: same members, and the same intra- and inter-structural relations among them (p. 15).
- Why groups usually have many members (p. 14). Most group structures contain an irreflexive relation (return-ball-to, has-more-power-than, seconds-a-motion-introduced-by, collaborates-with), and realizing one needs at least two occupants.
- All six criteria met (p. 15), with a group-as-many (the occupiers at t and w) delivered alongside the group-as-one, answering Russell’s class-as-one and class-as-many.
Claims
| id | claim | strength | support |
|---|---|---|---|
| C1 | Any adequate theory of groups must satisfy the six criteria | moderate | one example per criterion, pp. 2–3; Coincidence rests on how students and courts are described |
| C2 | Coincidence, not the other five, distinguishes groups from ordinary material objects | weak–moderate | p. 4; the contrast with tables and trees is by intuition |
| C3 | Groups as non-singular pluralities fail Members–Times and Members–Worlds | strong given the criteria | identity of pluralities, p. 6 |
| C4 | Groups as fusions fail Coincidence, and qua-counterparts do not rescue them | strong given the criteria | extensional identity, p. 7; argument p. 8 |
| C5 | Groups as Burge aggregates fail Members–Times and, with the same member-components, Coincidence | strong given the criteria | pp. 9–10 |
| C6 | Groups as Effingham sets fail Space, meet the existence criteria only ad hoc, and face a Benacerraf problem | moderate | pp. 11–12; Effingham’s own replies are discussed and found wanting |
| C7 | Groups are realizations of structures with functionally defined nodes, and this view meets all six criteria | moderate as a sketch | §6; checked criterion by criterion, p. 15; grain and persistence left open |
| C8 | Irreflexive relations in most group structures explain why groups usually have more than one member | moderate | p. 14 |
Concepts
- Coincidence — two groups of the same basic kind with the same members at a time (or at all times) that are not identical (p. 3).
- Structure — nodes and edges, the edges functional relations, some hierarchical (directed) (p. 12).
- Node — a place defined wholly by intra- and inter-structural relations (p. 13), possibly limited to one occupier.
- Realization — some things jointly occupying every node (p. 14).
- Inter-structural relations — relations to nodes of an embedding structure, such as a pitcher to the opposing batter in a game, or a team to its league (p. 13).
Connections
- Ritchie 2018 (LIT-486, NOTE-389). Keeps this view for “organized social groups”, adds that their structures are social structures with people as node occupiers, and amends the membership definition to a collective predicate after discussion of this paper’s definition (its n. 22).
- List & Pettit (LIT-391), List (LIT-401, NOTE-340). Not cited and not discussed. NOTE-340 records List’s functionalist definition of a group agent and his claim that the “black box” mechanisms are in List & Pettit. Ritchie’s “functional” relations are roles in a team’s or committee’s organisation, not the belief–desire functional profile List needs. The two are compatible: a group could be a realized structure in her sense and an agent in his. Her Coincidence criterion gives a sense of “over and above the members” (numerical distinctness) that holds of every structured group, agent or not.
- Schwitzgebel (LIT-159, NOTE-131) and the reply to Kammerer (LIT-459, NOTE-381). Not cited. If one population can realise several structures, each a distinct group, then “the United States” has several coincident candidates, which is the shape of the reply’s worry about condition A (NOTE-381, C2). The application is this record’s.
- Griesemer & Shavit (LIT-188, NOTE-173). Not cited. Their collections, conexuses and communities grade groups by interaction structure; Ritchie grades nothing, but both make structure, not membership, what a group is.
- Mereology. The paper is a contribution to the composition debate for one kind of whole; it relies on Sider’s and Burge’s formulations as stated.
Bearing on the record
- THEORY-043: no change. The paper’s structures are social-functional roles, not causal architecture, and it says nothing about minds. It offers no anti-nesting principle and no architectural criterion.
- For the group-agency strand. Cite it for what a group is and for why a group is not its members. Do not cite it for anything about agency or consciousness; it does not address either.
- No ML instruction. Nothing belongs in the anthology.
Limitations
- The positive view is four pages. Persistence conditions are not given beyond “continuity of the realization” (p. 14), and the grain of structures is left open (p. 13).
- Occupation is defined holistically. The first condition on occupying a node is that “every node in S is occupied” (p. 14), so whether one thing occupies a node depends on whether all others are filled; a structure with one empty node has no members at all. The paper does not discuss partial realization (a team one player short).
- The intention condition that would make these social groups is optional (p. 4), so as stated the view is a view of structured objects in general.
- The criteria are defended by single cases; a reader who doubts Coincidence (Uzquiano’s alternative is not discussed) loses the main argument.
Open questions
- What are the persistence conditions of a group through changes of structure, not only of members?
- Does the holistic occupation condition survive vacancies, which most standing bodies have most of the time?
- What, if anything, links a group’s structure to the group’s capacity to act as one? The paper does not ask.
Corrections
- No dossier existed, so there is no seeded skim to correct.
- Date. The request cited 2013, the issue year (166(2), November 2013). The article was published online on 10 October 2012 (Crossref); the PDF read is the Online First version, ”© 2012”.
- Slips in the paper. §2 glosses Members–Worlds as “the criterion that groups can have different members at different times” (p. 6); it should read “across worlds”. The reference list spells Benacerraf “Benacerraff”, and §4 has “Pleaides” for the Pleiades.