The 617 blog seems to have gone quiet after a noisy beginning, so let’s try to resolve one of the puzzles they left us with last week.
The issue is, roughly, What is a group? Groups are identified by examples, e.g. the group of people writing the 617 blog, and we are left to figure out their metaphysical status.

The problem arises because groups are neither fusions of their members nor sets of their members. There’s a good argument and a bad argument for each of these conclusions. Fortunately one good argument is enough in each case.

Groups are not fusions. The bad argument is that fusions have their parts essentially while groups could gain and lose members. The problem with this is that the premise, that fusions have their parts essentially, has some weaknesses. It is rather controversial, for one thing. For another, it is false. The good argument is that not all parts of the fusion are parts of the group. As they say, Sarah’s nose is part of the fusion of 617 bloggers, it is not part of the group of 617 bloggers.

Groups are not sets. Again, the bad argument relies on essentialism about membership, and I won’t describe it in detail. The good argument is that sets are extensional, while groups are intensional. If the 617 bloggers, all 10 of them, form a nudist a capella group, call it the Bare Plurals, that would be a different group to the group of 617 bloggers, even if they are co-extensional. The group of bloggers could survive all of its members catching permanent laryngitis, the Bare Plurals could not.

The two arguments put some interesting restrictions on what groups must be. The way they are constructed out of their parts must be set-like, not fusion-like, so Sarah is a distinctive part of the group in the way that Sarah’s nose is not. But the group cannot just be a set, because it has certain modal properties that are not recoverable merely from the membership list.

The way forward is to note that even though groups are intensional rather than extensional, two groups could actually have the same members, there is no reason to think groups are hyper-intensional. That is, there is no reason to think that two different groups could have the same members in all possible worlds. So there is nothing stopping us identifying groups with functions from worlds to sets of individuals. If the group of 617 bloggers is a function f, we solve the problem of Sarah’s nose by noting that Sarah is an element of f(@), while Sarah’s nose is not. And we solve the problem of the Bare Plurals by noting that there could be a distinct function g such that f(@)=g(@). In short, functions from worlds to sets of individuals lets us say that groups are in some way constructed out of their (actual and possible) members and are not new mysterious entities without falling into the problems associated with saying groups are either fusions or sets.

Now these functions should seem familiar. Andy Egan has argued in a few places (but not, to the best of someone’s knowledge, online) that properties are functions from worlds to sets of individuals. Putting it all together, we get the conclusion that groups are properties.