In my last post I talked about individuation of material objects by their branches. The proposal was, roughly, that material objects and events should be thought of as sets; in particular, pairs of a branch and some aggregate of temporal parts of that branch. The major worry I have with this approach, pointed out by Andrew in the comments, is that this will affect mereology. To make ordinary talk about parthood come out true, we’d have to adopt a mereology for sets whereby set {a,b} has as its parts not {a} or {b} but {a,c} where c is a part of b.

This deviance from normal mereology is bad enough. But we’d also need to stipulate that {d,b} would not be a part of {a,b} if a is larger than b. Otherwise pairs of non-maximal aggregates of temporal parts with other non-maximal aggregates of temporal parts would come out as material objects, even though they’re not individuated by any branch. This is a bad result.

There’s a very simple modification to the view which in a stroke avoids all the mereological problems, and also goes some way towards reducing the intuitive weirdness of the view. Instead of identifying all material objects and events with pairs, just identify spacetime points with pairs {a,b}, where a is a pointlike part of a branch, and b is a branch. Then identify regions with sets of points exactly as is usually done by a substantivalist. Then identify events with spacetime regions, and material objects with events, exactly as is usually done by a supersubstantivalist.

The resulting view avoids the problems with mereology which dogged the earlier proposal. The mereology of material objects works just as it usually does. Objects are still individuated by their branches, but in virtue of all of their pointlike parts being individuated by branches. Is there still a problem with the mereology of the spacetime points themselves? Not really – if we take it that sets are simple, then spacetime points have no parts (as is usually supposed). If we take it (with Lewis) that sets have their subsets as parts, then each spacetime point has as a part an entire branch – perhaps counterintuitive, but not in serious tension with ordinary usage.

The supposed counterintuitive consequences of the view are ameliorated, too. The identification of objects and events with spacetime regions is familiar from supersubstantivalism – no new counterintuitive consequences there. And the identification of spacetime points with sets is also familiar from Quine’s proposal in ‘Propositional Objects’ to identify points with quadruples of real numbers. Indeed, the current proposal seems less radical than Quine’s, since the elements of the set are more naturally thought of as concrete than real numbers are. Spacetime points are anyway a case where the abstract/concrete distinction is at its most problematic.

Very cunning. I’m going to have to think about this some more.

BTW, when you say “if we take it that sets are simple, then spacetime points have no parts” — presumably you don’t want to do this, otherwise ordinary objects will be simple (as you identified them as sets of point*s (where a point* is a point branch pair.))

What you could do instead is identify ordinary objects with *fusions* of point*s. If sets are simple you get the that point*s are simple, but ordinary objects still composite. If the parts of sets are their subsets, then fusion will be just union.

One thing to bear in mind: presumably space-time regions are *fusions* of space-time points, not sets of space-time points. Be wary that on the Lewis view the atomic parts of an ordinary object, Fred, say, won’t be space time-points or space-time point*s – they’ll be space-time point* singletons. So it’s not really supersubstantivalism. You’re not identifying objects with fusions of space-time points, you’re identifying them with sets of spacetime points.

Thanks – good points! (no pun intended) :)

I think the way to go will be to take regions as fusions of point*s, and then go supersubstantivalist. Point*s would be the atomic parts of both regions and objects. Would that resolve all your worries?