Wolfgang Schwarz

Monadic and Intrinsic Properties

I believe that the so-called problems of intrinsic change and accidental intrinsic properties are real problems. But I believe that their names are misleading, and that they have nothing to do with whether or not we construe properties as sets of things or as functions from worlds and times to sets of things.

Suppose we do the latter, and we also endorse counterpart theory and temporal parts theory. The property of being bent is a function that maps world-time pairs to sets of things. These things are temporal parts of world-bound individuals, ordinary fusions of particle segments, just like us, except that they are smaller along the time axis and all bent. This is a perfectly reasonable and common-sensical view, I believe (but of course I'm biased), and I don't think Lewis has any reason to reject it as turning properties into relations. There is after all a simple equivalence between being bent construed as a function and being bent construed as a Lewisian set: the set is the union of the range of the function; the function indexes all members of the set by their world and time.

But look what happens when we drop counterpart theory and temporal parts theory. Being bent is still a function from world-time pairs to sets of things. But these things are not bent. For the very same set of things is also in the range of being straight (for whatever is bent at one world can be straight at another world). These things in the values of the bent function are not ordinary material objects at all. They have no shape. They are not fusions of particles or particle-segments. They have no definite number of atomic parts. They are almost bare particulars. Perhaps they have some few properties. Perhaps they all have some shape or other, and being material, and having some definite number of atomic parts. But even that is doubtful. Is it really coherent to assume that there are things that a) have some definite number of atomic parts, but b) for all numbers x, they do not have that many atomic parts? I think it is better to deny that they have atomic parts. Now here's the problem: Are there really such things? In particular, are Hubert Humphrey and you and me and our friends and chairs and bicycles things like that? No!

There's a good way out of this problem. It goes like this: "I am bent now, but could be straight at another world. So I am in the set assigned by the straight function to other world-time pairs. You ask what this thing in the set is like? That's easy. This thing is none other than me, and I can tell you what I'm like. I'm not an immaterial entity with no shape and no parts. As everyone can check, I'm an ordinary material object, I'm bent, I have two arms, and so on." This is the actualist/presentist solution which Lewis agrees solves the problem. The things in the value of being straight for some world and time needn't be straight. Some of them can be bent. They have just the properties they have actually and now. The only price of this solution is that it privileges the actual and the present.

If we don't want to do that, and don't want counterparts and temporal parts, we have to accept the peculiar ontology described above. We can of course hide the peculiarity. We can say that the things in those sets do have all kinds of properties: they are bent now at our world, straight now at other worlds, and so on. We could even say that it doesn't make sense to speak of things being just bent simpliciter or having three parts simpliciter: you can only be bent at some time or other at some world or other; and you can only have three parts at some world and time. Maybe the whole idea of having any property simpliciter should be rejected. And maybe we can try to explain away the seeming peculiarity by pointing out that in ordinary cases, when we ask what shape something has, we mean what shape it has now and actually. And so understood, nobody needs to deny that Humphrey and you and me do have a shape (well, except for Humphrey, who is dead). But I don't think this really makes the peculiarity go a way. The question is how bad the peculiarity really is. It seems to me that Lewis gave it a little too much weight in regarding it as non-negotiably false. On the other hand, it also seems wrong to me to pretend, as Andy Egan does, that there is no problem here at all.

What does the problem have to do with intrinsicness? Couldn't we create the same problem with extrinsic properties? Consider being famous on the counterpart/temporal parts conception. It is out of the question that things are famous at times by having famous temporal parts at those times. So we can't say that the set of things which being famous assigns to a given world and time is a set of things that are famous simpliciter. So what are these things, are they famous or not? It seems that they are neither. Maybe they have some fame value or other, or being known by some definite number of people, without however being known by 0 or 1 or 2 or ... people. But again, it would be better to say that they lack these properties as well. They have no fame value at all. Are there really such things? And are Humphrey and you and me things of that kind?

If that problem is equally serious as the problem above, Lewis is in trouble. For this time he, too, has to say that we shouldn't speak of being famous simpliciter: things are famous only at specific times and worlds. But it seems to me that this time, the answer is not that bad. Things really are famous only relative to populations and times. Somebody who is famous among Germans might not be famous among Americans; somebody who is famous now might not have been famous 10 years ago. It really doesn't make sense to speak of the person herself being famous or not, irrespective of time and society and world. Perhaps there is some price in peculiarity to pay here as well -- it isn't obvious that some things have (simpliciter, as opposed to now and actually) no fame value at all, not even 0. But the price is much lower.

Being famous is a little special because unlike most properties things can have it even when they don't exist. But apparently Lewis accepted the same reply for other extrinsic properties as well. At least he accepted that properties like being an uncle are treated as disguised relations to times and worlds, as Ryan Wasserman reports here.

If Lewis really believed that his problem affects only intrinsic properties because all others can be understood as disguised relations, it is clear why he called the problem a problem of intrinsic change and accidental intrinsic properties. But some very bad things follow.

First, all monadic properties now appear to be intrinsic: the extrinsic properties are all disguised relations. But that's odd. Consider Lewis's definition of intrinsic properties as properties that are independent of loneliness (ignoring certain trouble-makers). Surely there are lots of classes of possibilia -- monadic properties -- that do not satisfy this condition: my unit set, the class of all possibilia, the class of things in our world, the class of lonely things, the class of uncles, and so on. Take any intrinsic property -- shape, spin, mass, whatever -- and throw out all the instances that are alone in their world, and you have an extrinsic property. Why on earth would Lewis say that these properties -- these classes! -- do not exist, or that they are in fact not classes of possibilia, but classes of tuples of possibilia? That makes no sense.

Second, the price he now pays for the problem I sketched above is about just as high as the price his opponent has to pay. It is fairly acceptable to say that people are not famous simpliciter; it is much worse to say that they are not uncles simpliciter; and it is very bad to say that they do not have colours simpliciter. (I assume colours are extrinsic.) Indeed, it isn't clear at all whether shapes are intrinsic. The only uncontroversial intrinsic properties I can think of (besides artificially defined ones) are mereological properties like having such-and-such a number of atomic parts. Are these supposed to be the only properties things have simpliciter?

Whether or not Lewis believed it, the claim that all extrinsic properties are disguised relations has no place in Lewis' metaphysics. Some extrinsic properties really are disguised relations: being famous, numbering the planets; being taller (badly disguised), and being somebody's favourite property (except that this one doesn't exist). Being an uncle, being red, being a rock, being pope, being bent are not. There is no need at all for Lewis to treat them as relations. With counterpart theory and temporal parts theory, there is nothing wrong with saying that the set of things assigned by uncle to the present and our world are things that are uncle simpliciter. For these very things will never occur in a value of not-uncle (or lonely or any other property incompatible with being an uncle).

So while there is a real problem of intrinsic change and accidental intrinsic properties, the problem is actually about monadic properties, not just intrinisic (monadic) properties. It doesn't matter at all whether shapes really are intrinsic. What matters is whether they can be had simpliciter.