Possiblities: Deflation vs. Inflation

Here is a very common philosophical scenario. I'll present it in terms of a dialog.

A: Possibilities are exhausted by BLAH. (Where BLAH could be the spatiotemporal arrangments of the particles, or the distributions of the qualities, or the distributions of the qualities plus the modal properties, or whatever.) Thus, if possibility X and possibility Y do not differ in terms of BLAH, then possibility X and possibility Y are one and the same possibility.

B: Ah, but consider these two possibilities. [Fill in the blank with the two descriptions for the possibilities]. Intuitively, these are two different ways the world could be.

A: Yes. It does seem that way. But what you have shown is that there are at least two ways of describing the same possibility. The difference that we feel in your two descriptions is a linguistic difference, not a metaphysical or modal difference.

B: But it seems to be a real difference. People might care about the difference. [Fill in other enjoining complaints].

A: Well, you agree that the two descriptions pick out possibilities that do not differ in terms of BLAH. In what might the difference consist? Could you design a test to determine whether you were in of the worlds and not the other?

B: No, I couldn't design such a test. And I already told you what the difference of the two possibilities consists in. They are the same in terms of BLAH, but differ in other terms. What more do you want from me,

A: I see only one possiblity and two ways of describing it.

Back to the main thread. I wish we had some rules for when A's move and when B's move are legitimate. Being in B's shoes more often than not, it seems to me that A could forever cling to her view that the difference I am positing is merely a linguistic difference. I can't think of any decisive way of putting the point that would rationally compel her to acknowledge what plainly seems to me two possibilities.

But now I think I might be able to turn that into an argument. Maybe A's position is unstable. Consider the person who think that possibilities are exhausted by the distribution of the qualities. And then consider a more conservative person who thinks that possibilities are exhausted by the spatiotemporal relations among the fundamental particles. The person who thinks that possibilities are exhausted by the distribution of qualities posits more possibilities than the person who thinks that possibilities are exhausted by the spatiotemporal relations among the fundamental particles.

But now we can put the person who thinks that possibilities are exhausted by the distribution of qualities in a tricky situation. Point out to this person that the person who thinks possibilities are exhausted by spatiotemporal relations could make the same moves that she is making right now trying to defend the view that possibilities are exhausted by the distribution of the qualities. Then ask her why the other person is mistaken in making that move. If she can't come up with something--as I think she can't--then either she has to grant you that there are distinct possibilities alike in terms of qualities or move to the more conservative position.

I will try to give an example of exactly this line of argument in a later post.

Distinct Qualtiatively Identical Possibilities

A possibility is a way that the world could be. Some philosophers hold that there cannot be distinct possibilities that are qualitatively identical. "Qualitatively identical" is a technical term. Think of it this way: two things are qualitatively identical if no matter how thoroughly we investigated, and no matter how good the tools we used in such an investigation, we couldn't tell the two objects apart.

I take it as a datum that there are possibilities in which there are qualitative duplicates. For instance, imagine a Max Black world. In the Max Black world there are only two objects, both are perfect spheres made of iron exactly three inches in diameter. No other objects exist in the Max Black world. If the two spheres of iron are just exactly alike, then they are qualitatively identical.

The question that I want to address is whether there are qualitatively identical possibilities. Sure, there can be qualitatively identical iron spheres. But are there different ways the world can be that are qualitatively identical? I think I have an argument that are qualitatively identical but distinct possibilities.

Imagine a Max Black world with two iron spheres. Bow imagine that there is a two-sided red arrow exactly between the balls. The world ends up looking something like this: [ O <--> O ].

Now imagine that the arrow has the following feature. At time T one of the sides of the arrow will randomly turn blue. So, at and after T one of the sides of the arrow is red and the other side of the arrow is blue. Let us agree to call the iron sphere closest to the red arrow the Red Sphere, and the iron sphere closest to the blue arrow the Blue Sphere. So here is one possibility. It could be that the by random the side of the two-sided arrow closest to the Blue Sphere turns blue.

But which side of the arrow turned blue was a random matter. It could just have easily been that the other side of the arrow turned blue. That is, here is another possibility. It could have been that by random the side of the two-sided arrow closest to the Red Sphere turned blue. This is a different possibility. At least it had better be. When considering the world in which the blue side of the arrow is closest to Blue Sphere we need to be able to truly say: it could have been the case, but actually isn't, that the blue side of the arrow was closest to the Red Sphere.

But now notice that we have two possibilities that are qualitatively identical. In both worlds we have two qualitatively identical iron spheres, and a two-sided arrow between them which is half red and half blue. Both worlds look something like this, where 'b' indicates the blue side of the arrow:
[ O <-->b O].

One interesting thing about this argument is that it suggests that there can be non-qualitative differences among possibilities originating from the identities of non-actual things like our non-actual iron sphere.

Vagueness and Identity

Many metaphysicians are interested in a question which can be put roughly in the following way: can it be vague whether A and B are identical?

Sometimes sloppy metaphysicians ask whether "identity can be vague." But this sloppiness borders on being a category mistake. Vagueness most naturally, and in the first instance, applies to questions, not objects or relations. It can vague as to whether Harry is bald, or vague as to how many grains of sand are in the Sahara Desert. But the notion of a vague object or a vague relation is confused. The best we can say of a "vague object" is that there are objects such that it is vague as to where their borders are. And the best we can say of "vague relations" is that there are objects and relations such that it is vague as to whether those objects bear the relation in question, or that it is vague how many pairs of objects bear that relation. If we want to investigate vagueness and its relation to identity, we must investigate it via a question, such as: can it be vague as to whether A and B are identical.

Here is an argument that it can be vague as to whether A and B are identical.

N.B., I will use 'clearly' in the following way: it is clearly the case that P iff it is true that P and it is not vague as to whether P.

Consider the Sahara Desert. There are grains of sand such that it is vague as to whether those grains of sand are parts of the Sahara Desert.

Now imagine that we discover a heretofore unknown tribe which uses the name 'Schmahara Desert' in the following two ways. First, the Schmahara Desert, like the Sahara Desert, is a desert. Thus (we may pretend) both the Sahara and the Schmahara are entirely composed of grains of sand. Second, the following bi-conditional holds: a grain of sand G is clearly part of the Schmahara Desert iff G is clearly part of the Sahara Desert.

There are three options:

(i) It is clearly the case that the Sahara Desert and the Schmahara Desert are identical.
(ii) It is vague as to whether the Sahara Desert and the Schmahara Desert are identical.
(iii) It is clearly not the case that the Sahara Desert and the Schmahara Desert are identical.

We can rule out (iii) straight away. For it to be clearly not the case that the Sahara Desert and the Schmahara Desert are identical, there would have to be some grain of sand such that it is clearly a part of one but clearly not a part of the other.

Here is a way to rule out (i). It might be that for every grain of sand G except for G*, it is vague as to whether G is part of the Sahara Desert iff it is vague as to whether G is part of the Schmahara Desert. But, we may imagine, G* is such that it is vague as to whether G* is part of the Sahara Desert but it is clearly not the case that G* is part of the Schmahara Desert. In other words there are more grains of sand by one for which it is vague whether they are part of the Sahara Desert than there are grains of sand for which it is vague whether they are part of the Schmahara Desert.

Because it is vague as to whether G* is part of the Sahara Desert, it is vague whether the Sahara Desert is bigger than the Schmahara Desert.

If it were clearly the case that the Sahara Desert and the Schmahara Desert were identical, then it could not be vague as to whether the Sahara Desert is bigger than the Schmahara Desert.

So not (i).

So, (ii), it is vague whether the Sahara Desert is identical to the Schmahara Desert.

So, in general, it can be vague as to whether A and B are identical.