Modal details in Unger's argument against his existence

Unger famously argues that he doesn’t exist, by claiming a contradiction between three claims (I am quoting (1) and (2) verbatim, but simplifying (3)):

1. I exist.

2. If I exist, then I consist of many cells, but a finite number.

3. If I exist and I consist of many but a finite number of cells, then removal of the least important cell does not affect whether I exist.

Unger then says:

these three propositions form an inconsistent set. They have it that I am still here with no cells at all, even while my existence depends on cells. … One cell, more or less, will not make any difference between my being there and not. So, take one away, and I am still there. Take another away: again, no problem. But after a while there are no cells at all.

But taken literally this is logically invalid. Premise (2) says that I consist of many but a finite number of cells. But to continue applying premise (3), Unger needs that premise (2) would still be true no matter how many cells were taken away. But premise (2) does not say anything about hypothetical situations. It says that either I don’t exist, or I consist of a large but finite number of cells. In particular, there are no modal operators in (2).

Now, no doubt this is an uncharitable objection. Presumably (2) is not just supposed to be true in the actual situation, but in the hypothetical situations that come from repeated cell-removals. At the same time, we don’t want (2) to be ad hoc designed for this argument. So, probably, what is going on is that there is an implied necessity operator in (2), so that we have:

4. Necessarily, if I exist, then I consist of many cells, but a finite number.

The same issue applies to (3), since (3) needs to be applied over and over in hypothetical situations. Another issue with (3) is that to apply it over and over, we need to be told that removal of the cell is possible. So now we should say:

5. Necessarily, if I exist and I consist of many but a finite number of cells, then removal of the least important cell is possible and does not affect whether I exist.

Now, I guess, we can have a valid argument in S4.

Is this a merely technical issue here? I am not sure. I think that once we’ve inserted “Necessarily” into (4) and (5), our intuitions may start to shift. While (2) is very plausible if we grant the implied materialism, (4) makes us wonder whether there couldn’t be weird situations where I exist but don’t consist of many but a finite number of cells. First, it’s not obviously metaphysically impossible for me to grow an infinitely long tail? That, however, is a red herring. The argument can be retooled only to suppose that I necessarily have many cells and I actually have a finite number. But, second, and more seriously, is it really true that there is no possible world where I exist with only a few cells? In fact, perhaps, I once did exist with only a few cells in this world!

Similarly about (5). It’s clear that right now I can survive the loss of my least important cell. But it is far from clear that this is a necessary truth. It could well be metaphysically possible that I be reduced to some state of non-redundancy where every cell is necessary for my existence, where removal of any cell severs an organic pathway essential to life. I would be in a very different state in such a case than I am right now. But it’s far from clear that this is impossible.

Perhaps, though, the modality here isn’t metaphysical modality, but something like nomic modality. Maybe it’s nomically impossible for me to be in a state where every cell is non-redundant. Maybe, but even that’s not clear. And it’s also harder to say that the removal of the least important cell has to (in the nomic necessity sense) be nomically possible. Couldn’t it be that nomically the only way the least important cell could be removed would be by cutting into me in ways that would kill me?

Furthermore, once we’ve made our modal complications to the argument, it becomes clear that of the three contradictory premises (1), (4) and (5), premise (1) is by far the most probable. Premise (1) is a claim about my own existence, which seems pretty evident to me, and is only a claim about how things actually are now. Premises (4) and (5) depend on difficult modal details, on how things are in other worlds, and on metaphysical intuitions that are surely more fraught than those in the cogito.

(One of the things I’ve discovered by teaching metaphysics to undergraduates, with a focus on formulating logically valid arguments, is that sometimes numbered arguments in published work by smart people are actually quite some distance from validity, and it’s hard to see exactly how to make them valid without modal logic.)

Relationship without belief

Consider this fairly standard version of the argument from hiddenness:

1. If God exists, he produces everything that is necessary for a personal relationship with every nonresisting person.

2. Belief in the existence of x is necessary for a personal relationship with x.

3. So, if God exists, every nonresisting person comes to believe in God.

4. Some nonresisting person does not come to believe in God.

5. So, God does not exist.

I noticed today that (2) is just plain false. My example is a skeptic about other minds. You can take seriously the hypothesis that you are the only real person around, seriously enough that you do not believe the hypothesis false, and still have a personal relationship with other people. Surely Unger, in his phase of believing that people don’t exist, had personal relationships with them!

A perhaps even better counterexample to (2) was given by one of my students. You can have a long-standing Internet-based personal relationship while taking seriously the possibility that the other person doesn’t exist (e.g., maybe you are interacting with a chatbot).

This observation doesn’t destroy the hiddenness argument. One might, for instance, replace (2) with:

6. A personal relationship with x is incompatible with consistent disbelief in the existence of x

and then replace (4) with:

7. Some nonresisting persons end up consistently disbelieving in God (e.g., due to their reasonable evaluation of the problem of evil, or due to low priors for theism).

But now (7) is less plausible than (4). One might well think that the evidence against theism is insufficiently strong to make it possible for a nonresister to disbelieve in God.

Alternately, one might replace the deductive hiddenness argument with a probabilistic one by noting that it’s a lot harder to have a personal relationship without belief in the other person, and it’s unlikely that a loving God would make it this hard. I think that’s not a very strong argument, but it is an option for the defender of hiddenness.

A problem of the many

Assume compositional universalism, the doctrine that any bunch of non-overlapping objects have a whole which they wholly compose. Unger's problem of the many is that there seem to be too many people who think my thoughts. After all, if I think my thoughts, so does the guy composed of the same parts as I have, plus one additional particle near me, as does the guy composed of the same as I have, minus one flake of skin. There are solutions to this problem, however. For instance, it might be that for some reason only one of the composites is a person—maybe a person has to be maximal in some way, including all the parts. Or maybe persons are souls, or matter connected with a soul (and there is a metaphysical fact as to which particles are connected to a soul).

The only consistently unrestricted universalism that has any hope of truth, however, is what one might call modal universalism. I will give the four-dimensionalist version, but a three-dimensionalist version is just as easy. Modal universalism says that for any function f from worlds to sets of objects, such that all the f(w) are non-overlapping, and such that for at least one w the set f(w) is non-empty, there is an object O_f such that:

1. For all w, O_f exists at w if and only if f(w) is non-empty.
2. For all w, if f(w) is non-empty, then O_f is composed precisely of the members of f(w) at w.

(For the three-dimensionalist version, replace worlds with world-time pairs.) Bald claim: Anything more restrictive than modal universalism will either not yield all the objects of common sense, such as organisms and artefacts, or else will be ad hoc.

Modal universalism, however, gives a particularly serious problem of the many. Here is a rough-and-ready thesis:

3. Whether x is a person in the actual world thinking about p depends only on what x is up to at w and at worlds sufficiently close to the actual world.

To make this precise, one would need an account of categorical properties to spell out the "is up to".

Anyway, for any at all reasonable story about what "sufficiently close" means, according to modal universalism, there will be infinitely many entities that are composed of the same parts as I am in all the sufficient close worlds, but that differ in some odd way in the further worlds. (There is a being that has the same parts as me in all sufficiently close worlds, but in all further worlds is composed of number seven, assuming the number seven is an object.) By (3), they will be thinking about the same thing as I am. And hence we get too many thinkers thinking my thoughts. Moreover, to make things worse, if there are no empty worlds, some of these thinkers will be necessary beings (e.g., the Pruss/Number-7 being of my previous paranthetical remark).

Now something like a maximality condition, or bringing in souls, may help with Unger's original problem. But there would still be this version to tackle.

Maybe introducing some story about naturalness will help. Maybe only the more natural entities think, and an entity that is composed of the same parts as I at all close worlds and of the number seven at all other worlds isn't natural. However, at some distant worlds, there will be multiple, equally natural (at least if natural is linked with simplicity of law and that sort of thing), choices for f(w), even if we constrain that f(w) = { me } at all close worlds. Unless, of course, naturalness is some kind of metaphysical primitive, having nothing much to do with simplicity of law and so on. So that's a way out, but I doubt it will appeal to many modal universalists.

Let me end with a note about a different topic. I suspect that the only ontology that will support a psychological theory of personal identity will be a universalist one. Thus, this might yield an argument against psychological theories of personal identity.

[Minor errors fixed.]