Wolfgang Schwarz :: Haecceities in Hilbert's Hotel

Haecceities in Hilbert's Hotel

Posted on Thursday, 31 Mar 2005.

Imagine a world with nothing but infinitely many duplicate dragons, aligned in one long row. Consider the second dragon in the row. Call it "Fred".

Fred could have failed to exist. There are many worlds where he does not exist. (The actual world is probably one of them). Some of these worlds where Fred does not exist contain no dragons at all, others contain some of the other dragons in Fred's row. In particular, there are worlds where all the other dragons exist, but not Fred. The dragons are after all distinct existences, and there are no necessary connections between those.

So consider a world where all the other dragons exist and stand in a row, like they do in Fred's world, except that dragon number three occupies Fred's place, dragon number four the place of number three, and so on. This world is a perfect qualitative duplicate of the original world. Hence if haecceitism is false, Fred must exist in that world. He probably is the second dragon in the row there, too. So if haecceitism is false, it is absolutely impossible for Fred not to exist while the other dragons stand in a row. It is probably also impossible for all and only the even-numbered dragons not to exist. For the resulting world looks suspiciously similar to the original one. If spacetime is relational, the two worlds will be absolutely indistinguishable.

Strange.

Well, if haecceitism is false, there is also no world where Fred and dragon number one have traded places. But Lewis argues that this is not too bad: it doesn't mean that it's absolutely impossible for Fred to trade places with dragon number one. For dragon number one can be an individual possibility for Fred, a way Fred might have been. It may even be true, as Lewis seems to have believed, that there is a world where Fred is the first dragon in the row: if the first dragon is a counterpart of Fred, then there is a world -- the original world itself -- where Fred is the first dragon in the row. Notice however that the second dragon resembles Fred more closely in every respect than the first; so if the counterpart relation here is any similarity relation, it will also be true that in that world, Fred occupies the second position. Hence unless sometimes the counterpart relation is not a similarity relation, there is definitely no world where Fred does not occupy the second place in the row of dragons.

Anyway, can we apply this solution to the present case? Could Fred have failed to exist in a world with a dragon row by having a non-existant counterpart there? No. Not to exist at a world means having no counterpart there. It does not mean having a non-existant counterpart there (at least not on Lewis's version of Counterpart Theory. Might be different on Forbes's.)

Then maybe that's the solution: we could accept a counterpart relation on which not even Fred counts as his own counterpart. (If the counterpart relation is a similarity relation, nothing at all will be his counterpart on this relation.) Then by this counterpart relation, there is a world -- again, the original world -- containing a row of dragons but not containing (any counterpart of) Fred.

Comments

# Brandt on 31 March 2005, 22:19

Interesting entry! Here's two comments.

Fred might have occupied the position of the first dragon. On Lewis' view, the first dragon (an actual individual) is a counterpart of Fred, and makes it true that Fred might have occupied the first position. On this counterpart relation, Fred is also a counterpart of itself. But I don't think you can conclude, as you do, 'that in that world, Fred occupies the second position'.

After all, the point of switching from possible worlds to possible individuals is to avoid talking of possible worlds representing de re things of actual individuals.

You also mention the possibility of the third dragon taking Fred's spot, the fourth dragon taking the third's spot, etc.

Lewis talks about the assignment of counterparts to pairs in the Postscript to his 1968. The possibility you sketch might be understood as a de re modal attribution of a property to an actual sequence of individuals, composed of the first dragon, the third, the fourth, etc... The ordered sequence (1, 2, 3, etc.) is a way for the actual sequence (1, 3, 4, etc) to be.

(The actual distinctness of the dragons influences the counterpart relation here, to keep dragons from being assigned the same counterpart.)

But I admit that this would not be a de re modal attribution of a property to Fred...

# wo on 01 April 2005, 19:32

Oh right, thanks, I had forgotton about the counterparts of tuples.

I'm not sure what exactly Lewis aims at by providing individual possibilities in addition to worlds. At least at times it sounds like he wants to save intuitions like that I could have been Fred. But unless he completely revised his analysis of modality (of which I see no sign), "I could have been Fred" means that at some world, one of my counterparts is a counterpart of Fred. That's true if Fred himself is my counterpart in the actual world. But this way, we cannot rescue the intuition that Fred the dragon could have failed to occupy the second position in a world with a dragon row.

# Brandt on 04 April 2005, 19:25

On Lewis? later view, not all possibilities are given by possible worlds. Some are given by possible individuals, or tuples of possible individuals.

So one cannot describe every possibility by saying, ?according to this possible world?? One might have to say instead, ?according to this possible individual??

Fred might have occupied the first position in the row. Lewis? later view accommodates this possibility by claiming that Fred has a counterpart realizing the property in question?-this counterpart is the first dragon, which happens to be in Fred?s own world.

You argue that Fred resembles himself at least as much as the first dragon resembles Fred. So if the first dragon is a counterpart of Fred, Fred himself is also a counterpart of Fred.

That?s true, but I don?t think it matters. Because we are no longer describing possibilities by saying ?according to this possible world??

(Compare the following. On Lewis' 1968 view, individuals were allowed to have multiple counterparts in one world, to deal with cases like, 'I might have been twins'. But you don't want to conclude that on Lewis' 1986 version, almost every possibility concerning some individual is one where the individual 'is' multiples! That would be a mistake.)

I?m not sure if Lewis? move to possible individuals requires such drastic changes in his theory of modality. ?a is possibly F? and ?a is necessarily F? still receive the same translations, for instance.

Wolfgang Schwarz

Haecceities in Hilbert's Hotel

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