Wolfgang Schwarz

The Brock/Rosen Objection: Lewis 1986 versus Lewis 1968?

The Brock/Rosen objection against modal fictionalism goes as follows. The modal fictionalist holds that

1) Necessarily p iff according to the modal fiction, at all worlds, P*,

where P* is the modal realist's paraphrase of P, and the modal fiction is the modal realists' theory. But the modal realist holds that it is true at every world that there are many worlds. That is,

2) According to the modal fiction, at all worlds, there are many worlds.

It follows from (1) and (2) that

3) Necessarily, there are many worlds.

But this kind of commitment is just what the modal fictionalist wanted to avoid.

Harold Noonan (1994) showed that this argument isn't sound because at least on Lewis' 1968 account, the reading of (2) that would licence the derivation of (3) via (1) is false: The 1968 paraphrase of (3) is

3*) For every world w there are many things that are in w and that are worlds.

But no world is in any other world. So the 1968 realist rejects (3), and (2) is false.

It seems to be generally agreed however that Lewis' 1968 analysis is different from his account in 1986. Hence Rosen (1995, p.68):

Noonan is wrong to represent this observation as a defence of the letter of modal fictionalism, since the original fictionalist proposal took it for granted that 'the modal realist's paraphrase' of an arbitrary modal claim was the translation implied by Lewis's later discussions, especially [1986]; and given this assumption the Rosen-Brock objection is cogent.

Similarly, Daniel Nolan writes:

Rosen has thus changed his preferred proposal, so that instead of a general endorsement of the position outlined by Lewis 1986, Rosen's recommendation for modal fictionalists now relies more heavily on Lewis 1968. Instead of the simpler biconditionals discussed [...] in Rosen 1990, the revised proposal is to take equivalences asserted by Lewis 1968 between modal claims and claims couched in terms of quantification over possible worlds [...].

But I can't see any such difference between Lewis 1968 and Lewis 1986. Here is the relevant passage from 1986:

So modality turns into quantification: possibly there are blue swans iff, for some world W, at W there are blue swans. [...] [T]he phrase 'at W' [...] works mainly by restricting the domains of quantifiers in its scope, in much the same way that the restricted modifier 'in Australia' does. [...] At some strange world W, all swans are blue -- all swans are indeed blue, if we ignore everything that is not part of the world W; quantifying only over things that are part of W, all swans are blue. [p.5]
As possibility amounts to existential quantification over the worlds, with restricting modifiers inside the quantifiers, so necessity amounts to universal quantification. Necessarily all swans are birds iff, for any world W, quantifying only over parts of W, all swans are birds. [p.7]

That sounds very much like the 1968 analysis. In particular, we don't get (2) if we follow this analysis because the other worlds mentioned in (2) are certainly not part of every world. Lewis is very explicit about this a few pages later, where he discusses supervenience:

We wanted to ask whether two worlds could differ in their laws without differing in their distribution of local qualitative character. But if we read the 'could' as a diamond, the thesis in question turns into this: it is not the case that, possibly, two worlds differ in their laws without differing in their distribution of local qualitative character. In other words: There is no world wherein two worlds differ in their laws without differing in their distribution of local qualitative character. That's trivial -- there is no world wherein two worlds do anything. At any one world W, there is only the single world W. [p.16]

The only change I can see between Lewis 1968 and Lewis 1986 in the quantificational analysis of modal statements is that in 1986 he says (on p.6) that pragmatic rules may overwrite the restricting modifiers.

(3) might indeed be such a context in which pragmatics removes the restriction, since otherwise what is said -- (3*) -- would be so obviously false. Of course, on this reading (3) doesn't licence (2). The modifier in (3) is then completely vacuous. I think this is in fact the best interpretation of modal talk about the possible world structure from the point of view of modal realism:

3) Necessarily, there are many worlds

and

4) Possibly, there are many worlds

both collapse into

5) There are many worlds.

On the alternative, orthodox reading, (3) is obviously false since it means (3*). Similarly

6) Possibly, there aren't many worlds

is obviously true. That sounds slightly strange, which is why I would prefer the vacuous interpretation.

Most importantly, on both readings nothing interesting can be said by applying modal operators to possible world talk. This is not bad for Lewis; it is exactly what he needs. He has to get rid of concerns about what would happen if there just happened to be no world containing a blue swan:

There is but one totality of worlds; it is not a world; it could not have been different. [1986: 80]