Draft: From Possible Worlds to Possible Universes

I have uploaded a draft of a paper I've been working on on and off for quite a while. The paper develops a complete unorthodox possible-world analysis of modal sentences that can deal with modal possible-world sentences (i.e. sentences such as 'It is possible that there is a possible world at which there are talking donkeys'). I'd be interested to hear what people think about it. (For the record, as many of you already know, I believe that no possible world analysis of modal sentences is correct--the truthmakers for true modal propositions are irreducibly modal features of the actual world, not possible worlds)

In particular, I'd like to get some feedback on the argument I develop in Section 2. Most people don't seem to take modal possible-world sentences very seriously, but, if they take non-modal possible-world sentences seriously, I think they should. My main reason for thinking so is that, if basic modal sentences (e.g. ‘It is not possible that there are talking donkeys’)) are correctly analyzed as non-modal possible world sentences (i.e. ‘At no possible world, there are talking donkeys’)) (and incidentally I think they are not), then complex modal sentences (e.g. ‘It is possible that it is not possible that there are talking donkeys’)) should be analyzed as modal possible-world sentences (i.e. ‘It is possible that, at no possible world, there are talking donkeys’).

In my argument, I focus on that example and argue that, if 'It is not possible that there are talking donkeys’ is true if and only if there is no possible world at which there are talking donkeys, then ‘It is possible that it is not possible that there are talking donkeys’ is true if and only if it is possible that there is no possible world at which there are talking donkeys.

The argument for, if ‘It is possible that it is not possible that there are talking donkeys’ is true, then it is possible that there is no possible world at which there are talking donkeys goes like this.

1. ‘It is possible that it is not possible that there are talking donkeys’ is true. (A)
2. [It is necessary that] 'It is not possible that there are talking donkeys’ is true if and only if there is no possible world at which there are talking donkeys. (A)
   
3. For all p, ‘It is possible that p’ is true if and only if it is possible that ‘p’ is true. (A)
4. For all p and q, if [it is necessary that] p if and only if q, then it is possible that p if and only if it is possible that q. (A)
   
5. It is possible that ‘It is not possible that there are talking donkeys’ is true. (from 1 and 4)
6. It is possible that there is no possible world at which there are talking donkeys. (from 2, 3 and 5)

Here is the argument for the converse claim—if it is possible that, at no possible world, there are talking donkeys, then ‘It is possible that it is not possible that there are talking donkeys’ is true.

1. It is possible that, at no possible world, there are talking donkeys. (A)
   
2. [It is necessary that] 'It is not possible that there are talking donkeys’ is true if and only if at no possible world, there are talking donkeys. (A)
   
3. For all p and q, if [it is necessary that] p if and only if q, then it is possible that p if and only if it is possible that q. (A)
4. For all p, ‘It is possible that p’ is true if and only if it is possible that ‘p’ is true. (A)
5. It is possible that 'It is not possible that there are talking donkeys’ is true. (1 and 4).
6. 'It is possible that it is not possible that there are talking donkeys’ is true. (2, 3 and 5).