Is My 3-and-1/2-Year-Old Daughter A Modal Realist?

This morning over breakfast my 3-and-1/2-yr-old daughter told me 'Golden shoes do not exist in this world'. 'Where do they exist then?' I asked. 'In another world' she replied with the tone of someone who is saying something obvious. I always thought modal realism was semantically revisionary but apparently this does not apply to the pre-school crowd! :-) (I still hope she just believes in island universes, though!)

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).

Was Lewis wrong or a relativist about counterfactuals?

David Lewis persuasively argued that counterfactuals are sensitive to context. As a consequence, Lewis claimed, counterfactuals don’t obey rules that other types of propositions do, like antecedent strengthening, hypothetical syllogism and contraposition. (From the fact that, were I to strike the match, it would light, it does not follow that, were I to strike the match and were I underwater, it would light.)

Just how is context relevant? Let’s make two distinctions. First, distinguish between a counterfactual sentence, “P > Q”, and a counterfactual proposition, {P > Q}. (I can’t quite figure out how to use the less than sign for some reason, as is typical to denote a proposition, so I’ll use curly brackets.) Second, distinguish between relativism and contextualism. According to relativism, a given proposition {P} might be true in one context, but false in another. (Note: I’m speaking of the proposition; one and the same proposition can be true in one context but false in another.) According to contextualism, a given sentence, “P”, might express one proposition in one context and a different proposition in another context.

I should note two things about these definitions. First, I don’t know if they are the standard uses of the terms “relativist” and “contextualist”. But they sound appropriate to me, so I’ll use them here. Second, relativism and contextualism are independent. One could deny both, accept one but not the other, or accept both.

There are at least two ways context might be relevant to counterfactuals: 1) In determining the truth conditions for a given counterfactual proposition; 2) In determining which counterfactual proposition a given counterfactual sentence asserts.

Suppose that Lewis was a contextualist but not a relativist about counterfactuals. Context determines when a given counterfactual sentence expresses a given counterfactual proposition, but the truth conditions are fixed for counterfactual propositions. Were that Lewis’ view, then he would be wrong about the failure of, say, weakening with respect to counterfactuals. That’s what Berit Brogaard and Joe Solerno argue in “Counterfactuals and Context” (Analysis, 68(1), 2008). After all, when examining an argument for validity, we don’t allow context to shift from premise to premise or between premises and conclusion. Suppose I utter the words “I am hungry,” and you utter the words, “Therefore, I am hungry and tall.” If validity didn’t require us to hold context fixed, we’d have a counterexample to and introduction. Yet all of the supposed counterexamples to, say, antecedent strengthening, involve a shift in context. Moral: If Lewis is a contextualist, he was wrong to think that antecedent strengthening, hypothetical syllogism and contraposition are invalid.

Suppose we hold fixed, then, that Lewis believed these arguments invalid (and that he didn’t hold a false belief!). Then Lewis must have been a relativist about counterfactuals. Or is there some other option?