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Linguistic Ersatz Modal Realism and Types of Modality

(Note: I tried to write this post last night and lost it when my powerbook overheated. Here goes the second time.)

David Lewis is best known for his modal realism, the view that all possible worlds exist in precisely the same sense that the actual world exists. He holds this view because he believes that it solves all sorts of philosophical problems related to modality, counterfactuals, properties, and so forth. However, there are a number of philosophers who think that the benefits of modal realism can be had without actually supposing that the possible world really exist. These philosophers Lewis calls ersatzers and in the section entitled "Paradise on the Cheap" in his book On the Plurality of Worlds Lewis attempts to reply to the ersatzers.

The first type of ersatzism to be dealt with is linguistic ersatzism. According to this view, possible worlds are linguistic constructs and therefore have only the ontological status of abstract objects like mathematical sets (whatever that might be) and not the status of concrete objects like the actual world. The linguistic ersatzer sets up a "world-making language" and asserts that possible worlds are maximal consistent sets of sentences in this language.

Lewis's first objection to this view (pp. 150-157) is that the ersatzer is required to assume certain facts about modality, which he is supposed to be explaining. In particular, Lewis wants to know whether it is possible for a particle to be both positively and negatively charged. Since these are (presumably) distinct predicates ("negatively charged" means more than just "not positively charged"), an axiom will be needed to enforce this rule (it's not a basic rule of the language). Lewis thinks that the ersatzer's axioms must come from some facts of modality distinct from his theory, so that his theory doesn't actually explain the facts of modality. In shot, Lewis claims that the ersatzer must be a primitivist about modality. To drive the point home, he wonders whether, according to the ersatzer, it is possible that there is a talking donkey. Again, Lewis says an axiom will be needed, and the axiom will depend on primitive facts of modality.

I suspect that Lewis is mistaken in his argument and that there is a reply open to the ersatzer based on distinguishing between different types of modality. By a "type of modality" I here mean a set of meanings that modal terms (e.g. "possible," "necessary," "impossible," etc.) can take in a certain context. Let's first distinguish between these types of modality and then consider the reply. The terms of modality can all be defined in terms of one another, so in my descriptions I will use whichever term is easiest to define.

In his discussion of possible worlds (and possible talking donkeys and positively and negatively charged particles) Lewis is talking about metaphysical or real modality. I've never heard a generic explanation of this type of modality that was more illuminating than its name, so suffice it to say that something is really possible just in case it really might have been actual, whatever really means. Lewis thinks this means that it really is actual for someone (the word "actual", according to Lewis, is an indexical like "here" or "now" - the actual world is just whatever world the speaker is in).

The next type of modality is narrowly logical or formal modality. A sentence is formally impossible relative to a language just in case the deductive calculus of that language can be used to derive an explicit contradiction (e.g. "A & ~A" in propositional logic) from it. Note that formal modal statements can be predicated of sentences, not of propositions and not of anything else. Also note that formal modal statements are always relative to a language.

The next concept is semantic or conceptual modality . A proposition is conceptually necessary just in case its truth is implicit in the definitions of the terms involved. For instance, it is conceptually necessary that a bachelor be an unmarried man (unless the context indicates that "bachelor" means "the recipient of a bachelor's degree" or something else, in which case it is not conceptually necessary).

Finally, there is broad logical modality. A proposition is broadly logically possible just in case all sentences that express it in some idealized language are formally possible relative to that language and it is conceptually possible. Now, of course, to give a full account of broad logical modality, you would have to give an account of the idealized language involved, but that's another story. Let's just suppose that there is some best formal logical language and we know what it is.

Now, Lewis seems to think, as I do, that real possibility and broad logical possibility are coextensive. Suppose the ersatzer also takes this view. Then what is the ersatzer doing? Well, he already has formal possibility by way of his language. The axioms Lewis wants him to add are the conceptually necessary truths. This isn't actually a problem for the ersatzer, because these are truths about language so they carry no additional commitments.

Considered from this direction, Lewis's objection seems a bit silly, especially when you consider that at the end he criticizes the ersatzer's introduction of axioms about talking-donkeyhood, saying "The job was to analyse modality ... It was not also part of the job to analyse 'talking donkey' (p. 156). The argument actually goes roughly like this (most of this is paraphrase of Lewis; the parts in italics I've added on behalf of the ersatzer):

LEWIS: Is it really possible that a single particle should be both positively and negatively charged?

ERSATZER: I don't know. What do you mean by positive and negative charge?

LEWIS: It's your theory, so you tell me what positive and negative charge are.

ERSATZER: Well I don't know what positive and negative charge are, but if the definition of positive charge is such as to exclude its coexistence with negative charge in a single particle, then the answer to your question is yes. If the definition doesn't exclude this, then the answer is no.

LEWIS: Aren't you assuming facts about modality independent of your theory?

ERSATZER: No, I'm just assuming that terms like "positive charge" mean something, and that they mean the same thing when we're talking about modality as they do in the real world.

LEWIS: Well, then tell me this: is it possible that there should be a talking donkey?

ERSATZER: What do you mean by "talking donkey?"

LEWIS: You know, a donkey that talks!

ERSATZER: Well, it so happens that I know more about donkeys and talking than about positive and negative charge. A donkey is a certain arrangement of matter, and talking is a certain event having to do with vocal chords and sound waves, and these arrangements of matter are possible, so, yes, it is possible that there should be a talking donkey.

LEWIS: I asked you to analyze modality - why are you analyzing talking donkeys?

ERSATZER: How on earth am I supposed to tell you whether a talking donkey is possible without establishing what is meant by the words "talking donkey?"

Of course, this discussion is sympathetic to the ersatzer; from Lewis's perspective the objection is not so silly since I don't suppose he thinks these facts are just linguistic. Nevertheless, it seems to me that this reply on the part of the ersatzer is a simple and effective one.