Wolfgang Schwarz

Lewisian Semantics for Restricted Type-Identities

This is going to get a bit weird and technical. I wonder how a Lewisian semantics (along the lines of "Index, Context and Content" and "General Semantics") for terms like "pain" can make true everything Lewis says about such terms.

Assume that

1) Necessarily, for all x, x is in pain* iff x is in a state that plays the pain-role in normal members of the kind to which x belongs.

By "the pain-role" I mean the causal role attributed to pain by folk psychology. By "pain*" I mean whatever satisfies the condition expressed by (1). So (1) is more like a definition than an assumption. Lewis believes that our ordinary concept of pain roughly satisfies (1), but for what follows this doesn't matter. I think it's clear that we could have concepts for which something like (1) holds. Lewis's example of having a certain number stored in memory, as denoting a state of pocket calculators, sounds plausible to me (with the pain-role replaced by the role attributed to the state of having a certain number stored in memory by folk pocket calculator theory).

What's the semantic value of "pain*" in a Lewisian semantics?

I think "pain*" should be treated as a predicate and hence be assigned a function from contexts and indices to extensions (or something equivalent to that). Alternatively, we could regard "pain*" as denoting a state or event type, but for Lewis I guess such types are also just classes of tokens, in which case we get exactly the same semantic value as if we regard "pain*" as a property of states or events. Anyway, what follows doesn't depend much on this.

What do we put into the range of the semantic value, i.e. what's the extension of "pain" at different contexts and indices? One possibility is to rely on the context to determine the relevant kind. For example, if in context C we're talking about humans and state A plays the pain-role in humans, the semantic value could simply assign A (i.e. the relevant class of A-tokens) to each pair of C and any index. But I don't think this will work. To make (1) true,

2) For all x, x is in pain* iff x is in a state that plays the pain-role in normal members of the kind to which x belongs.

must be true at every world-index at the current context. Now suppose the current context determines A as the extension of "pain*" at every index. Then (2) is false because the pain-role is realized by other things in other worlds. The same obviously holds for any other state in place of A.

So perhaps "pain*" is not context- but index-dependent. But at least world-index-dependence also seems unable to account for (2): what should we assign to "pain*" at a context where (2) is true and a world-index where pain* is multiply realized? Assume in world w, the pain-role is realized by state A in humans and by state B in Martians, and that state A plays some other role in Martians. Is pain* at this world A or B, or both? None of that will deliver the desired results. For we don't want so say that Martians are in pain* at w when they are in A.

One could say that "pain*" is not world-dependent but kind-dependent. But kinds are hardly index coordinates, and we've already seen that contextually determined kinds don't suffice. So where do we locate the kind-dependence?

The only answer I can see is to put the kind-dependence into the extensions: At (any context and) the world-index w, the extension of "pain*" is neither all of A nor all of B nor both, but rather some of A together with some of B; namely all the A that occur in humans and all the B that occur in Martians. This way, (2) is rendered true at w, and similarly at every other world-index, thereby making true (1) (at every context).

There is still a role for context-dependence in this picture: If in a certain context all non-humans at w are ignored, the Bs in the extension of "pain*" might also fall out of the domain of quantification. In this context it would then be true to say that pain* = A (and even that necessarily, pain* = A).

If the context is less restricted, that will be false. Lewis says that pain*-in-humans = A will still be true. Thus "Pain*-in-humans" presumably denotes at w the class of states that play the pain-role in humans at w. Which is indeed (the class of) A. Interestingly, if what I've said above is correct, this class is not a subclass of the extension of "pain*" at w. For the extension of "pain*" contains only those A that occur in humans -- otherwise we don't get (2) at w --, but the extension of "pain*-in-humans" contains all A, including those in Martians -- otherwise we don't get "pain*-in-humans = A" at w.

So far no problem. But now what do we make of Lewis's claim that "pain*" denotes a realizer, not a role? Doesn't my semantics make it a role-property? According to my interpretation, at other world-indices "pain*" picks out whatever states play the pain-role in the kinds at the respective world. Even worse, if there are Martians in our own world, the extension of "pain*" at our world is itself a disjunctive or higher-order property common to states of Martians and humans, but not shared by other, intrinsically very similar states. Which is just what Lewis wants to avoid, arguing that such a disjunctive or higher-order state can't occupy the pain-role.

So because of multiple realizability, merely rigidifying "pain*" wouldn't help. At any rate, it would also make (1) false. I'm not sure where to go from here. It's easy to make "pain*-in-humans" rigid and thereby denote a non-disjunctive realizer, by ruling that it denotes at every world v the state (type) that plays the pain-role in humans at our world. But pain*-in-humans is not pain*. I'm afraid one has to say that pain*-in-humans, but not pain*, occupies the pain-role

I'm not happy with this as an interpretation of Lewis because it contradicts some of what he says.