Different Levels of Modality

So I started reading John Divers' book Possible Worlds, and luckily I started in the chapter (#8) on Counterpart Theory.  I say this is lucky because I have the weird feature that if I don't understand a point in something I'm reading, it's really hard for me to continue and read past it.  This became relevant when I flipped back and started reading at the beginning of the book in order to better understand the Counterpart Theory chapter, but got stuck on page 5.

Divers is explaining different types of possibility, and says:  "In general, the M-possible worlds (logically possible worlds, analytically possible worlds, nomologically possible worlds, etc.) are those among the genuinely possible worlds that conform to or comply with the set of M-constraints (the laws of logic, the strictures of meaning, the laws of nature, etc.).  Then, what is M-possible is true at some M-possible world; what is M-impossible is not true at any M-possible world; what is M-necessary is true at all M-possible worlds, and what is M-contingent is true at some but not all M-possible worlds" (p. 5).

So I was wondering about this proposition:  In this world (let's name it 'alpha'), there is a tree outside my window.  Suppose there is not a tree outside my window.  Though the actual world could have been otherwise (in virtue of having been a world other than alpha), it's not true that alpha could have been otherwise.  So that means that it's necessarily false that in alpha there is a tree outside my window.  But this proposition is false not only in the metaphysically possible worlds, it's false in the logically possible ones as well (I’m assuming some modal logic axioms).  So this seems to have the result that the proposition is logically impossible.  But this seems bad - Divers, on the previous page, says:  "The intuitive variety of kinds of impossibility reflects that there are different kinds of consideration that exclude something from the realm of possibility.  If the salient excluding considerations are logical (no proposition is such that both it and its negation are true) we might speak of logical impossibility" (p. 4).

I’ll bet there are lots of ways to respond (and I’m hoping you guys might share some with me, or just tell me where I’ve completely misunderstood this stuff!), but here’s the response I’m leaning toward: Some propositions (such as genuine logical impossibilities) that are false in all metaphysically possible worlds are not merely metaphysically impossible (and thus not impossible due to considerations involving "the natures and identity conditions of things"), because there is a broader type of impossibility that applies to them.  We could say something similar about the impossibility of the proposition above: though it’s false in all logically possible worlds, it’s not the case that the considerations that exclude it from possibility are logical ones. Rather, they’re considerations that apply to a broader type of possibility (of course, this type of possibility wouldn’t be a type of genuine possibility, which most people identify with metaphysical possibility). Though I suspect people won’t like positing a type of possibility broader than logical possibility . . .

Any thoughts?

Comments

[Jonas!]

i have not read the divers book, and i am not sure what you mean by possible worlds.

if you're talking about lewisian possible worlds, then it is my understanding that within every world, everything is not contingent. possibility is mapped to indexicality. and so it is important to make the distinction true of a world and true in a world. (see stalnaker's response to williamson, for example. kit fine also wrote something about that i believe.)

so the proposition you gave is false in alpha, but not false of alpha, given transitivity of worlds. i don't know how much i believe in that distinction.

[Shieva]

Hi Jonas,
I'm not sure if the distinction helps - it seems that it's false _of_ alpha that there is a tree outside my window in alpha.
And it's false of each possible world that in alpha there's a tree outside my window.
So I'm guessing I'm not understanding what you're getting at - can you explain it a bit more?

[mode mode]

Necessarily, every world is self-identical. Contingently, the actual world is alpha. Necessarily, in alpha there is a tree. Contingently, in the actual world there is a tree. Necessarily, IF the actual world is alpha, (necessarily) there is a tree in the actual world.

[Shieva]

The conclusion should be either:
(1) Necessarily, if the actual world is alpha then there is a tree in the actual world.
Or:
(2) If, necessarily, the actual world is alpha, then, necessarily, there is a tree in the actual world.
What should I be taking from these conclusions?

[Jonas!]

it is true that in alpha, it is necessary that 'there is a tree outside' is false.
it is not true that of alpha, it is necessary that 'there is a tree outside' is false. (it is contingently false.)

unless i misunderstood the proposition in the post.

[Shieva]

The proposition must include 'in alpha'. Rather than being 'there is a tree outside my window', it's 'in alpha there is a tree outside my wondow'.

[Jonas!]

i think i would still say the same thing.

it is true that in alpha, it is necessary that 'there is a tree outside in alpha' is false.
it is not true that of alpha, it is necessary that 'there is a tree outside in alpha' is false. (it is contingently false.)

[Shieva]

Jonas,
Why do you think that? Can you explain it to me, or point me to some relevant reading?

[Jonas!]

tim williamson, "necessary existents", 7-11.
robert stalnaker, "on what there isn't", 13.
kit fine, "plantinga on the reduction of possibilist discourse", ???.

those are the only ones i know. sorry i can't be more helpful! i am but a blog commenter! i am not sure if that is a real distinction anyway.

basically my reasoning is that in worlds, everything is necessary. but not so of worlds.

[mode]

"(2) If, necessarily, the actual world is alpha, then, necessarily, there is a tree in the actual world.
What should I be taking from these conclusions?"

It is a strict implication that is also equivalent to: Necessarily (If the actual world is alpha, there is a tree in the actual world). Where 'Necessarily' ranges over the entire conditional.

What you should be taking is this. For all possible worlds it is either true that (i) it is not the case that alpha is the actual world, or (ii) there is a tree in the actual world. Or equivalently, take any possible world. In that world, if that world is alpha, then it must be the case that there is a tree in the actual world.

Why? Because alpha, by stipulation, is the world with a tree and alpha is alpha necessarily. So, if the actual world is alpha, then the actual world is the world with a tree. However, if alpha is not the actual world, then the conditional cannot be made false (since it has a false antecedent), so the actual world may or may not have a tree.

[Rich]

"In this world (let's name it 'alpha'), there is a tree outside my window. Suppose there is not a tree outside my window. Though the actual world could have been otherwise (in virtue of having been a world other than alpha), it's not true that alpha could have been otherwise."

Hang on, i'm really not seeing how the alpha couldn't have been otherwise? Surely, on counterpart theory, there are contexts in which alpha could have been different viz. those in which there is some alpha-counterpart which is different from alpha.

Linking this back to the grades of possibility issue. The point is that in de re modalizing, the relevant modalities are highly context sensitive. In one context, it will be impossible that i could have run a 100 metres in ten seconds (because we are restricting our attention to certain counterpart relations). In other contexts, it is true to say i could run 100 metres in under 10 seconds, because the salient counterpart relations are wider. So what is possible, de re, varies from context to context since the sphere of relevant counterparts change from context to context.

Rich

[Shieva]

Hi Rich,
By using ostension and then naming what I'd picked out, I was trying to get us to focus on the world qua worldbound individual.
But here's another proposition that does the trick:
There are at least two merely possible worlds.
This proposition, if true, is true in all possible worlds. And if it's false, it's false in all possible worlds. So it has that truth value in all logically possible worlds. But it doesn't have its truth value in virtue of its logical features.

[Rich]

Right, but the point about context still stands even if we stipulate that we focus on alpha qua worldbound individuals.

In the other case, take a look at a latter bit of Possible Worlds where John does the semantics for GR. In particular, focus on the bit about 'extraordinary interpretations'. The rough claim is that when we modalise about unrestricted quantificational claims, we don't actually alter the semantic content of the unmodalised unrestricted quantificational claim. That might answer a few questions.

Second, the claim you cite will have its truth-value in virtue of certain semantic features: its a modal claim, and given S5, it has its truth-value in all possible-worlds. Armstrong, for instance, rejects S5 and hence there is no semantic guarantee for him that the claims you offer is necessary.

[Rich]

shieva,

i re-read your post and got confused about something. you write

"Some propositions (such as genuine logical impossibilities) that are false in all metaphysically possible worlds are not merely metaphysically impossible (and thus not impossible due to considerations involving "the natures and identity conditions of things"), because there is a broader type of impossibility that applies to them"

Here's my problem: you say that some propositions that are false in all metaphysically possible worlds are not false in all metaphysically possible in virtue of the "natures and identity conditions of things", but because of some non-metaphyscial constraint. But aren't the metaphysical and logical modalities absolute in the sense that they what is metaphysically/logically necessary is necessary in all possible-worlds simpliciter? It appears that the worry then is 'how do we seperate the modalities if they are both absolute'?