First thing to note, possible worlds can’t be specified at different levels of detail. When doing so we are either specifying partial possible worlds or sets of possible worlds. As rigid designation is a claim about worlds, it can’t be relative to the level of detail utilised as it only applies to things specified at one level of detail.
Second, you still seem to be treating possible worlds as concrete things rather than something in the head (or, at least, making substantive assumptions about possible worlds and relying on these to make claims about possible worlds generally). Let’s take possible worlds to be sets of propositions and truth values. In this case there’s no reason to find transworld identity puzzling. H2O exists in this world just if a relevant proposition is true (like, “I am holding a glass of H2O”). There’s also no room for this transworld identity to be relative to a context. Whether these things are puzzling depends on your account of possible worlds and it seems like if you’re account of possible worlds can’t account for transworld identity it can’t do the work required of possible worlds and so it is open to the challenge that it should be abandoned in favour of some other account.
Third, it’s important to distinguish questions about the way worlds are from questions about how they can be specified. It’s an interesting question how we should specify individual possible worlds and another interesting question whether we often do so or whether we normally specify sets of possible worlds instead. However, difficulties with specification do not undermine the concept of a rigid designator.
Fourth, even if it were a relative matter whether H2O exists in a world this wouldn’t undermine the concept of rigid designation. Rigid designation would simply imply that if this were the case then it would also be a relative matter whether water existed in that world.
The summary of what I’m trying to get at is the following: you have raised concerns for practical issues (how we specify worlds) and epistemic issues (how we know what’s in worlds) but these aren’t really relevant to the issue of rigid designation. So, for example, I don’t think your claim that:
I think what I’m actually trying to say is that what constitutes a rigid designator, among other things, seems to depend very strongly on the resolution at which you examine possible worlds.
Follows from your argument (for the reasons I’ve outlined above, recap: from the fact that humans often specify sets of worlds rather than worlds nothing about rigid designation follows), even though I think your argument is an insightful one that raises interesting epistemic and practical issues for possible worlds.
First thing to note, possible worlds can’t be specified at different levels of detail.
Let’s take possible worlds to be sets of propositions and truth values.
I think that these two desires are contradictory. Part of what I’m trying to say is that it’s a highly nontrivial problem which propositions are even meaningful, let alone true, if you specify possible worlds at a sufficiently high level of detail. For example, at an extremely high level of detail, you might specify a possible world by specifying a set of laws of physics together with an initial condition for the universe. This kind of specification of a possible world doesn’t automatically allow you to interpret intuitive referents like “I,” so the meaning of a statement like “I am holding a glass of water” is extremely unclear.
you have raised concerns for practical issues (how we specify worlds) and epistemic issues (how we know what’s in worlds) but these aren’t really relevant to the issue of rigid designation.
How do you know what things are rigid designators if you neither know how to specify possible worlds nor how to determine what’s in them?
Okay, perhaps I can have another go at this.
First thing to note, possible worlds can’t be specified at different levels of detail. When doing so we are either specifying partial possible worlds or sets of possible worlds. As rigid designation is a claim about worlds, it can’t be relative to the level of detail utilised as it only applies to things specified at one level of detail.
Second, you still seem to be treating possible worlds as concrete things rather than something in the head (or, at least, making substantive assumptions about possible worlds and relying on these to make claims about possible worlds generally). Let’s take possible worlds to be sets of propositions and truth values. In this case there’s no reason to find transworld identity puzzling. H2O exists in this world just if a relevant proposition is true (like, “I am holding a glass of H2O”). There’s also no room for this transworld identity to be relative to a context. Whether these things are puzzling depends on your account of possible worlds and it seems like if you’re account of possible worlds can’t account for transworld identity it can’t do the work required of possible worlds and so it is open to the challenge that it should be abandoned in favour of some other account.
Third, it’s important to distinguish questions about the way worlds are from questions about how they can be specified. It’s an interesting question how we should specify individual possible worlds and another interesting question whether we often do so or whether we normally specify sets of possible worlds instead. However, difficulties with specification do not undermine the concept of a rigid designator.
Fourth, even if it were a relative matter whether H2O exists in a world this wouldn’t undermine the concept of rigid designation. Rigid designation would simply imply that if this were the case then it would also be a relative matter whether water existed in that world.
The summary of what I’m trying to get at is the following: you have raised concerns for practical issues (how we specify worlds) and epistemic issues (how we know what’s in worlds) but these aren’t really relevant to the issue of rigid designation. So, for example, I don’t think your claim that:
Follows from your argument (for the reasons I’ve outlined above, recap: from the fact that humans often specify sets of worlds rather than worlds nothing about rigid designation follows), even though I think your argument is an insightful one that raises interesting epistemic and practical issues for possible worlds.
I think that these two desires are contradictory. Part of what I’m trying to say is that it’s a highly nontrivial problem which propositions are even meaningful, let alone true, if you specify possible worlds at a sufficiently high level of detail. For example, at an extremely high level of detail, you might specify a possible world by specifying a set of laws of physics together with an initial condition for the universe. This kind of specification of a possible world doesn’t automatically allow you to interpret intuitive referents like “I,” so the meaning of a statement like “I am holding a glass of water” is extremely unclear.
How do you know what things are rigid designators if you neither know how to specify possible worlds nor how to determine what’s in them?
I think this conversation is now well into the territory of diminishing return so I’ll leave it at that.