Thank you for the clarification. I agree that the question of what a possible world is is an important one, but the answer seems obvious to me: possible worlds are things that live inside the minds of agents (e.g. humans).
Water is one of the examples I considered and found incoherent. Once you start considering possible worlds with different laws of physics, it’s extremely unclear to me in what sense you can identify types of particles in one world with particles in another type of world. I could imagine doing this by making intuitive identifications step by step along “paths” in the space of possible worlds, but then it’s unclear to me how you could guarantee that the identifications you get this way are independent of the choice of path (this idea is motivated by a basic phenomenon in algebraic topology and complex analysis).
possible worlds are things that live inside the minds of agents (e.g. humans).
Yes, but almost everyone agrees with this (or at least, almost all views on possible worlds can be interpreted this way even if they can also be interpreted as claims about the existence of abstract—non-concrete—objects). There are a variety of different things that possible worlds can be even given the assumption that they exist in people’s heads (almost all the disagreement about what possible worlds are is disagreement within this category rather than between this category and something else).
Water is one of the examples I considered and found incoherent. Once you start considering possible worlds with different laws of physics, it’s extremely unclear to me in what sense you can identify types of particles in one world with particles in another type of world.
Two things: first, the claim that “water” rigidly designates H2O doesn’t imply that it must exist in all possible worlds—just that if “water” exists in a possible world then it is H2O. So if we can’t identify the same particles in different worlds then this just means that water exists in almost no worlds (perhaps only in our own world).
However, the view that we can’t identify the same particles in other worlds is a radical one and would be a strong sign that the account of possible worlds appealed to falls short (after all, possible worlds are supposed to be about what is possible and surely there are possibilities that revolve around the particles existing in our world—ie. surely it’s possible that I now be holding a glass of H2O. If your account of possible worlds can’t cope with this possibility it seems to not be a very useful account of possible worlds).
Further, how hard it is to identify sameness of particles across possible worlds will depend on how you take them to be “constructed”—if they are constructed by stipulation, ie. “consider the world where I am holding a glass of H2O” then it is very easy to get sameness of particles.
I’m not saying there’s not room for your criticisms but for them to hold requires substantial metaphysical work showing why your account, and only your account, of possible worlds works and hence that your conclusions hold.
Okay. 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.
When you say the phrase “imagine the possible world in which I have a glass of water in my hand” to a human, that human knows what you mean because by default humans only model the physical world at a resolution where it is easy to imagine making that intervention and only that intervention. When you say that phrase to an AI which is modeling the world at a much higher resolution, the AI does not know how to do what you ask because you haven’t given it enough information. How did the glass of water get there? What happened to the air molecules that it displaced? Etc.
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?
I think this is getting past the point that I can useful contribute further though I will note that the vast literature on the topic has dealt with this sort of issue in detail (though I don’t know it well enough to comment in detail).
Saying that, I’ll make one final contribution and then leave it at that: I suspect that you’ve misunderstood the idea of a rigid designator if you think it depends on the resolution at which you examine possible worlds. To say that something is a rigid designator is to say that it refers to the same thing in all possible worlds (note that this is a fact about language use). So to say that “water” rigidly denotes H2O is just to say that when we use the word water to refer to something in some possible world, we are talking about H2O. Issues of how precisely the details of the world are filled in are not relevant to this issue (for example, it doesn’t matter what happens to the air molecules—this has no impact on the issue of rigid designation).
The point you raise is an interesting one about how we specify possible worlds but not, to my knowledge, one that’s relevant to rigid designation. But beyond that I don’t think I have anything more of use to contribute (simple because we’ve exhausted my meagre knowledge of the topic)...
Thank you for the clarification. I agree that the question of what a possible world is is an important one, but the answer seems obvious to me: possible worlds are things that live inside the minds of agents (e.g. humans).
Water is one of the examples I considered and found incoherent. Once you start considering possible worlds with different laws of physics, it’s extremely unclear to me in what sense you can identify types of particles in one world with particles in another type of world. I could imagine doing this by making intuitive identifications step by step along “paths” in the space of possible worlds, but then it’s unclear to me how you could guarantee that the identifications you get this way are independent of the choice of path (this idea is motivated by a basic phenomenon in algebraic topology and complex analysis).
As I said, these are complex issues.
Yes, but almost everyone agrees with this (or at least, almost all views on possible worlds can be interpreted this way even if they can also be interpreted as claims about the existence of abstract—non-concrete—objects). There are a variety of different things that possible worlds can be even given the assumption that they exist in people’s heads (almost all the disagreement about what possible worlds are is disagreement within this category rather than between this category and something else).
Two things: first, the claim that “water” rigidly designates H2O doesn’t imply that it must exist in all possible worlds—just that if “water” exists in a possible world then it is H2O. So if we can’t identify the same particles in different worlds then this just means that water exists in almost no worlds (perhaps only in our own world).
However, the view that we can’t identify the same particles in other worlds is a radical one and would be a strong sign that the account of possible worlds appealed to falls short (after all, possible worlds are supposed to be about what is possible and surely there are possibilities that revolve around the particles existing in our world—ie. surely it’s possible that I now be holding a glass of H2O. If your account of possible worlds can’t cope with this possibility it seems to not be a very useful account of possible worlds).
Further, how hard it is to identify sameness of particles across possible worlds will depend on how you take them to be “constructed”—if they are constructed by stipulation, ie. “consider the world where I am holding a glass of H2O” then it is very easy to get sameness of particles.
I’m not saying there’s not room for your criticisms but for them to hold requires substantial metaphysical work showing why your account, and only your account, of possible worlds works and hence that your conclusions hold.
Okay. 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.
When you say the phrase “imagine the possible world in which I have a glass of water in my hand” to a human, that human knows what you mean because by default humans only model the physical world at a resolution where it is easy to imagine making that intervention and only that intervention. When you say that phrase to an AI which is modeling the world at a much higher resolution, the AI does not know how to do what you ask because you haven’t given it enough information. How did the glass of water get there? What happened to the air molecules that it displaced? Etc.
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.
I think this is getting past the point that I can useful contribute further though I will note that the vast literature on the topic has dealt with this sort of issue in detail (though I don’t know it well enough to comment in detail).
Saying that, I’ll make one final contribution and then leave it at that: I suspect that you’ve misunderstood the idea of a rigid designator if you think it depends on the resolution at which you examine possible worlds. To say that something is a rigid designator is to say that it refers to the same thing in all possible worlds (note that this is a fact about language use). So to say that “water” rigidly denotes H2O is just to say that when we use the word water to refer to something in some possible world, we are talking about H2O. Issues of how precisely the details of the world are filled in are not relevant to this issue (for example, it doesn’t matter what happens to the air molecules—this has no impact on the issue of rigid designation).
The point you raise is an interesting one about how we specify possible worlds but not, to my knowledge, one that’s relevant to rigid designation. But beyond that I don’t think I have anything more of use to contribute (simple because we’ve exhausted my meagre knowledge of the topic)...
I assume the AI could concoct some plausible explanation(s).