What is the argument for possible worlds? It sounds a bit crazy, but I would need to see the argument.

The argument seems to be that it is a way of explaining modality and subjective probability. E.g. "necessary" means in all possible worlds. A subjective probability of 50% would mean in half the possible worlds.

Is it not a possible world, that one where we do not talk about possible worlds?

He he

According to the SEP:

A rigid designator designates the same object in all possible worlds in which that object exists and never designates anything else. This technical concept in the philosophy of language has critical consequences felt throughout philosophy. In their fullest generality, the consequences are metaphysical and epistemological. Whether a statement's designators are rigid or non-rigid may determine whether it is necessarily true, necessarily false, or contingent. — Joseph LaPorte

If possible worlds talk is nonsense, then rigid designators are undefined.

First, it is unnecessary. As we can have no epistic access to any world but our own, actual world, anything we can learn, we can learn from the real world. — Dfpolis

I don't see what the argument is for the claim that it's unnecessary. We don't even have direct access to our own world, so are we able to learn anything about the actual world?

Second, if the purpose of possible worlds talk is to define the meaning of modal statements, it is circular. If a person does not understand modality, they will not understand the meaning of "possible worlds."

This is confused. Yes modal semantics are used to define modal terms like "possibility" and "necessity" and the like. That doesn't mean you cannot understand what possible worlds are, they are part of how you define the terms. How does this even follow? I could just call them "alternate world" and use the same definitions of these terms, so surely the argument isn't that the world "possible" is used to refer to these.

Third, speaking of worlds as simply "possible" allows one to confuse logical, physical and ontological possibility. — Dfpolis

Then just stipulate what type of possibility intended. This doesn't seem like a real worry.

If possible worlds talk is nonsense, then rigid designators are undefined.

Um, didn't the SEP define it in your quote?

A rigid designator designates the same object in all possible worlds in which that object exists and never designates anything else. — SEP

We don't even have direct access to our own world, so are we able to learn anything about the actual world? — MindForged

Of course we have access to our own world. The dogma of an epistic gap is nonsense to anyone schooled in Aristotle. For example, an object's modification of our sensory state is identically our sensory representation of the object. As one state belongs both to the sensed object and to the sensing subject, there is an existential penetration, not a gap. This analysis can be elaborated at length and extended to cognition, but I've already done so recently in other threads.

Yes modal semantics are used to define modal terms like "possibility" and "necessity" and the like. That doesn't mean you cannot understand what possible worlds are, they are part of how you define the terms. How does this even follow? I could just call them "alternate world" and use the same definitions of these terms, so surely the argument isn't that the world "possible" is used to refer to these. — MindForged

No, it is not confused. If you do not understand "possible" or "necessary" you will not understand "possible world." I do not define "possible" in terms of worlds. P is possible if P does not contradict the set of propositions which it is possible with respect to. P is metaphysically possible if it does not contradict the nature of being. P is logically possible if it does not contradict what we know. P is physically possible if it does not contradict the laws of nature. No appeal to "alternate facts" a la Kelly Ann Conway.is required.

Further "alternate world" does not mean "possible world." I may imagine any number of alternate worlds that are not self consistent, and so impossible. If you want to bring in the concept of self-consistency, you may, but then you're not defining modality in terms of a set of worlds, but following my definition of the last paragraph.

Then just stipulate what type of possibility intended. This doesn't seem like a real worry. — MindForged

Yes, it is, because it leads back to circularity. To define any type of possibility you must specify what makes a world "possible" in that way -- which means that you need an independent definition of that mode of possibility -- in other words, the worlds cease to be a primitive, and are merely an unparsimonious wart on your theory.

If possible worlds talk is nonsense, then rigid designators are undefined.

Um, didn't the SEP define it in your quote? — MindForged

Yes, in terms of the nonsensical concept of "possible worlds." Let's take Kirpke's famous example, "Hesperus is identical with Phosphorus." According to the SEP "an identity statement in which both designators are rigid must be necessarily true if it is true at all, even if the statement is not a priori."

Is there an a priori possible world in which one planet appear in the sky in the evening and another in the morning? I don't see why not. It might be argued that such a world would violate some law of nature, but the laws of nature are known a posteriori. So, if you use this argument, "Hesperus is identical with Phosphorus" not by necessity, but contingently.

So, Kirpke is pulling a swindle. There is nothing about "Hesperus is identical with Phosphorus" that makes it anything but contingent. "Hesperus" does not mean "Venus." it means a planet seen in the evening, which we have since identified as Venus. Similarly, "Phosphorus" does not mean "Venus." It means a planet seen in the morning, which we have since identified as Venus.

Now you can say that "Hesperus" and "Phosphorus" are "rigid designaters," but there is no intelligible property that allows us to determine one way or the other if they are. Then, you can hypothesize people in all possible worlds will apply these terms as we do. Again, there is no factual basis for doing so. Then, because of these arbitrary and baseless constructs, you can say that "Hesperus is identical with Phosphorus" is necessarily true.

Clearly, the conclusion is nonsense, because "necessarily," does not even follow the norms of possible worlds talk. There are many worlds that seem perfectly possible where this is not so, but they are excluded by hypothesis and arbitrary dictate.

For example, an object's modification of our sensory state is identically our sensory representation of the object. As one state belongs both to the sensed object and to the sensing subject, there is an existential penetration, not a gap. — Dfpolis

There's no possible way to justify this, you only have access to your perceptions. The world of perception is not identical to the world itself. It would be akin to treating a photograph as identical to the scene it depicted. Neither are identical, some things are true of one that is not true for the other. Ergo they are not identical. That is an epistemic gap, even if we made the stupid assumption that our sensory representations were perfect.

If you do not understand "possible" or "necessary" you will not understand "possible world." — Dfpolis

Demonstrate that. Possible world's really just a tool to explain set of concepts. You're getting hung up on the name for and leaping of the conclusion that it's circular.

I do not define "possible" in terms of worlds. P is possible if P does not contradict the set of propositions which it is possible with respect to.

That isn't an explanatory definition at all. You just defined possibility and used possibility within the definition. That's a complete failure as an understanding of modal concepts.

Further "alternate world" does not mean "possible world." I may imagine any number of alternate worlds that are not self consistent, and so impossible. If you want to bring in the concept of self-consistency, you may, but then you're not defining modality in terms of a set of worlds, but following my definition of the last paragraph.

It means the same thing if I define that way. The issue is you getting hung up on the word possible appearing in the name of the concept. As it doesn't appear in the definition of possible worlds, your criticism of it are off base. That said, some alternate worlds can exist and some cannot. The criterion of consistency doesn't favor your definition at all because it was a circular definition. That's why no one uses that understanding of modality in philosophy.

Yes, it is, because it leads back to circularity. To define any type of possibility you must specify what makes a world "possible" in that way -- which means that you need an independent definition of that mode of possibility -- in other words, the worlds cease to be a primitive, and are merely an unparsimonious wart on your theory. — Dfpolis

Lack of parsimony as compared to what? Not only are the usual definitions of the various modalities almost exactly as you defined them in your post, it's only your provided definition that was circular.

Now you can say that "Hesperus" and "Phosphorus" are "rigid designaters," but there is no intelligible property that allows us to determine one way or the other if they are. — Dfpolis

No intelligible property? Seriously? So taking a particular path in the sky, being the second planet from the Sun, having a particular level of brightness, having a certain atmospheric composition (etc) are unintelligible properties? The whole point is that we are talking about worlds in which Venus (and the solar system) exists and that the identity statement "Hesperus is Phosphorus" is therefore necessarily true because they pick out the same object *in worlds where the relevant objects exist*. So when you say things like this:

Is there an a priori possible world in which one planet appear in the sky in the evening and another in the morning? I don't see why not — Dfpolis

I can only conclude you don't know what a rigid designator is beyond reading the introductory sentence on the SEP, because as the article goes on to say:

Hesperus = Phosphorus’ is necessarily true if true at all because ‘Hesperus’ and ‘Phosphorus’ are proper names for the same object. Like other names, Kripke maintains, they are rigid: each designates just the object it actually designates in all possible worlds in which that object exists, and it designates nothing else in any possible world. The object that ‘Hesperus’ and ‘Phosphorus’ name in all possible worlds is Venus. Since ‘Hesperus’ and ‘Phosphorus’ both name Venus in all possible worlds, and since Venus = Venus in all possible worlds, ‘Hesperus = Phosphorus’ is true in all possible worlds.
— SEP

Clearly, the conclusion is nonsense, because "necessarily," does not even follow the norms of possible worlds talk. There are many worlds that seem perfectly possible where this is not so, but they are excluded by hypothesis and arbitrary dictate. — Dfpolis

There's is no world where the planet Venus and our solar system exists like ours and in which "Hesperus is Phosphorus" is false.

This thread is confused. Possible worlds are pieces of a technical apparatus that allow a model-theoretic interpretation of a language with modal operators. They have no metaphysical or ontological import in of themselves – only a supplementary theory as to what they are intended to model can provide this. If you want to get into possible world semantics, my suggestion would be to actually study the formal systems themselves, rather than leaping into metaphysical speculation about its consequences – this is useless unless you first know what you're dealing with.

It is possible to be a realist about possible worlds, like David Lewis, but his position isn't one anybody takes seriously. If you're curious about what the more or less mainstream position is regarding them, check out Jaakko Hintikka's 1969 chapter, 'Semantics for Propositional Attitudes.'

Is there an a priori possible world in which one planet appear in the sky in the evening and another in the morning? I don't see why not. It might be argued that such a world would violate some law of nature, but the laws of nature are known a posteriori. So, if you use this argument, "Hesperus is identical with Phosphorus" not by necessity, but contingently.

So, Kirpke is pulling a swindle. There is nothing about "Hesperus is identical with Phosphorus" that makes it anything but contingent. "Hesperus" does not mean "Venus." it means a planet seen in the evening, which we have since identified as Venus. Similarly, "Phosphorus" does not mean "Venus." It means a planet seen in the morning, which we have since identified as Venus.

Now you can say that "Hesperus" and "Phosphorus" are "rigid designaters," but there is no intelligible property that allows us to determine one way or the other if they are. Then, you can hypothesize people in all possible worlds will apply these terms as we do. Again, there is no factual basis for doing so. Then, because of these arbitrary and baseless constructs, you can say that "Hesperus is identical with Phosphorus" is necessarily true.

Clearly, the conclusion is nonsense, because "necessarily," does not even follow the norms of possible worlds talk. There are many worlds that seem perfectly possible where this is not so, but they are excluded by hypothesis and arbitrary dictate. — Dfpolis

This fundamentally misunderstands Kripke. Read Naming and Necessity.

If a person does not understand modality, they will not understand the meaning of "possible worlds — Dfpolis

My understanding is that the modality the possible worlds paradigm seeks to explain is not the fancy modality of modal logic, but the modality of everyday speech, when we say something is possible, impossible or certain.

If that's correct then it would be hard to find someone that doesn't have at least a folk understanding of those notions. I think only a small proportion of those could clearly articulate their folk understanding.

FWIW my attempt at articulating what I understand by those concepts is:

- if somebody says X is impossible (certain) they mean they expect that, if X happened (didn't happen), they would be so astonished that they would have to revise major parts of their worldview
- if somebody says X is possible they mean they expect that, if X happened (didn't happen), they would NOT be so astonished that they would have to revise major parts of their worldview

There's no need for possible worlds in that interpretation. I can't personally see any value in the possible worlds paradigm.

My understanding is that the modality the possible worlds paradigm seeks to explain is not the fancy modality of modal logic, but the modality of everyday speech, when we say something is possible, impossible or certain. — andrewk

But the everyday use of modal notions are what goes into how they're used in modal logic, no? Otherwise it would just be another area of pure mathematics that would be of little interest to mainstream philosophy, and yet there it is.

There's no need for possible worlds in that interpretation. I can't personally see any value in the possible worlds paradigm. — andrewk

Well the value is giving real, rigorous definitions of these notions that allows us to be confident in using them in theorization. The definitions you gave don't work. When people say "It's impossible that X", they do not always mean the "it would astonish" me stuff you used. Consider a regular Joe hearing someone say "It's raining and it's not raining outside". Understood naturally, he's obviously going to respond "That's impossible" because it's contradictory. Not that it happening we require large changes to his world view, but that the described scenario could not occur. Possible worlds talk allows us to give a more solid definition and semantics without being circular. Notice that I said "could not", which is a modal notion - it's just another way of saying "imppssible' - so that was technically circular.

My understanding is along the lines of what @Snakes Alive said (I think). For a modal realist like Lewis possible worlds serve as a reductive explanation of (one type of) modality, but that is a minority view. For the rest, possible worlds talk is just that - talk. It's a metaphorical interpretation of (some) modalities. It neither explains (in the way Lewis's realism does) nor replaces modality - it's just an informal and intuitive language. Whenever possible worlds language is used, you can replace it with the appropriate formalism.

That example is of something nobody would ever say and expect to be taken seriously. I don't regard the lack of applicability to something nobody would ever seriously say as any reason to discount a definition.

I am pretty confident that, given the choice between my interpretation and one involving all the metaphysical baggage of the possible worlds paradigm, that average person would say that mine is the closest to what they meant.

Possible worlds is just a way of talking and reasoning about modal logic.

necessarily p (holds for all consistent worlds): □p ⇔ ∀w∈W p
possibly p (holds for some consistent world): ◊p ⇔ ∃w∈W p

where W = consistent or non-contradictory worlds, or some subset thereof under consideration

If you don't like it or don't like modal logic, well, then you're free to throw it out or ignore it. :)
I guess we sometimes think of (alternate) possibilities in terms of "free will", "could have done differently".

Modal realism is the hypothesis that all possible worlds are real (not just hypothetical).

I am pretty confident that, given the choice between my interpretation and one involving all the metaphysical baggage of the possible worlds paradigm, that average person would say that mine is the closest to what they meant. — andrewk

That may be so but if you ask ordinary people what they mean when they say that something is possible or impossible (and not provide determinate contexts of use of those words) they aren't likely to disambiguate between different senses of 'possibility', which a somewhat more careful conceptual analysis would. The specific paradigm of use that will first come to their mind likely will orient their initial responses in a way that wouldn't match the way in which they actually use and understand those modal operators in accordance with several other paradigms of use. If you look at the arguments that Kripke adduces in Naming and Necessity -- for instance, arguments in favor of the thesis that proper names are rigid designators or that numerical identity is a metaphysically necessary relation -- most of them aren't grounded into contentious metaphysical theses but rather into ordinary intuitions and ordinary linguistic practices.

That example is of something nobody would ever say and expect to be taken seriously. I don't regard the lack of applicability to something nobody would ever seriously say as any reason to discount a definition. — andrewk

That's irrelevant, the point can be generalized to instances where speakers don't know they're contradicting themselves but other people do and thus they say the asserted contradiction is impossible without any recourse to "it would tear apart my worldview". And further, I don't regard narrowly applicable conceptualization of these ideas as any reason to endorse the definitions you gave.

The problem is the common sensical notions won't be able to be used broadly to understand many instances of how we use modal concepts and so it fundamentally doesn't do the job we use possible worlds semantics to accomplish (that is, to give a rigorous account of these ideas).

There's no possible way to justify this, you only have access to your perceptions. — MindForged

Perceptions aren't simply physical states, they're intentional states. While physical states have no intrinsic significance, intentional states do. Perceptions are invariably perceptions of something. (Think of Brentano and aboutness.) Whatever you may think of that something, it's what we mean by "the object of perception." So, to say that we do not perceive what we are perceiving is an oxymoron and an abuse of language.

Consider this in a different Aristotelian way: In coming to know, we are informed. Whatever informs us must have the capacity to inform us (intelligibility), or it couldn't inform us. Further, in coming to know, a single act actualizes both our capacity to be informed and the intelligibility of the object. Since the identical act makes both the object's intelligibility actually known and informs us, there is no epistic gap between knower and known.

Locke was wrong in saying we only know our ideas. Rather, our ideas are means or instrumentalities by which we know. It is only in retrospect that we realize that some means, which we call "ideas," must have been employed. So, ideas are not the primary object of our knowledge, but only inferred retrospectively as means.

The world of perception is not identical to the world itself. — MindForged

On the Kantian interpretation, this is meaningless. Meanings need to be cashed out in terms of human experience. What possible experience could cash out "the world itself," when, by hypothesis it is inaccessible to experience?

By "reality" we mean what's revealed in reliable experience. So, to say that what we experience is not "real" is an oxymoron. It's a sign of deep confusion and wanton disregard of parsimony to posit something intrinsically unknowable -- all the more if one thinks the posit is more "real" than reality.

On a different interpretation, perception is not identical with, nor does it exhaust, reality. Still, it is a projection of reality in two senses: (1) It is reality dynamically projecting itself into us. (2) It provides a projection (a dimensionally diminished map) of reality. Perception presents only part of reality. Full identity would be an absurd claim. Still, the world informing us is identically us being informed by the world..

Lack of full identity is not an epistic gap. Thinking knowledge can't be true unless it is exhaustive is the Omniscience Fallacy -- making divine omniscience the paradigm of human knowing. We're not omniscient, but that doesn't mean we're out of touch with reality -- as "gap" implies.

Possible world's really just a tool to explain set of concepts. — MindForged

Yes, most of which are modal concepts, hinging on possibility and its correlative, necessity. So, yes, possible worlds talk is circular. I have seen "necessary" defined as true in all possible worlds. Since "necessary" means the contrary is not possible, this is circular.

I do not define "possible" in terms of worlds. P is possible if P does not contradict the set of propositions which it is possible with respect to.

That isn't an explanatory definition at all. You just defined possibility and used possibility within the definition. — MindForged

Yes, I used "possible" -- not essentially, but to avoid circumlocution. So, here's the same definition restated: "P is possible with respect to a set of facts, S, if P does not contradict the propositions expressing S." Again, there is no need to violate parsimony with the possible worlds construct.

It means the same thing if I define that way. — MindForged

No, a circular definition is no definition, whereas my proposal is an actual definition.

The issue is you getting hung up on the word possible appearing in the name of the concept. — MindForged

No, what I'm "hung up" on is the construct of unknown and unknowable worlds when all actual knowledge is based on the one real world. The more "moving parts" in your philosophy, the more there is to go wrong. Still, one can't know if a world is possible unless you know what possible means.

The criterion of consistency doesn't favor your definition at all because it was a circular definition. — MindForged

Really? My definition uses no modal concepts. So it reduces modality to more fundamental, non-modal concepts. It does not assume, as possible worlds definitions do, that one already knows what "possible" means.

Lack of parsimony as compared to what? — MindForged

Compared to not positing an indefinite number of "possible worlds" when we don't know that even one beyond the actual world is possible.

Not only are the usual definitions of the various modalities almost exactly as you defined them in your post — MindForged

Doesn't this contradict your earlier claim: "no one uses that understanding of modality in philosophy"?

No intelligible property? Seriously? So taking a particular path in the sky, being the second planet from the Sun, having a particular level of brightness, having a certain atmospheric composition (etc) are unintelligible properties? The whole point is that we are talking about worlds in which Venus (and the solar system) exists and that the identity statement "Hesperus is Phosphorus" is therefore necessarily true because they pick out the same object *in worlds where the relevant objects exist*. So when you say things like this: — MindForged

I stand by what I said. "Rigid designator" is supposed to be a property of a term. The properties you mention are properties neither of "Hesperus" and "Phosphorus," nor of the concepts, <Hesperus> and <Phosphorus>, they express. They are properties of reality (which you inconsistently claim is not knowable). Further, they are not metaphysical properties (as would be required by Kripke's claim of metaphysical necessity), but contingent physical properties.

Neither the concept <Hesperus> nor the concept <Phosphorus> necessarily includes notes such as <taking a particular path in the sky> or <being the second planet from the Sun>. These are empirical discoveries.

While "Hesperus," "Phosphorus," and "Venus" all name the same planet, they don't all express the same concept. Concepts are elicited by specific kinds of experiences. <Hesperus> and <Phosphorus> are elicited by the experience of seeing a light in the evening and morning skies respectively. So, "Hesperus is Phosphorus," literally means "The experience of seeing a light in the evening sky is the experience of seeing a light in the morning sky" -- a claim that is not only false, but nonsensical.

What Kirpke did, then, is ignore a conceptual analysis in favor of a theory of meaning based on logical atomism. In it, "Hesperus," "Phosphorus," and "Venus" all have the same meaning because they all name the same planet. He sees meaning as no more than naming objects. Venus seen in the morning is not Venus seen in the evening, even though both are seeing Venus.

As I pointed out in my critique, your analysis does not consider all possible worlds, only those consistent with certain contingent facts. As you are constraining possibility with contingent facts, the result is only necessary contingently, not metaphysically necessary. For there are possible worlds in which the light in the morning sky has a different source than the light in the evening sky -- even though they both exist, along with a second planet from the sun.

Propositions are only metaphysically necessary if they are true independently of contingent facts.

I can only conclude you don't know what a rigid designator is beyond reading the introductory sentence on the SEP — MindForged

No, I used the SEP quote to define "rigid designator." Let's look at the argument you go on to quote.

Hesperus = Phosphorus’ is necessarily true if true at all because ‘Hesperus’ and ‘Phosphorus’ are proper names for the same object. Like other names, Kripke maintains, they are rigid: each designates just the object it actually designates in all possible worlds in which that object exists, and it designates nothing else in any possible world. — SEP

This is a baseless assertion by Kripke.

First, proper names name one, not multiple, individuals. So, to say it's nonsense to say that "Venus" names the same object in every possible world because Venus does not exist in every possible world. We might find a planet corresponding to Venus in various possible worlds (if there are any), but they would be different individuals (because things are individuated by their relational context and the worlds would not be different unless they provided different contexts). Calling them all "Venus" means that "Venus" ceases to be a proper name and becomes a universal term.

Second, as I argued above, "Hesperus" and "Phosphorus" express different concepts and so they are never identical.

Third, how does Kripke know what "Hesperus" and "Phosphorus" mean in any possible world? As their meaning is conventional, the denizens of each possible world might use them to designate other objects or not use them at all. Kripke has no way of knowing. So, when Kripke says they designate the same object in every possible world in which the object exists, he means he has decided to use the terms in this universal way. So, there is no fact of the matter beyond Kripke choice of naming conventions. Thus, all Kripke has done is define his conclusion into existence: the claim "'Hesperus is Phosphorus' is metaphysically necessary" has no factual basis beyond Kripke's choice of naming conventions.

There's is no world where the planet Venus and our solar system exists like ours and in which "Hesperus is Phosphorus" is false. — MindForged

And there is none in which it is true, because merely possible worlds do not exist.

Dfpolis: you can stop writing paragraphs and paragraphs of text. Read my previous posts – you're uninformed about this matter. Read up on it. You're wasting energy.

Possible worlds are pieces of a technical apparatus that allow a model-theoretic interpretation of a language with modal operators. They have no metaphysical or ontological import in of themselves – only a supplementary theory as to what they are intended to model can provide this — Snakes Alive

I agree. My main problem with possible worlds semantics is pragmatic. By placing a layer of construct between reality, which alone can be a source of actual knowledge, and theoretical conclusions, it obscures the irrationality of conclusions such as Kripke's that "'Hesperus is Phosphorus' is metaphysically necessary."

There's no need for possible worlds in that interpretation. I can't personally see any value in the possible worlds paradigm. — andrewk

We agree. If it does not help clarify, but does help obscure, it is of little value.

Well the value is giving real, rigorous definitions of these notions that allows us to be confident in using them in theorization. — MindForged

But, how can we be certain about anything that does not really exist? We know our world is possible because if it were not, it would not be actual, but when we are dealing with possible worlds all we have is worlds we imagine to be possible, but which might have covert inconsistencies. The idea that there could be worlds with slightly different physical constants and life seems possible, but it's not. Another example is the problem is making proper names universal to apply them to individuals in other worlds a la Kripke. A third problem, the one that got me thinking about this, is using possible worlds to give meaning to subjective probabilities.

Dfpolis: you can stop writing paragraphs and paragraphs of text. Read my previous posts – you're uninformed about this matter. Read up on it. — Snakes Alive

Feel free to tell me why 'Hesperus is Phosphorus' is metaphysically necessary when it is actually false. Or, how anyone can know what "Hesperus" and "Phosphorus" mean to the denizens of a possible world. Or, how a proper name can be universally predicated and remain a proper name.

Feel free to tell me why 'Hesperus is Phosphorus' is metaphysically necessary when it is actually false. Or, how anyone can know what "Hesperus" and "Phosphorus" mean to the denizens of a possible world. Or, how a proper name can be universally predicated and remain a proper name. — Dfpolis

If you're going to rail against someone's claims, it would be best to read that person's work and understand what those claims are first.

Read up on it. — Snakes Alive

Yes. The SEP has a good entry on rigid designators. Another good place where to start is Gregory McCulloch's book The Game of the Name: Introducing Logic, Language, and Mind, Clarendon Press, 1994.

The SEP article is what I read.

Then you should have read this in it, for instance, at the beginning of section 1.2:

First, a rigid designator is used in a certain way in the actual world. Given that meaning, it designates the same object with respect to all possible worlds, regardless of how this term is used, or not used, in those other possible worlds...

which would have told you that this purported objection is misguided:

Or, how anyone can know what "Hesperus" and "Phosphorus" mean to the denizens of a possible world. — Dfpolis

A term being a rigid designator does not mean that the term means the same thing as used in any possible world, as if the word itself necessarily meant a certain thing, and couldn't have been used another way. Rather, it means that its actual meaning is such that, as evaluated in the modal logic with respect to other worlds, its denotation is constant.

which would have told you that this purported objection is misguided:

Or, how anyone can know what "Hesperus" and "Phosphorus" mean to the denizens of a possible world. — Snakes Alive

If you read the full objection, you'd see that this is a rhetorical step, not the full objection.

If you read the full objection, you'd see that this is a rhetorical step, not the full objection. — Dfpolis

I don't understand what your full objection purports to be either. Your objection seems to rely on analyzing "Hesperus" and "Phosphorus" as definite descriptions rather than proper names. If they are thus analysed, then Kripke's remark about the metaphysical necessity of numerical identity don't apply. Kripke would readily agree that the statement "Hesperus is Phosphorus" expresses a contingent identity in the case where "Hesperus" and "Phosphorus" are shorthand expressions for definite descriptions that merely happen to have the same reference in the actual world.

The full objection was:

how does Kripke know what "Hesperus" and "Phosphorus" mean in any possible world? As their meaning is conventional, the denizens of each possible world might use them to designate other objects or not use them at all. Kripke has no way of knowing. So, when Kripke says they designate the same object in every possible world in which the object exists, he means he has decided to use the terms in this universal way. So, there is no fact of the matter beyond Kripke choice of naming conventions. Thus, all Kripke has done is define his conclusion into existence: the claim "'Hesperus is Phosphorus' is metaphysically necessary" has no factual basis beyond Kripke's choice of naming conventions. — Dfpolis

I am sorry if my shorthand reference to my objection was misleading. The objection is that since we can't know what the denizen call things, "Hesperus" and "Phosphorus" are applied as a result of Kripke's fiat and not as the reflection of any known fact. In other words, they designate, not the same thing, but the same kind of thing, in all possible worlds in which that kind of thing exists solely by fiat. So, there is no fact of the matter -- only an arbitrary convention.

I am sorry, I accidentally clicked post before I was done, and there seems to be no way of undoing a post. So I continued in another post.

Your objection seems to rely on analyzing "Hesperus" and "Phosphorus" as definite descriptions rather than proper names. — Pierre-Normand

That part of my objection is that words express concepts, so if you want to know what they mean, you have to examine the concepts in terms of the experiences that elicit them. The reason that an empirical discovery is required for the identification is that the concepts are anything but identical.

So, to say that we do not perceive what we are perceiving is an oxymoron and an abuse of language. — Dfpolis

That's not what I said. I said that perception is not identical to reality, which is what you said.

Yes, I used "possible" -- not essentially, but to avoid circumlocution. So, here's the same definition restated: "P is possible with respect to a set of facts, S, if P does not contradict the propositions expressing S."

A consistent "set of facts" is one way of articulating what a possible world is so I don't even know what you think you're arguing against at this point.

No, a circular definition is no definition, whereas my proposal is an actual definition. — Dfpolis

The standard definitions are not circular at all. Now you're just making things up.

By "reality" we mean what's revealed in reliable experience. So, to say that what we experience is not "real" is an oxymoron — Dfpolis

Naturally "reliable" is doing all the work here, being used to obfuscate the fact that there's no guarantee that perception maps to reality such that we can have an infallible means by which to say some experience is reliable. It's like you've never considered any objection to your views ever.

Yes, most of which are modal concepts, hinging on possibility and its correlative, necessity. So, yes, possible worlds talk is circular. I have seen "necessary" defined as true in all possible worlds. Since "necessary" means the contrary is not possible, this is circular. — Dfpolis

What? Necessity is indeed defined as truth in all possible worlds [of the set of worlds being quantified over], and yes X being necessary entails that it's negation is not possible. Where is the circularity? Necessity and possibility are simply dual concepts, and thus like may logical and mathematical things they are defined in terms of each other. What are you on about?

First, proper names name one, not multiple, individuals. So, to say it's nonsense to say that "Venus" names the same object in every possible world because Venus does not exist in every possible world. — Dfpolis

This is exactly what I was talking about, you don't understand this topic. These name something in the actual world. The meaning of the term is fixed across worlds within modal logic because it's a name, not a description. A definite description like "The brightest star in the sky" will fail to pick out the same object across worlds for obvious reasons. But that's not how proper names work, they pick out a specific object in the actual world, and the meaning of that name is fixed in modal logic (unless you just reject modality outright in which case this thread is pointless).

As I pointed out in my critique, your analysis does not consider all possible worlds, only those consistent with certain contingent facts. As you are constraining possibility with contingent facts, the result is only necessary contingently, not metaphysically necessary. For there are possible worlds in which the light in the morning sky has a different source than the light in the evening sky -- even though they both exist, along with a second planet from the sun. — Dfpolis

I'm done, you are literally ignoring key parts of the theory (or you don't know them) and thus are somehow skipping over the obvious. Obviously "Hesperus=Phosporus" isn't true in the possible worlds where the references to the terms do not exist. That in itself constrains the worlds being quantified over to the set of worlds where the object exists. That fixed denotation is exactly what makes these rigid terms, and thus examples of metaphysically necessary, a posteriori truths.

That part of my objection is that words express concepts, so if you want to know what they mean, you have to examine the concepts in terms of the experiences that elicit them. The reason that an empirical discovery is required for the identification is that the concepts are anything but identical. — Dfpolis

As Frege pointed out, names have a sense and a reference. For a time, it has been contentious whether the Fregean senses of proper names are equivalent to definite descriptions or if they rather are object dependent (i.e. "singular senses"). Kripke has argued for the latter thesis (as have Hilary Putnam, Gareth Evans, David Wiggins, John McDowell and several others). If we accept that the senses of proper names are object dependent, that doesn't preclude them having conceptual contents as well. The objects that we name typically fall under sortal concepts that express their conditions of persistence, identity and individuation. This is all consistent with Kripke's claim that proper names function as rigid designators, and also with his claim that statements of identity of the form "A is B", where "A" and "B" are proper names, are metaphysically necessary.