So in a world where the apple does not exist, the haecceity "being that apple" exists, and is unexemplified. — Banno

To my present understanding:

If I say “the apple might be on the table”, then there is a possible world where the apple is on the table.

Following (23) ◇∃xTx is true if there is an accessible world in which ∃xTx, it is possible that for some apple, the apple is on the table is true if there is an accessible world in which for some apple, the apple is on the table.

As you say, we need to specify what kind of worlds we are talking about, and may decide to limit possible worlds to those worlds that have the same natural laws as ours. The SOA, the apple is on the table, may exist even though it does not obtain. One advantage of the Trace Actualists is that a State of Affairs (SOA) may exist even though it does not obtain.

Here, “exist” is being used in a particular way. This has a different meaning to ordinary language, where exists means obtains.

For Wittgenstein in The Tractatus, if a SOA obtains then it is a fact in our actual world. Then it is a fact that the apple is on the table.

However, if in our actual world the proposition “the apple is on the table” is false because there is no apple on the table, the proposition “the apple might be on the table” is true because there might be an apple on the table, prescribing accessible worlds as having the same laws of nature as ours.

Therefore, in order to accommodate modal semantics, even though the SOA the apple is on the table does not obtain, the possibility of there being an apple on the table requires some kind of existence.

The New Actualists solution is that the apple exists in a concrete sense. Even if not necessarily concrete in an actual world, contingently concrete in a possible world.

The Haecceitists' solution, as for Plantinga, the apple exists in its haecceity, both in the actual world and all possible worlds. This haecceity is not Platonic Realism, where the property of appleness exists even if never instantiated by an apple. This haecceity is not that of mental abstract concepts independent of any physical manifestation.

Heicceity is an historic term, going back to John Duns Scotus in the 13th C, who proposed that although an object is no more than its set of properties, haecceity makes the object unique and different to any other object.

The idea was continued by Leibniz in his Principle of the Identity of Indiscernables, where even though two objects sharing the same properties must be identical, they remain unique and different to all other objects because of their haecceity.

For Plantinga, every entity exists and has a unique haecceity, a primitive “thisness” that cannot be reduced to anything else, and has this haecceity even in those worlds where the entity does not obtain.

Then how to explain Plantinga’s haecceity as something that exists in a mind-independent world, especially as he is neither proposing Platonic Realism nor suggesting that haecceity exists as a mental concept.

How can the haecceity of an apple exist in the world even though no apples exist in the world?

Perhaps the answer to this may be given by those who believe that numbers are discovered and not invented. I personally believe that numbers are invented in the mind. However, there are those who believe that numbers are discovered in the world, such that the number 9 exists in the world even though never instantiated in the world. In this sense, numbers may also have an haecceity.

If there were, problems would arise. Suppose an haecceity of Theseus’s ship existed in the world even though Theseus’s ship did not obtain in the world. We know that parts of Theseus’s ship can be removed. Then for every possible configuration of Theseus’s ship there world be a different haecceity in the world, becoming infinite in number.

Even if Platonic Realism is dismissed, haecceity as a mental concept can be understood, but Plantinga is suggesting the haecceity of an individual exists in a mind-independent world even in the absence of that individual.

The fact that Alvin Plantinga is a Christian philosopher, and a defender of theism, may take the nature of his haecceity into the spiritual realm and away from the material realm. But that is another story.

Several ideas are introduced here, one being to obtain. — frank

My understanding of 2.2.3

There are Concretists such as Lewis and Abstractionists such as Plantinga.

For the Abstractionsists:
There is the actual world, an actual world, a State of Affairs that exists and obtains.
There are possible worlds, non-actual worlds, States of Affairs that exist but fail to obtain.

Most Abstractionalists are Actualists.

There are two types of Actualists, Trace Actualists and No-trace Actualists.

The problem with No-trace Actualists is that they cannot explain standard modal semantics, in that it is possible that for some x, x is an Exotic. But for the No-trace Actualists, there is no x.

There are two types of Trace Actualists, New Actualists and Haecceitists.

Trace Actualists can explain standard modal semantics, in that things, whether objects or properties, do exist in possible worlds. It is possible that for some x, x is an Exotic (so different to an actual object that no actual object could be an Exotic)

It is possible that on the table is an apple. There is a possible world where the apple is on the table.

For the New Actualists, the apple necessarily exists, but is not necessarily concrete. The apple is only contingently concrete.

For the Haecceitists, such as Plantinga, even though in a possible world the apple does not exist, the property “being an apple” does exist.

For Trace Actualists, things in possible worlds can exist. This allows the modal semantics of (23) ◇∃xEx is true if there is a world in which ∃xEx

Both parts are "from the viewpoint of a mind". — Metaphysician Undercover

You say “The place signified "Chicago" is not an imaginary thing, it is understood as real, actual.”

The fact that I imagine the city of Chicago to be a real and actual place, means that the city of Chicago is in addition also an imaginary thing in my mind.
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So there is no way that we can get to the conclusion that the people in an imaginary world have a real and actual perspective. — Metaphysician Undercover

I cannot know that people in other possible worlds are real, but I can theorise that they are.

I can never know for certain that the person I am talking to is as conscious as I am, but I can theorise that they are.

Well, Homer is the author of the Iliad and the Odyssey. So presumable "Homer" designates that person whoever he may be. — Ludwig V

Continuing:

1) Suppose a single person originated the Iliad, which was either written down or passed down as part of an oral tradition.
2) Whoever originated the Iliad has been given the name “Homer”.
3) Suppose, in fact, that the Iliad was originated by Hesiod.
4) Hesiod had a friend, Homer, who was in fact a baker.

Does the name “Homer” designate Hesiod, as for Kripke’s Rigid Designation, or does “Homer” refer to “the person who originated the Iliad”, as for Russell's Theory of Descriptions?

The place signified "Chicago" is not an imaginary thing, it is understood as real, actual. — Metaphysician Undercover

This statement needs unpacking.

The first part of the statement, “The place signified "Chicago" is not an imaginary thing” is from a mind-independent viewpoint.

The second part of the statement, “it is understood as real, actual” is from the viewpoint of a mind.

The first part of the statement linguistically clashes with the second part of the statement, making it difficult to answer.
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In the case of possible worlds, they are imaginary things, not real or actual, but possible. — Metaphysician Undercover

Again, this statement needs expanding. “For whom”?

For Lewis’ Concretism, the statement is true from our viewpoint, in that from our viewpoint, these worlds are imaginary worlds, not real or actual.

But the statement is not true from the viewpoint of those people living on these worlds, in that from their viewpoint, these worlds are not imaginary worlds, are real and actual.

And the one being used in the article is Tarski’s Truth Definition. — Banno

:up:

At any rate, anyone who chooses to take possible world analysis seriously ought to understand the dependency on coherence theory of truth. — Relativist

Yes, there are many different definitions of truth (SEP - Truth). The question of what establishes the truth of a statement then depends on which definition of truth is being used.

Determinism only blocks alternative futures for this world, not alternative worlds altogether. — Banno

:up:

So is the name "Homer" a rigid designator in this case? — Ludwig V

Wikipedia Homer notes

The identity of "Homer" is a mystery, and scholars generally regard the ancient conception of a single author behind the Iliad and the Odyssey as a fictional narrative

If everything I know about Aristotle is false, how do I know that Aristotle actually existed, or is in fact a fiction.

If Aristotle, and perhaps Homer, never actually existed, yet Aristotle and Homer are rigid designators, then what is Aristotle and Homer actually designating.

Using Kripke’s necessary a posteriori, it may be that in the future it is known without a doubt whether Aristotle and Homer were real or fictional. We may only know in the future what Aristotle and Homer are designating.

Wikipedia Rigid Designator

One puzzling consequence of Kripke semantics is that identities involving rigid designators are necessary. If water is H2O, then water is necessarily H2O.

Wikipedia

In modal logic and the philosophy of language, a term is said to be a rigid designator or absolute substantial term when it designates the same thing in all possible worlds in which that thing exists.

However, if in the future it is discovered without doubt that Aristotle and Homer were not real but fictional, then today what is Aristotle and Homer designating? Presumably in that case, the names Aristotle and Homer are designating descriptions of Aristotle and Homer.

What you learnt about Aristotle enables you to refer to Aristotle — Ludwig V

Wikipedia Naming and Necessity has the comment

Scott Soames: In the philosophy of language, Naming and Necessity is among the most important works ever, ranking with the classical work of Frege in the late nineteenth century, and of Russell, Tarski and Wittgenstein in the first half of the twentieth century

For me, the Aristotle I know has a cluster of properties. Even though “Aristotle” is a rigid designator, and refers to the actual Aristotle born 384BCE and died 322 BCE, none of the properties I know Aristotle by may in fact be true.

However, Kripke argues for necessary a posteriori knowledge, that some truths can only be known through empirical observation. Therefore, even though my knowledge of Aristotle may be totally false, when I use the name Aristotle, it is still a rigid designator because the name still refers to the actual Aristotle.

We produce a fictional idea, a possibility, then to make it fit within the possible worlds semantics, we assign concrete existence to it. — Metaphysician Undercover

I have never been to Chicago, but I imagine what it could be like, and I imagine it as an actual concrete place. I can imagine that the inhabitants of Chicago think of themselves as actual and concrete as I think of myself as concrete and actual.

There is no logical problem with imagining something as being actual and concrete.

For example, if you plan on a holiday to somewhere you have never been before, you presuppose that where you are going is an actual and concrete place. As with David Lewis, in this instance, you are also a Modal Realist, a Concretist.

Therefore the description is of what the concrete possible world is like, not of what it could be like. — Metaphysician Undercover

At the end of the day, It would be logically impossible to describe something that has no causal, spatial or temporal connection to us.

======================================================

That's a very significant connection. Don't you think so? — Metaphysician Undercover

Yes, the mind is central.

There is a causal, spatial and temporal connection to the fictional world of Middle Earth, through books, films, etc.

But there is no causal, spatial or temporal connection to an actual world of Middle Earth, as we have no knowledge about it having any mind-independent existence.

A name is not like a tag, though a tag is, in some ways, very like a name. — Ludwig V

As I understand Kripke’s theory of naming, my knowledge of Aristotle is not directly tied to the reality of Aristotle in 350 BCE, but is tied to where I learnt about Aristotle, which could have been a TV program five years ago. The producers of this TV program in turn could have got their knowledge about Aristotle from Jonathan Barnes’ book “Aristotle”. Jonathan Barnes also got his knowledge from somewhere. There is a chain going back in time from my knowledge of Aristotle to the reality of Aristotle in 350 BCE.

Therefore
1 - For me, the name Aristotle is a tag to what I learnt about Aristotle.
2 - For me, I don’t know the reality of Aristotle in 350 BCE, all I know is what I have learnt about Aristotle.
3 - There is a reality to Aristotle in 350 BCE, even though I may not know what it is.
4 - I agree that we only know what we know.

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I find that remark almost impossible to understand. Such understanding as I have of it rests on my knowledge of who and what Aristotle is. — Ludwig V

Yes, you only know what you know about Aristotle.

I think that there is common agreement that Aristotle was around in 350 BCE, even if no one knows exactly what he was doing at the time.
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I've puzzled about this a great deal. Can you explain the difference to me? — Ludwig V

De re and de dicto
A de re proposition could be “Paul's favourite number 11 is necessarily prime. A de dicto proposition could be “it is necessary that Paul's favourite number 11 is prime”.

There is a difference between saying i) “your favourite drink is necessarily a hot drink” and ii) “it is necessary that your favourite drink is a hot drink”

Modal Logic K Distribution axiom
□(p→q)→(□p→□q).
If "p implies q" is true, then if p is necessarily true, q is also necessarily true

The given example

i) “Your favourite drink is possibly a hot drink” presupposes you have a favourite drink
ii) “It is possible that your favourite drink is a hot drink” does not presuppose you have a favourite drink

iii) “There are possible concrete worlds other than ours” presupposes that there are other concrete worlds
iv) “Possibly there are concrete worlds other than ours” does not presuppose that there are other concrete worlds

If a person like me, in this concrete world can describe another concrete world, then I must have some access to it, and it cannot be absolutely separate. — Metaphysician Undercover

You are not describing this other concrete world, you are describing what this other world could be like as a concrete world.
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The spatial temporal conditions of one must be similar to the spatial temporal conditions of the other, implying that there is a connection between them. — Metaphysician Undercover

In the same way that between the fictional world of Middle Earth there is no causal, spatial or temporal connection to our world other than in our mind.

Another way to ask this: what is it that establishes the truth of the statement, "there is a possible world in which Hobbits, Trolls and Orcs exist"? — Relativist

The truth of a possibility in language cannot be established using a correspondence theory

Using Donald Davidson’s truth-conditional semantics:
“There is a possible world in which Hobbits, Trolls and Orcs exist” is true IFF there is a possible world in which Hobbits, Trolls and Orcs exist.

If Determinism is true, there can only be one actual world, meaning that there cannot be possible worlds.

If Indeterminism was true, there can still only be one actual world, again meaning that there cannot be possible worlds. Ontologically, where could possible worlds exist even in an indeterminate world?

Therefore, possible worlds in language cannot correspond to possible worlds in the world.

The truth of a possibility in language can only be established using a coherence theory

From Wikipedia Cohrence (Linguistics)

Robert De Beaugrande and Wolfgang U. Dressler define coherence as a "continuity of senses" and "the mutual access and relevance within a configuration of concepts and relations".[1] Thereby a textual world is created that does not have to comply to the real world. But within this textual world the arguments also have to be connected logically so that the reader/hearer can produce coherence.

Therefore, if we can coherently talk about the possibility of Hobbits, Trolls and Orcs, which we can, then this is sufficient to ensure the truth or falsity of our statements.

But I might just suggest that there does not appear to be any reason to think there must be One True Account of reference - there may be many ways in which we can use a proper name. — Banno

Yes, there can be more than one valid performative utterance about a particular subject.

This cannot be correct. If each possible world is separate from every other, in an absolute sense, then there would be no point to considering them, as they'd be completely irrelevant. — Metaphysician Undercover

If there is no causal connection sometime in history, in what sense are they possible? — Relativist

On the other hand, I can imagine a possible world that is as concrete as ours, where the Hobbits, Trolls and Orcs that inhabit this world believe themselves as real as we believe ourselves.

But we also know that there is no causal, spatial or temporal connection between this possible concrete world of Middle Earth and our actual concrete world.

This is not saying that Middle Earth exists within literature within our world. I am not saying that Middle Earth is an imaginary world, but I am saying that Middle Earth is a possible concrete world, as concrete as our world.

It is because of the fact that there is no causal, spatial or temporal connection between Middle Earth and our world is why we can say it is a possible world.

If there was a casual, spatial or temporal connection to our world, we would know whether this world of Middle Earth existed or not, thereby negating its very possibility.

There is a difference between saying “there are possible concrete worlds other than ours” and “possibly there are concrete worlds other than ours.”

I think I am right in saying that Lewis is saying that “there are possible concrete worlds other than ours” rather than “possibly there are concrete worlds other than ours”

This cannot be correct. If each possible world is separate from every other, in an absolute sense, then there would be no point to considering them, as they'd be completely irrelevant. — Metaphysician Undercover

For Lewis’ Concretism, these possible worlds are concrete worlds.

Perhaps that why the SEP article Possible Worlds wrote:

Perhaps the biggest — if not the most philosophically sophisticated — challenge to Lewis's theory is “the incredulous stare”, i.e., less colorfully put, the fact that its ontology is wildly at variance with common sense.

Perhaps this is why the SEP article follows Lewis' Concretism with 2.2 Abstractionism, where possible worlds are abstract entities rather than concrete ones, .

Contradictory propositions cannot both be true 'at the same time and in the same sense. I was responding to your statement that the propositions needed context. — Relativist

I agree, the propositions “the sun is shining” and “the sun is not shining” cannot both be true by the law of non-contradiction if referring to the same event in the world.

How would we be able to communicate, and make sense of the things around us, when contradictory things would be true for each of us? — Metaphysician Undercover

For Lewis, possible worlds are absolutely separate, causally, temporally and spatially.

No individual in one possible world has any kind of access to any individual in a different possible world.

Certain characteristics belong with an individual in every possible world in which it exists. This account of essence is quite different to scholastic notions, but has many advantages, not the least being a clear definition. — Banno

A rich and interesting topic.

In Kripke’s theory of naming, the same name refers to the same object through time because of a causal connection of that object through time, such that Aristotle in 350BC is the same individual as Aristotle in 384BC.

However, the object in 350BC had the properties named Aristotle, a teacher, born in Stagira, bearded, etc, whilst the object in 384BC had the properties named Aristotle, not a teacher, born in Stagira, not bearded, etc.

There may appear to be a causal chain between these two objects, but as David Hume pointed out, there is no necessary connection between two events that appear to follow each other.

How does Kripke get around a name being a rigid designator when it is not known that in a causal chain one event necessarily follows another. For example, being a rigid designator would require there was a necessary connection between two events.

Also, if the set of properties of an object changes with time, how is it decided which are essential properties and which are not. For example, why should one’s parents be more essential to the identity of a person rather than their moral character.

But if the sun is actually shining, then although you don't know this fact, it is physically, metaphysically, and logically impossible for the sun to not be shining at that point of time. (Law of noncontradiction). — Relativist

There are two aspects, language and facts in the world.

“The sun is shining” is true IFF the sun is shining.

By the Law of Non-Contradiction, it is logically impossible for the fact in the world i) the sun is shining and the fact in the world ii) the sun is not shining.

However, in language, the Law of Non-Contradiction does not apply to the propositions “the sun is shining” and “the sun is not shining”.

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Yet another issue: is the sun shining at that point of time a contingent fact, or a necessary fact? — Relativist

It depends whether you have a belief in Determinism, where it would be a necessary fact, or had a belief in Indeterminism, where it would be a contingent fact.

Wikipedia
Determinism is the metaphysical view that all events within the universe can occur only in one possible way.
Indeterminism is the idea that events are not caused, or are not caused deterministically. It is the opposite of determinism and related to chance.

But Lewis' interpretation appears to be that each possible world "is" an actual world. — Metaphysician Undercover

Your statement is incomplete as it needs to add “for whom”.

For Lewis, it seems that between our world and possible worlds no world is especially favoured. Therefore, for anyone living in a world, their world is the actual world.

For us, we live in the actual world. For us, other worlds are possible worlds, but for anyone living in such a possible world, they would also consider their world to be the actual world.

A possible rewording would be “But Lewis' interpretation appears to be that each possible world "is" an actual world for the inhabitants of that world”

And yet all these people can communicate. How is that possible? There must be common elements to all these different meanings that enable communication across contexts. Those common elements are what we might call ordinary life, which is the common context that links all three people. — Ludwig V

Kripke’s solution in his Theory of Naming is that there is an historic causal chain from a something that has a name, such as Aristotle, to the initial baptism of a something given that name, such as Aristotle’s parents naming their baby Aristotle. In a sense, this baptism is the same as JL Austin’s performative utterance. Kripke’s solution bypasses any metaphysical problems as to the essence of Aristotle. The name Aristotle is just a tag to something else, and in this case that something baptised Aristotle.

Wittgenstein’s approach in Philosophical Investigations is similar. Names exist within the context of a Form of Life, “the shared background of human cultural practices, activities, and ways of living that provide the context within which language and meaning operate” (Wikipedia). When the assistant walks onto a building site for the first time, the assistant may see the builder pick something up and say “slab”. For the assistant, this is the initial baptism of something given the name “slab”. Subsequently, when the builder says to the assistant “slab”, the assistant knows what the builder is referring to. As before, the assistant does not need to know about the essences of slabs. “Slab” just means a tag in an historic causal chain going back to an initial baptism.

Similarly with “water”, as you say, me, the scientist and the linguist share a common Form of Life, where the meaning of words is understood through historical causal chains back to a common source. These common sources may be, for example, dictionaries, school, television, newspapers, etc.

There is an implied difference between the perceived world and the imaginary worlds, but both those categories are actual, so "actual" serves no purpose. — Metaphysician Undercover

I can imagine a possible world where aliens live. This imagined possible world may in fact be an actual world.

I agree that if my perceived world was “actual” and all imagined possible worlds were “actual”, then the word “actual “ would be redundant.

However, if my perceived world was “actual” and some imagined possible worlds were “actual”, then the word "actual “ would not be redundant (because some imagined possible worlds would not in fact be “actual”.)

The difference is in the quantifiers all and some.

What meaning does "actual" have here? You could remove it from your example without changing the meaning of anything. — Metaphysician Undercover

The words actual and possible are still needed.

In conversation, I might say “the sun might not be shining”, but would be confusing to a listener as it lacks context. It would be better to say “it is possible that the sun might not be shining”, as this does infer a context.

Similarly, my saying “the sun is shining” lacks context. It would be better to say “the sun is actually shining”.

The words "possible" and "actual" add context.

Well, you/Kripke have your reasons for saying that, I suppose. But it is clear that whatever "water" means is not based on that information. — Ludwig V

What does “water” mean? "Water" means different things to different people. To a scientist, "water" is necessarily H2O. To me, "water" is necessarily wet, in that if not wet it cannot be water. To a linguist, “water” is necessarily a noun. There is no one meaning of “water”, though each meaning is necessary within its own context.
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Again, perhaps so. But it follows that, whoever is called Aristotle is not necessarily the philosopher that we know and love. — Ludwig V

You love Aristotle for his philosophy. But instead of being born in Stagira, he could have been born in Athens and grown up to be a carpenter. So do you love Aristotle because of who he was or what he did?

as Berkeley pointed out, unless you can compare a representation with its original, you can't establish what, if anything, it is a representation of. — Ludwig V

True. But in our daily lives we don’t need to know what the representation is of, all we need to know is the representation.

The SEP article Possible Worlds writes “The idea of possible worlds is evocative and appealing.”

Sometimes in our daily lives we need to imagine possible worlds, and sometimes we only need to know the actual world.

For example, I perceive the colour red but believe that the colour red does not exist in a mind-independent world. Something else may exist, for example a wavelength of 700nm.

When driving and I see a red traffic light, All I need to know is that I perceive the colour red in order to stop my car. It is immaterial to me what really exists in a mind-independent world. Possibly a wavelength of 700nm exists, possibly something else. In this situation, I don’t need to know a possible world of reality, all I need to know is the actual world of representations.

As you say “It is immaterial what really exactly exists in a mind-independent world because "unreal" in this context does not have a clear meaning.”
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The implication is that the existence of the causal chain is necessary and sufficient, presumably whether or not we know it. That's extremely hard to understand, because it suggests that we do not necessarily know who Aristotle is, if anyone. — Ludwig V

Perhaps this is a similar situation to Kripke’s argument for the necessary a posteriori. Water is necessarily H20 even before anyone knew that this was the case.

Aristotle is necessarily Aristotle even if no one knows it. An instance of necessary a posteriori.
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But all possible worlds are possible actual worlds. — Ludwig V

I agree, as this seems to follow what @Banno wrote:

In standard modal logic there is exactly one actual world………………………We've a set of possible worlds, W, and we can label any one of these the actual world, w₀.

In standard modal logic there is exactly one actual world..........................We've a set of possible worlds, W, and we can label any one of these the actual world, w₀. — Banno

:grin: IE, it is wrong to say that there are actual possible worlds.

Importantly, accessibility is not causal, temporal, or epistemic unless specified. And it can be so specified. It constrains what worlds we have access to. — Banno

:grin: IE, there are different types of modal logic, and we always need to be clear which type we are referring to.

So he's saying an individual is essentially tied to particular features of its origin in a way that it is not essentially tied to particular features of its subsequent history. Further, he's saying that origin is a necessary condition, not a necessary and sufficient condition. — Relativist

The reasoning is inescapably circular! It starts with the assumption an object is the same object in a (non-actual) possible world (it has a trans-world identity) and then conclude that the object must have an essence that accounts for it being the same object. — Relativist

For Kripke, that an object, an individual such as Aristotle, is the same object in all possible worlds, is a Rigid Designator, is a consequence of his Theory of Naming.

That Aristotle is the same individual is not because of any knowledge about his essence or identity, but because of a casual chain linking Aristotle back through time to being the son of his parents at the moment of his baptism.

Kripke’s Theory of Naming thereby avoids any philosophical problems with the ontological nature of essence or identity.

That Aristotle is the same individual in different possible worlds, has the same identity and has the same essence, does not mean that Aristotle cannot be a teacher in one possible world and a carpenter in another possible world.

The individual Aristotle in all possible worlds is necessarily tied through Kripke’s Theory of Naming to his origin.

Aristotle's origin is necessary and sufficient for the identity and essence of the individual Aristotle in all possible worlds’

However, his origin is not necessary for contingent features of Aristotle, such as being a teacher or carpenter.

I don't see how actual world could only possible exist — Ludwig V

Yes, agreeing what a word means is problematic. Perhaps it is standard practice in philosophy that only our world is the actual world, and possible worlds cannot be called actual worlds .

It gets complicated. For the Indirect Realist, we only know the actual world as representations in the mind, whereas for the Direct Realist, we directly perceive an actual world existing independently of our representations of it.

You left out the other condition, "pain" must refer to everything as well. If pain refers to everything, as "actual" refers to all possible worlds, and there is no definition for "pain", then it's meaningless. — Metaphysician Undercover

There is a difference between “pain refers to everything” and “pain refers to everything that is painful.”
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The concept of "quark" misleads intellectually, by producing the illusion that something not understood is understood. — Metaphysician Undercover

Perhaps that is true. In the same vein, every concept we have misleads intellectually by producing the illusion that something not understand is understood.

For example, we have the concept of numbers, but who knows what a number is. We have the concept of pain, but who knows what pain is. We have the concept of consciousness, but who knows what consciousness is.

All concepts may mislead us, but what other choice do we have?
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Even the experience of our perceptions must be put into descriptive words before it becomes a part of the modal model. If the modal model is "the actual", then our perceptions are not. — Metaphysician Undercover

I perceive that the sun is shining. In my actual world the sun is shining.

I imagine a possible world in which the sun is not shining. It is possible that there is an actual world where the sun is not shining.

Actual worlds may exist or possibly exist.

The reasoning is inescapably circular! — Relativist

There is an escape.

Essence does not play a part in Kripke’s Rigid Designator.

As the Wikipedia article of Naming and Necessity writes:

Kripke's theory of naming, presented in his book "Naming and Necessity," argues against the descriptivist theory of names, proposing instead that names refer to objects through a causal chain originating from an initial act of naming. This means that a name's reference is fixed by its original use, rather than by a set of descriptive properties associated with the name.

Hesperus is Phosphorus is necessarily true as both refer to the same thing, Venus. That Hesperus and Phosphorus have the same identity is only known a posteriori because of empirical observation.

In Kripke’s theory of naming, there is an initial naming of a person, their baptism. In a sense, JL Austin’s performative utterance.

There is then a recursive process, a causal link between this baptised object and future objects.

For example, in possible world 5, there is a causal chain going back from Aristotle 5 to the original baptised Aristotle, meaning that Aristotle 5 is necessarily baptised Aristotle. In possible world 9, there is a causal chain going back from Aristotle 9 to the original baptised Aristotle, meaning that Aristotle 9 is necessarily baptised Aristotle. Therefore, Aristotle 5 is necessarily Aristotle 9. This means that Aristotle is a rigid designator because necessarily and causally linked to all other Aristotles.

Thereby, the baptised Aristotle = casually linked to {Aristote 1 in possible 1, Aristotle 2 in possible world 2, Aristotle 3 in possible world 3, etc}

This is an extensional definition. No intensional definition is required.

Knowing that baptised Aristotle is causally linked to Aristotle 1 tells us nothing about Aristotle’s essence.

For example that a snooker ball moves when hit by a snooker cue tells us nothing about the intrinsic nature or essence of either the snooker ball or snooker cue.

Kripke's Rigid Designator avoids such philosophical problems as to the nature of essence because based on a particular theory of naming.

Sure, but in the situation we're talking about every possible world is actual, and there's no definition as to what actual means. So "actual" is meaningless. — Metaphysician Undercover

That is like saying because there is no definitive definition of “pain” the concept of pain becomes meaningless.

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Then there is the source of my empirical experience, which is not one of the possible worlds (as these are what are in the model), therefore not actual. So I concluded that it is an illusion. — Metaphysician Undercover

No one has directly seen a quark, but only theorised about them. The Merriam Webster dictionary defines “illusion” as “something that deceives or misleads intellectually”. “Illusion” would be the wrong word to describe our understanding of quarks. Similarly with theorised possible worlds.

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No, the actual world we live in is not actual, the possible worlds are actual. — Metaphysician Undercover

It depends what the expression “the actual world we live in” is referring to.

Is it referring to i) the world as we perceive it through our senses or ii) the external world that is causing our sensations?

OK, but then "actual" has no real meaning. The world we live in isn't distinct as "the actual world", all the possible worlds are actual worlds, and there is no point to calling the world we live in "the actual world", because it's just one of many, which are more properly called possible worlds. — Metaphysician Undercover

On the keyboard in front of you are several keys. The key “t” is an actual key on the keyboard. The key “k” is an actual key on the keyboard. Because there can be more than one actual thing does not make the word “actual” meaningless.

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That the world I live in and provides my empirical experience is "the actual world" must be an illusion........................Now this produces the age old metaphysical question of why do I experience this world, and not some other......................But we still have the same sort of question, why am I in this world, not in one of those others. — Metaphysician Undercover

Because there are more than one actual keys on the keyboard in front of you does not mean that each key is an illusion. We can also ask the question, when you are pressing the actual “t” key why are you not pressing the actual “k” key instead. One answer is that you can only press one key at a time. Not a metaphysical problem but just the nature of time.

Similarly, because there are more than one actual possible worlds does not mean that each actual possible world is an illusion. We can also ask the question, when you are looking at actual possible world 5 why are you not looking at actual possible world 9. One answer is that you can only look at one actual possible world at a time. Not a metaphysical problem but just the nature of time.

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If all the possible worlds are equally "actual", how could one be presupposed and the others theoretical? Doesn't this give unequal status to their actuality? — Metaphysician Undercover

For Lewis and Concretism, we know the actual world we live in and theorise that other possible worlds are also actual.

It is true that there is an unequal status in that we inhabit one of these worlds and theorise about the others, but there is no unequal status in that all these worlds are actual

I didn't see that coming! — frank

A thought:

It seems that it is impossible to understand something from the inside. One has to step outside in order to understand something.

For example, language cannot be understood using language, it can only be understood using a meta-language.

Similarly, modal logic cannot be understood using modal logic. Lewis’s Concretism was attempting this, even though it seems he failed.

SEP - Possible Worlds
Furthermore, because worlds are (plausibly) defined entirely in nonmodal terms, the truth conditions provided by Lewis's translation scheme themselves appear to be free of any implicit modality. Hence, unlike many other popular accounts of possible worlds (notably, the abstractionist accounts discussed in the following section), Lewis's promises to provide a genuine analysis of the modal operators.

Therefore, what is needed is another way to understand modal logic without using modal logic.

Yes that's exactly the problem. What we know as the independent, physical world, source of empirical observations, can no longer be accepted as such. It gets barred off as a sort of unreal illusion, and what we're left with is an extreme idealism where the ideas (possible worlds) are the reality. — Metaphysician Undercover

Davis Lewis in his Concretism presupposes an “actual world” that we live in and theorises about possible worlds where our counterparts live in. These possible worlds are also as “actual” as our world.

However, it is not part of his theory how we have knowledge of our “actual world”.

An Indirect Realist, such as Descartes, Locke, Leibniz, Hume and Russell, or a Phenomenologist, such as Husserl, would disagree that we can know an independent, physical world independent of empirical observations.

For the Indirect Realist and Phenomenologist, an independent, physical world is not barred off as an unreal illusion, and we are not left with an extreme idealism. The Indirect Realist is a believer in the concept of Realism, and the Phenomenonologist never doubts a reality behind the phenomena.

Wikipedia - Direct and Indirect Realism
Indirect perceptual realism is broadly equivalent to the scientific view of perception that subjects do not experience the external world as it really is, but perceive it through the lens of a conceptual framework

SEP - Phenomenology (Philosophy)
The epoché is Husserl's term for the procedure by which the phenomenologist endeavors to suspend commonsense and theoretical assumptions about reality (what he terms the natural attitude) in order to attend only to what is directly given in experience. This is not a skeptical move; reality is never in doubt.

For Lewis’s Concretism, it is not a problem as how we know the "actual world” that we live in, as this knowledge is presupposed, and outside the scope of his theory about possible worlds.

It is also not a problem as to how we can know possible worlds, as this is a theory. In the same way what we know about quarks is a theory, something that has such explanatory power that it is axiomatically assumed to be true.

SEP - Possible Worlds
His theory of worlds, he acknowledges, “does disagree, to an extreme extent, with firm common sense opinion about what there is” (1986, 133). However, Lewis argues that no other theory explains so much so economically.

Lewis’s Concretism attempts to analyse modal operators in non-modal terms using the theory of possible worlds. These possible worlds are as real, actual and concrete as the world we actually live in. The “actual” world we live in is presupposed and the possible worlds are theoretical.

SEP - Possible worlds
Furthermore, because worlds are (plausibly) defined entirely in non-modal terms, the truth conditions provided by Lewis's translation scheme themselves appear to be free of any implicit modality…………………Lewis's promises to provide a genuine analysis of the modal operators.

True, although isn't there an extra conundrum with direct realism: that if it's true, then it must be false (by virtue of what we observe about how the senses work). — frank

Even though quarks cannot be directly observed through the senses, they are accepted as being real because they explain so much and so economically.

Lewis is also saying that his theory, even if not empirically verifiable, because it is so elegant and explanatory should not be dismissed because it initially seems to be against common sense.

The problem being that the possible worlds model produces a separation between the possible worlds and the actual ontological world. Then one has to be selected as the real. — Metaphysician Undercover

As I understand it, for Lewis, it is not necessary to select one of the possible worlds as real, as all possible worlds are as real as each other. All possible worlds are real concrete worlds, actual ontological worlds.

SEP - Possible Worlds
But, for the concretist, other possible worlds are no different in kind from the actual world

As an analogy, the world you live in is more than likely very different to the world I live in (the people you know, the history of your country, the local climate, the geography, the architecture), but it would be wrong to say that your world is more real than my world.

As a science fiction fan, the idea of modal realism doesn't seem all that strange. — frank

His theory of worlds, he acknowledges, “does disagree, to an extreme extent, with firm common sense opinion about what there is” (1986, 133). However, Lewis argues that no other theory explains so much so economically. SEP Possible Worlds

Just a thought, but Lewis’s approach seems very similar to that of Direct Realism.

Lewis argues that because the concept of concrete possible worlds explains so much and so economically, this overcomes any common sense objections we may have to it.

Similarly for the Direct Realist, who argues that the tables and chairs we perceive are ontologically real, rather than indirect representations, because this explains so much and so economically.