but how are they absolutely separate? — Metaphysician Undercover

Again, that's explained in AW1.

But you claim to have read and understood that... :roll:

How can you expect to be taken seriously?

What would make such a world POSSIBLE? IOW, how do you account for its existence? — Relativist

AW1 w is a possible world =def w is a maximal connected object. — SEP

I'd sugest you go back and read that section.

I think you're alluding to modal logic as a formal system. — Relativist

No allusion. I was quite specific.

One can utilize the formal system to go through the mechanics of the logic, without committing to possibilism/actualism much less necessitarianism/contingentarianism. — Relativist

Yep. I've pointed this out, several times. see for example

Filling out that last point, Kripke and Lewis give different ontological readings of the same formal machinery. Their logic is the same, but the metaphysical story differs.

Kripke (Naming and Necessity):
Proper names refer rigidly to the same individual across worlds.
Necessity is primitive and tied to rigid designation.
Modality is not reduced to something non-modal; it is taken as metaphysically basic.


Lewis (Modal Realism / counterpart theory):
Worlds are concrete; individuals do not literally exist in more than one world.
Identity across worlds is determined via counterpart relations.
Modality is reduced to quantification over concrete worlds.

Shared Logic / Semantics
Possible worlds semantics: Both use worlds as the basis for evaluating modal statements.
Quantified modal logic: Both accept first-order quantification over individuals.
Transworld reference: Both presuppose a way to interpret identity or counterparts across worlds.
Truth-at-a-world: Both define modal truth in terms of what holds at particular worlds.
Accessibility relations: Both can accommodate structured relations between worlds (for temporal or metaphysical distinctions).
Formal rigour: Both agree that modal claims can be modelled systematically, independent of metaphysical interpretation.

Summarised by ChatGPT — Banno

Yep.

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

You'd think the penny had dropped... but:

So, it's kind of clear that you aren't reading along. Can you remedy that? — frank

Yep. And

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

Fucksake.

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. — RussellA

Kripke did not fill out his theory of reference. Never did.

It was offered only as an example of how references might be fixed apart from a definite description. At the time his audience would have bee somewhat incredulous; this kid (he was a teenager when he published the first few articles) saying that Russell's logic was wrong.

So he suggested a possible (!) alternative, more as a rhetorical tool than a tight bit piece of argument.

I hope we might leave the theory of reference to one side - we have enough distractions. 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. What is salient is that Kripke and Donnellan showed that proper names do not always and only refer in virtue of an attached definite description.

It appears like Banno is trying to hijack the thread to enforce his own brand of modal sophistry when the SEP clear indicates three distinct types: — Metaphysician Undercover

Yep. Guilty as charged. I'm trying to discuss Possible World Semantics, and the three interpretations of it that are listed in the SEP article.

But again, it's not My brand of modal sophistry. It's the standard, accepted logic of modality.

The nature of possibility is such that it is impossible to give "precise truth-conditions for modal claims". That's the fundamental reality of what is referred to by "possibility", it violates the basic truth conditions of the law of non-contradiction, or the law of excluded middle. This was demonstrated by Aristotle with examples like the possible sea battle. — Metaphysician Undercover

And yet, here it is.

If that is what Aristotle claimed — and that reading is itself highly questionable — then Aristotle was wrong. He lacked the resources to do better. You do not.

n a sense, this baptism is the same as JL Austin’s performative utterance. — RussellA

That was the topic of my Honours thesis.

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

Yep. Spot on. It needs to specify w₀.

So, if there exists possible worlds, are they all existing together as a collection in some world that contains them all? — QuixoticAgnostic

Since @Ludwig V quotes this, I might address it.

In Lewis' system, each world is spaciotemporally distinct - that is how they are defined. SO there is no "place" in which they hang out together.

But for my part, the idea of a world occupying a space appears to be a category error. What space is the Universe in? I don't think that question can be made to work.

Don't we need to mark a distinction between that world and any world we choose to treat as actual for purposes of logical analysis? j — Ludwig V

Not within the logic. We might do that when we give the edifice an interpretation.

Is it really impossible that Aristotle could not have had some other name, if he was born at the right time of the right parents and did all the right things? — Ludwig V

Yep. Have a look at your question. See how it is about Aristotle? there is a possible world in which Aristotle was given a different name. Who was given the different name? Aristotle.

In w₀ there is an individual named Aristotle. In w₁ that individual is named Barry. w₁ is accessible from w₀. Therefore, in w₀, ◇(Aristotle was named Barry)

Something that I'd like to draw your attention to, Ludwig, is the size of the argument here. It's worth mentioning that the argument does not include anything outside of what is needed in order to shoe the point. It's quite discreet. To a Wittgensteinian ear, that might be important. The grand theories we are discussing from the article - counterpart theory and so on - work on a somewhat different scale to the actual arguments philosophers usually use.

Anyway, note that the name of that individual in w₀ - Aristotle - is used as a rigid designator in order to stipulate the very same individual in a different possible world in which he is called Barry. See how the designation w₀ functions in this game? It's the from where that the rigid designation is fixed.

By your definition of existence... — QuixoticAgnostic

Not mine. Standard definitions for modal logic.

"Meta-worlds" sounds like virtual reality? Not too familiar with it. The question of 'where"possible worlds exist is answered differently by different folk. Given that we are talking about possible worlds, they are in the domain of discourse and so we can quantify over them and they exist in that sense.

Might not be a bad idea to go over the terms being used, since it seems there is some confusion.

Exists
A thing exists if it is in the domain of a world. That is, if it can be used in an existential quantification. Existence is what the existential quantifier expresses. Things can exist in one world and not in another. One point of difference between Lewis and Kripke is that for Lewis things exist only within a world, while for Kripke the very same thing can exist in multiple worlds.

A thing that exists is also possible.

In Kripke a thing can exist and not be actual or concrete.
In Lewis if a thing exists then it is concrete, and actual in some world.

Possible
It's possible if it's “true in at least one accessible world”.

Something might be possible and yet not exist - by not existing in w₀ but in some other possible world

Simialrly, a sentence is possible if it is true in some accessible world.

Actual
Actual is indexical. It works like here, or like now. We designate a world as the actual world, w₀, and then the things that exist in that world are actual.

In modal logic being actual is a label. In metaphysics being actual is usually a special ontological state. Lewis rejects this, since everything is actual in some world.

Contingent
A modal variability across worlds, something is contingent if it exists in some, but not all, possible worlds. And similarly, sentences are contingent if ◇P ^ ◇~P. If it exists in all possible worlds it is necessary. If it doesn't exist in any world, it is impossible.

Contingency is assessed modally, not temporally. So an event can occur and still modally contingent.
The fact that it happened does not make it necessary.

Concrete
This one is less clear. If something is physical, spatiotemporal, or causal it might be considered concrete.

In Lewis' system everything is concrete, in a world that is spatiotemporally separate and distinct from every other possible world.

In actualist accounts, only the things in the actual world are concrete. The other stuff is abstract.


Real
A claim of Metaphysical status. In Lewis something is real if it exists. In actualist accounts it is real if it both exists and is actual.


What fun.

I offered an alternative theory. — Metaphysician Undercover

Well, no. What you have offered, a set of assertions, isn’t a theory on a par with possible-worlds semantics. It doesn't provide a formal semantics. Possible-worlds semantics gives precise truth-conditions for modal claims, compositional rules for complex sentences, and a mathematically explicit structure (models, accessibility relations, evaluation clauses). Your proposal is a taxonomic distinction, a mere set of metaphysical labels separating ontology, epistemology, and counterfactual talk, without rules that determine when modal statements are true or false, or how they interact logically. It replaces a working semantic framework with intuitive metaphysical assertions, so it cannot do the same explanatory or inferential work.

The rest is layered confusion on your part.

ok.

Well, I do't see an argument that has as it's comnclusion:

The notion that "actual" is indexical is not consistent with the terminology in the SEP article, The Possibilism-Actualism Debate: — Relativist

So we agree that for Possibilists reality includes possibilia, things that could exist but do not actually exist, that there’s a broader realm beyond the concrete world. And that Actualists suppose only what actually exists counts as real. There’s no domain of merely possible entities. And that Lewis treates "actual" as indexical. To show inconsistency, one would have to demonstrate that the SEP article’s definitions cannot accommodate an indexical sense of “actual”, or that indexical “actual” violates SEP’s logic. I don't see that here.

But as noted, I'm more interested in the main article here than in this side issue. Once we have an agreed view on what the possibilities are for possible worlds, then we might better treat the possible and the actual.

Small steps.

, that quote doesn't seem to do what you think it does.

But, fine, carry on.

See my post

Oh, very good. — Ludwig V

Pleased someone notes the drollery! :grin:

a) that the actual world is the one in which we are constructing the possible worlds and the point of view from which we are surveying them and identifying which world we wish to treat as actual — Ludwig V

Yep. Hence the sometime definition of truth simpliciter as "true in w₀"... All of our modal logic is "true in w₀"!

b) that we do not choose that world - we are lumbered with it - even thrown into it. — Ludwig V

Pretty much.

What we don't have here is any inconsistency...

Leastwise, none I can see.


I was thinking about the "books" analog the other day, but can't now recall what it was I thunked. I think something like that is going on in the article, with the tree differing accounts of what possible worlds are; and I think it is somehow off-centre. But I haven't yet worked out quite how.

Part of the problem is that the books analogy and the three accounts picture the world as complete.

The notion that "actual" is indexical is not consistent with the terminology in the SEP article... — Relativist

How?

Here's what I think you did:

• summarises the SEP article on actualism vs possibilism.
• bring in Lewis’ supplementary discussion, noting that Lewis treats “actual” as indexical: it picks out this world, not a mode of existence.
• note that Lewis says all worlds in his plenitude exist equally.

This does not show any inconsistency with the article, nor any inconsistency in treating actual as an indexical.

Can you complete your argument?


--------------------
For my own part, the possiblism/actualism debate is much ado about very little.

The SEP distinctions and Lewisian subtleties revolve around how we use words like “actual” and “possible,” rather than revealing any deep metaphysical truth.

But to get to that, we should first get to Combinatorialism.

Irreducible Modality and Intensional Entities

For @frank, by way of moving along...

Put simply, and no doubt losing a whole lot of import thereby, here's how I read that section.

We saw previously that in Lewis' system possibility and necessity become bigger forms of quantification - quantification over multiple concrete worlds. Modality is reduced to quantification. Lewis can do this because his definition of a world does not contain any modal terms.

That doesn't work for abstractism. Possibility and necessity remain primitive. This happens because the definition of possible worlds makes use of modal notions.

And arguably, this is a positive. What we do is start with our natural language notions of possibility and necessity and then give then a firm, consistent grounding by introducing possible worlds.

Oh, yes - I emphatically agree - natural language comes first; indeed I'd suggest that formal logic is just a game within our natural language, and not something seperate from it.

But just as you can learn about life by playing Poker, we can learn about language by playing logic.

We set up things like validity, coherence and cogency as worthwhile. Then we look at how language might be if we value validity, coherence and cogency. And what we get are formal systems, little packages of language that show how it might hang together. We find it useful in putting our words together in our natural languages to borrow from these little packages.

And some find it interesting in its own right. it's how ex falso quodlibet looks odd that encourages discussion of non-classical logics.

So, what conclusions do we draw here?

It's probably a collision of possible worlds. — frank

Maybe "number of posts" is indexical.

I haven't been replying to you, . Doing so didn't look productive.

Is it illegal in NZ for folk without a disability to use a disabled toilet? That would be odd. How is it policed?

Are any of these concerns peculiar to the word "normal," or are we using "normal" here just as an exemplar term to show the limitations of language generally and how error might creep in? — Hanover

Not peculiar, but part of the make up of the language game around its use.

I'm certainly using this discussion to show the many problems with thinking that definitions are central to philosophy, that definitions give the meaning of a word, that we ought first define our terms, and so on.

Maybe the term "normal" with all its connotations provides us with a better diagnostic tool to show how usage and meaning are tied together... — Hanover

Yep.

Lewis does believe that all possible worlds are actual worlds, but that's not a common view. — Relativist

It might be better - and here I go against my desire not to multiply terms unnecessarily - to say that Lewis thought all possible worlds were concrete; and that we could call the concrete world in which we find ourselves, the actual world. Lewis thought of actuality as indexical.

In everyday discourse it's ambiguous, but it appears to me that among philosophers, there's no ambiguity about what it means. There are controversies, but not about the basic definition. — Relativist

Spot on.

Just a note, I've bowed out of the above discussion, but when Banno is ready to move on, I'm all in. — frank

Yes, cheers - understood. I find it easier to answer these odd little objections than to move on with the harder stuff of the article, so I find myself somewhat distracted. There's a chance that the explanations I'm giving will help folk see the direction the article is taking. It's already very clear that Meta - for whom you started this thread - is for whatever reason incapable of following the discussion. But others may be coming along.

I do what to get my head around the section Irreducible Modality and Intensional Entities, and I don't think the material there especially deep. But finding the right words will take time.

In standard modal logic there is exactly one actual world.
— Banno

This states very clearly and precisely, in a nutshell, the significant and substantial problem with possible worlds semantics. We must deny what you yourself acknowledged as the very real and important difference, between the "actual world" of ontology, and the "actual world" of modal logic. To avoid the fallacy of equivocation, there must be "exactly one actual world". The glaring problem though, is that "actual world" is assigned to the modal model, not the ontological world, plunging modal logic deep into Idealism. — Metaphysician Undercover

This shows very clearly and precisely, in a nutshell, the significant and substantial problem with your understanding of possible world semantics. In standard modal logic, the term “actual world” is an indexical label applied to one world in the model—it does not make any ontological claim about that world being the only real or “ontologically actual” world. It is a convenient reference point for evaluating modal statements, just as “here” or “now” is in ordinary language.

Equating the “actual world” of a model with an ontologically privileged world is a misunderstanding. Modal logic does not commit to idealism or deny the existence of the external, physical world; it merely provides a framework for reasoning about possibility and necessity. The indexical nature of “actual” dissolves the apparent problem: there is exactly one designated actual world in the model, but this says nothing about reality beyond the model.

You confusion comes from thinking that the world given the title w₀ in a modal interpretation must be our world - the confusion of the modal and the metaphysical. Think I've mentioned that before.

As I explained, that renders "actual" as meaningless. By "meaningless" I mean you could give it any meaning you want, but you haven't so it has no meaning. The world you perceive is "actual". The world you imagine is "actual". You could imagine anything, and that could be said to be "actual". — Metaphysician Undercover

Treat "actual" as an indexical, and this dissipates.

It is as if you were arguing that "over there" is meaningless, because it can be made to refer to any place at all. :lol:

When you ask someone to go and stand over there, you might indeed be indicating any place at all; but it is fixed by the context.

As I explained, that renders "over there" as meaningless. By "meaningless" I mean you could give it any meaning you want, but you haven't so it has no meaning. The place you perceive is "over there". The place you imagine is "over there". You could imagine anything, and that could be said to be "over there". — Metaphysician Undercover

Yep. That's how indexicals work.

"Contingent" has varied meaning, it's quite ambiguous. — Metaphysician Undercover

That's a choice you make, Meta.

For the rest of us, some proposal is contingent if and only if it is true in some, but not all, possible worlds.

As regards water and H₂O; Kripke pointed out that if water is H₂O, if they are indeed identical, then necessarily, they are identical. If they are the very same, then they are the very same in every possible world.

Now pointing out that sometimes water is not the very same as H₂O, because it sometimes contains impurities, is not a counter to this.

Because it denies the antecedent.

Kripke's point is logical, not physical. He is not telling physicist their job.

We have to be very careful about our terms here. As a result of reading this thread, I have become quite confused about what "actual" actually means (!) and how it relates to "exists" (and "real"). I don't see how actual world could only possible exist. It seems to mean something close to "exists" and like it, in that neither are, in Kant's sense, predicates. (Nor, come to think of it, is "real") — Ludwig V

Yeah, and it doesn't help when folk throw "concrete" into the mix...

Seems to me that the answer is to understand "actual" as an indexical. It's our world. It will change as "our" changes.

In the modal logic, the actual world is w₀. It is just the one from which whatever accessibility relations we specify originate. For example, “◇P” (possibly P) is true at w₀ if P is true in some world accessible from w₀. It's indexical. It could be any possible world.

In English, the actual world is the one we are in. It's also indexical. The upshot: being the actual world depends on who is talking.

The most clearly consistent way to talk about existence is via quantification. And that is defined in terms of the domain of discourse. If something is in the domain, then we say that it exists. So Frodo exists if the domain is Middle Earth.

"Being actual" and "existing", used in this way, become quite distinct, dissolving much of the muddle.

"Real" is best treated as Austin suggested, as a relative term - it's not real, it's a counterfeiter; it's not real, it's artificial... and so on.

Chomsky misunderstood Kripke. He got it arse about.

Kripke starts with a formal modal logic which fixes individuals across possible worlds in order to achieve consistency. He did this in his papers “A Completeness Theorem in Modal Logic” (1959) and “Semantical Analysis of Modal Logic I” (1963)

He then takes that modal logic and looks to see how it might be understood in English or other ntural languages. That's Naming and Necessity.

Chomsky looked at Naming and Necessity as a theory of linguistics, with modal implications. So he thought of rigid designation as a semantic thesis about how names function. But it is a conjecture about how names might be understood in a way that is compatible with the formal logic.

Kripke is not offering a theory of linguistics or physics. He is saying something more like "Here is a coherent and consistent grammar for talking about modality. If we want to be coherent and consistent, these are the consequences".

Chomsky and can't use linguistics or physics to show that the logic is inconsistent.

What they might do is adopt the grammar and see what the implications are for linguistics and physics.

So again, first make sure you have understood what Kripke is doing.

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

Or, any possible world might have been actual, but only the actual world is actually actual... :wink:

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

Yep.

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. — RussellA

Yours is a good account. That's why I have come back to it - it's close enough to what I understand that I can use it in these explanations.

However I think the quote is around the wrong way.

We have a formal account that talks of things in possible worlds. We want to take that back to our natural language. We have so far two ways of doing this. the first is Lewis' idea that the possible worlds are all concrete, and we look for and match the most similar individuals in each. The second is Kripke's idea that we simply refer to the same individuals with the same name in any possible world in which they exist.

What Kripke expresses that view in natural languages, the result is that proper names are used to refer to the very same individual in every world in which they exist.

So, it's not that rigid designation is a consequence of his theory of meaning, but that his account of modal logic has as a consequence that proper names rigidly designate, and his theory of naming tries to account for that.

That is, the "a"'s and "b"'s in formal logic are most simply understood as cognates of proper name sin English. So since those "a"'s and "b"'s refer to the same thing in different possible worlds, then it seems we might do well to presume that the proper names of English do likewise.

You are right that what Kripke calls an "essence" are those properties that belong to an individual in every possible world.

He uses the example of Queen Elizabeth; we might think the following is an innocent question: "What if Queen Elizabeth had different parents?" It might have been that the babes were swapped at birth, for instance, or some such muck up. But then the person who, in the actual world, is Queen Elizabeth, would, in that other possible world in which the babies were swapped, not have gone on to become queen - perhaps she ran a fish and chip shop in Bristol instead - and the baby for whom she was swapped went on to become the Queen.

Now look carefully at what just happened. We asked the innocent question, "What if Queen Elizabeth had different parents?", and it turned out that this could not have happened! The person who, in the actual world, became Queen Elizabeth, could not have had different parents.

What might have happened is that some other baby, with different parents, could have become the queen.

That's a very different situation.

In parsing the English sentence "What if Queen Elizabeth had different parents?" into our modal logic, we find that what looks to be a question about Queen Elizabeth is better considered as a question about two different people.

So being the child of King George VI and Elizabeth Bowes-Lyon is true of Queen Elizabeth in every possible world, and in those worlds in which the apparent Queen of England is not the daughter of King George VI and Elizabeth Bowes-Lyon, we are talking about some other individual becoming the Queen...

Think on it a bit. 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.

but in most modern discussions of logic) to have got to a situation where what logic one uses is just a function of what project one is pursuing. — Ludwig V

Logical pluralism rather than pragmatism. The challenge is to use formal grammar to exhibit the incoherences and inconsistencies in our philosophical meanderings. It's not picking a logic that gives the answer we want, but looking at what we have to say using formal tools that set out clearly the problems.

See, for a small example how

What this shows is that Meta's way of talking is incompatible with the formal account. Meta is helping himself to the expressive resources of possible-worlds semantics (modal operators, actuality, evaluation) while rejecting the background grammar that makes those resources coherent. He's not offering an alternative theory. He is attempting to take something he expresses in informal talk, and express it in our best formal language. And in doing so we find that it becomes incoherent. This is precisely where formalisation earns its keep; not by settling metaphysical conundrums, but in exhibiting ways of speaking that cannot be regimented without contradiction. Once that’s shown, the choice is stark: revise the talk, or abandon the framework. You don’t get to keep both - unless you are Meta, and simply double down on your errors.

Looks right.

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

In terms of modality, w₀ is not treated any differently to any other world within the formal semantics. It's a convention of the interpretation, an indexical, like "here" or "now"; a thing of convenience. It usually marks the place who's access relations we are considering

What we haven't looked at much is how accessibility works. It's not mentioned much in the article. Accessibility is the relation that sets out which worlds we can "get to" from a given possible world.

So if I am about to flip a coin, I am in a world that can access a world in which the coin comes up "heads", or a world in which the coin can come up "tails". Both are available. But if I just flipped a coin, and it came up "tails", the possible world in which it came up "heads" is no longer accessible.

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

Let's look at temporal logic. A simple temporal logic sets the accessibility relation between possible worlds so that one possible world is the past and other possible worlds are the future. From the past world, many future possible worlds are accessible. But from those future worlds, only one past world is accessible.

We might specify w₀ as now, and various other worlds as possible futures and pasts. In our world it is true that Caesar crossed the Rubicon, and if we want to model history, we stipulate that we cannot access those worlds in which he disbanded the 8th and returned to Rome. But if we want to write an historical fiction, we would thereby access a world in which he did just that. The access relations depend on what it is we wish to model.

To be clear, there are a range of temporal logics, and which you make use of depends on what it is you wish to model. This is just one example.

And there are similarly logics that model causation in terms of accessibility. Lewis constructed such a logic. The coin flip mentioned earlier is a simple example of one possible approach, but there are many others.

The take-away: the structure of possible world semantics that Kripke set up has been used to formalise a wide variety of situations by amongst other things constructing suitable accessibility relations. Since these are dependent on the core possible world semantics, it might be good practice to make sure we understand what that is before we go off talking about these applications of that logic.

Folk hereabouts who jump to causation and temporality quickly become quite muddled.

Puzzling.

RIghto. Carry on.

it ignores the controversies... — Relativist

Clarifies, would be a better word.

Your

You're conflating possibility with potential. There is no potential for a different past, but we can consider whether a past event was necessary or contingent. — Relativist

is pretty much right. Contingency is modal, potential is causal, such that if we mix the two, then we ought keep close track of which is which.

Unfortunately your definition of contingency mixes causality and and modality. If it were a definition of determinacy, it would work.