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. — RussellA

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

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"?

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

What's with the nonsense frank? Honestly, your posts directed at me are ridiculous. If you think I'm off topic of the thread and a distraction, then please report me to the mods, and have me removed. Thank you.

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

Yes, the possible worlds are concrete worlds, that's what the SEP calls concretism, but how are they absolutely separate? 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.

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. — RussellA

The words you use to describe that imaginary world have meaning derived from your experiences in your concrete world. This implies that things within the two worlds have some similarity. How can there be that type of similarity without some sort of spatial temporal consistency, or continuity, between the two? 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.

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.

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.

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.

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.

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.

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.

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.

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

I think you're alluding to modal logic as a formal system. One can utilize the formal system to go through the mechanics of the logic, without committing to possibilism/actualism much less necessitarianism/contingentarianism.

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.

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

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.

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?

@frank, it's clear and got lost somewhere. I'm not going back for Meta, who will double down and object to whatever is suggested. Relativist might catch up.

So I think we move on?

I'm not going back for Meta, who will double down and object to whatever is suggested. — Banno

Me neither. I'm just ignoring him at this point.

So I think we move on? — Banno

:up:

I read 2.1 and 2.1.1 of the Possible Worlds article, but have not yet read the rest of whatever literature has been mentioned in this thread. I can try to follow along with whatever's posted next, and go back as necessary.

"Meta-worlds" sounds like virtual reality? — Banno

All I mean by "meta-world" is, basically, some world where all possible worlds exists. Based on the definitions given wrt AW1, that seems impossible, because possible worlds exist maximally, and a "meta-world" would connect possible worlds, hence not maximal, hence a contradiction.

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. — Banno

I'm curious what those answers might be. It seems you're suggesting that worlds can and do "exist" in some sense (they can be quantified over in the domain of discourse). Is this different from how things exist in worlds? And does that not introduce a conflict with how we describe existence?

Also, I happen to disagree greatly with this idea of worlds being defined spatiotemporally. I think existence behaves more abstractly beyond that, but I'm willing to discuss in those terms.

@frank

One last word on intensionality for Abstractionism, concerning that paragraph about methodology.

We saw earlier how speaking roughly, the intension of π is the rule that tells you what π’s truth-value would be in every possible world. At issue now is, which is to be master?

The concretist starts with worlds as given (from AW1) and treats intensions as derivative: once we have worlds, an intension is just a way of tracking truth across them.

The abstractionist reverses the order. Intensionality, understood as truth-at-a-world, is taken as basic, and possible worlds are introduced as whatever is needed to make sense of modal variation.

My own intuition is that the disagreement is not about whether worlds or intensions exist; it’s about which we take as explanatorily primary. Seen this way, the two positions, concrete and abstract, are complementary rather than contradictory: they are different “perspectives” on the same metaphysical landscape. That it's more a difference about how we say it than about what is being said.

All I mean by "meta-world" is, basically, some world where all possible worlds exists. Based on the definitions given wrt AW1, that seems impossible, because possible worlds exist maximally, and a "meta-world" would connect possible worlds, hence not maximal, hence a contradiction. — QuixoticAgnostic

Yep. Nice.

And does that not introduce a conflict with how we describe existence? — QuixoticAgnostic

It's a neat point to put pressure on. The simple answer is that the possible worlds are in w₀, the actual world. But all this means is that it is we, in this world, who are talking about them and quantifying them, and they are in our domain of discourse.

What looks a bit paradoxical is actually a recursion. That recursion enters when we describe all possible worlds from the standpoint of a particular world — that’s the “loop” that looks tricky, but it isn’t a real contradiction.

An interesting point, though.

See the Island Universe for a related reflection.

And yet, here it is. — Banno

We already read through the truth conditions in the SEP article. And, I showed how the stated conditions of truth are impossible to completely fulfil. There is a big difference between being able to state truth conditions, and being able to fulfil the stated conditions. But whenever fulfilment is close, the correct result is probable, and we can pretend to have satisfied the conditions.

Truth as described in possible worlds semantics is actually impossible, and there ought not be any pretense to it. So topological semantics, and probability theory (instead of truth and falsity) are proving to be much more productive in applications like AI.

I have a lot of thoughts about the soundness of this concretist approach to possible worlds, and one of them I think has to do with your answer as well as, not the Island Universe section, but the Alien Properties after it.

It seems you're saying possible worlds are relative to actual worlds. So we can speak of the possible worlds based on our actual world, and presumably, if any of those worlds were the actual world, we'd be a possible world to them. The question I have then is about the scope of possible worlds, and what exactly their metaphysical claim is to reality.

I want to say that because possible worlds have no greater claim to existence than our actual world, the whole "possibility space" of worlds can be said to exist, but that's not all that exists. It wouldn't be everything because the possibility space is relative to our actual world, and one could imagine a world, by Alien Properties arguments, that is completely orthogonal to how our world is. If the world is completely unlike our world, then it is unlike any possible world, yet we can't claim it does not exist because no world has a greater claim to actuality than any other. The only way would be to deny that there could be a world that is completely unlike our own, but I'm not sure how one would argue that.

Does this account of possible worlds subject us to so-called "impossible worlds"? Is that the point, perhaps, that there exist plentiful worlds out there beyond our reach, and it's only those within our reach that we can call possible? Because I don't have any problem with such impossible worlds existing, but it seems to wander from the spirit of using possible worlds in the first place, although I can't articulate where it goes wrong at the moment.

My own intuition is that the disagreement is not about whether worlds or intensions exist; it’s about which we take as explanatorily primary. Seen this way, the two positions, concrete and abstract, are complementary rather than contradictory: they are different “perspectives” on the same metaphysical landscape. That it's more a difference about how we say it than about what is being said. — Banno

I'll have to ponder this

I think I understand where you're coming from, but my attempts to get people to understand where I'm coming from haven't gotten traction. I'll start a new thread with my issues, and let you carry on here.

You are babbling. Kripke showed how give truth conditions for modal claims using Tarski's semantics.

The question I have then is about the scope of possible worlds, and what exactly their metaphysical claim is to reality. — QuixoticAgnostic

The logic itself is (almost) metaphysically neutral. The concrete approach is one interpretation among many. And the answers to your questions will depend on what approach is adopted. Alien Properties are intriguing, but the response will very much depend on what else one accepts. It's not difficult so much as complex.

Impossible worlds. Have a look, but we might here stick to the present article.

As you wish.

"there is a possible world in which Hobbits, Trolls and Orcs exist" — Relativist

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. — Banno

On the account given here we make sense of existence within worlds. Frodo is a Hobbit - h(a). By existential generalisation there is something that is a hobbit - ∃(x)(h(x) - which can be read as "something is a hobbit" or as "hobbits exist".

There is a world w whose domain contains at least one object satisfying each of the predicates hobbit, troll, and orc.

The claim that “there is a possible world in which hobbits exist” amounts to nothing more than the claim that the predicate hobbit is satisfied by at least one object in the domain of some world. No commitment follows to hobbits existing outside that domain, nor to their being actual, concrete, or real in any further sense.