I'm not following. What does this have to do with the Barcan formulas?

In your standard modal semantics, all formulae are evaluated with respect to a possible world. This will include conditional or counterfactual formulae, however you translate or interpret them. Actualism about modality isn't a position affecting the modal logic per se. It's a metaphysical position, so when you're committing to using a modal logic, it becomes an interpretation of the metaphysical commitments of that logic.

What does this have to do with the Barcan formulas? — Snakes Alive

The Wikipedia entry on the Barcan formula states:

The Barcan formula has generated some controversy because—in terms of possible world semantics—it implies that all objects which exist in any possible world (accessible to the actual world) exist in the actual world, i.e. that domains cannot grow when one moves to accessible worlds. This thesis is sometimes known as actualism—i.e. that there are no merely possible individuals. There is some debate as to the informal interpretation of the Barcan formula and its converse. — Wiki

Therefore, if we are limited to the actual world when positing counterfactuals, then how are necessary conditionals possible to stipulate for other possible worlds?

In your standard modal semantics, all formulae are evaluated with respect to a possible world. — Snakes Alive

You mean, that all formulae are evaluated with respect to the actual world?

it implies that all objects which exist in any possible world (accessible to the actual world) exist in the actual world, — Wallows

Question: Are not all worlds accessible to the actual world part of, or in or attached to, the actual world? If yes, then "possible" worlds are actually impossible worlds. If no, then the implication is denied. Yes?

Question: Are not all worlds accessible to the actual world part of, or in or attached to, the actual world? If yes, then "possible" worlds are actually impossible worlds. If no, then the implication is denied. Yes? — tim wood

Yes, but, I don't see how a possible world can be determined as impossible? It merely states that the state of affairs of a possible world is always going to be dependent on our own. Counterfactuals can only exist wrt. to events in the actual world and cannot be quantified beyond that. This is what actualism in philosophy asserts to the best of my knowledge.

Ours is the actual world (whatever that means - possibly it implies there might be worlds that we are not in, and thus that they are not actual). I take that to mean that whatever is accessible to this actual world is in some sense in or of or attached to this actual world, which bestows actuality on the "world" in, of, or attached to, this actual world. That takes in a lot of ground. It leaves only im-possible worlds outside the actual world.

That takes in a lot of ground. It leaves only im-possible worlds outside the actual world. — tim wood

Well, there can exist an infinite amount of possible worlds, just originating from this one. But, I think the word "real" needs to be dropped into the discussion here. What is a "real" world? One where our set of circumstances have dictated its evolution?

@andrewk, what do you think about all this?

You mean, that all formulae are evaluated with respect to the actual world? — Wallows

No.

What do you mean?

Sorry to necromance an old thread, mods...

I am feeling audacious and have a nagging interest in utilizing the Barcan formula to prove the coherence of the thought that within a possible world scenario, there can only be a finite amount of possible worlds given that entities (a priori) cannot be multiplied into existence. I know this smells of essentialism given the ambiguity surrounding the definition of what constitutes an entity; but, if we expand the scope to the sum total of possible worlds, then God is the only entity that can be stipulated to inhabit every possible world, leading to a solipsistic conclusion that either God inhabits every possible world or the ineffable assertion that s/he/it transcends it.

Thoughts?

There was a question posted on StackExchange about this issue. I'm just sharing what the Barcan Formula is all about: