Barcan Formula
I'm interested if anyone knows of any interpretations of the Barcan Formula.
My intuition tells me that actualism is the right theory of Quantified Modal Logic. It seems like a perfect balance for applying Occam's Razor to possible world semantics.
Just as a preliminary, if anyone is interested to see:
https://math.berkeley.edu/~buehler/First-Order%20Modal%20Logic.pdf
The domain or framing condition for any set of counterfactuals is intuitively linked to the actual world, and there's no room for ascertaining the truth of necessary conditionals in other possible worlds. And, if so then what criteria would one need to judge the merit of a necessary condition in another possible world? It's hopelessly inchoate or self-refuting!
Thoughts and criticism welcome.
My intuition tells me that actualism is the right theory of Quantified Modal Logic. It seems like a perfect balance for applying Occam's Razor to possible world semantics.
Just as a preliminary, if anyone is interested to see:
https://math.berkeley.edu/~buehler/First-Order%20Modal%20Logic.pdf
The domain or framing condition for any set of counterfactuals is intuitively linked to the actual world, and there's no room for ascertaining the truth of necessary conditionals in other possible worlds. And, if so then what criteria would one need to judge the merit of a necessary condition in another possible world? It's hopelessly inchoate or self-refuting!
Thoughts and criticism welcome.
Comments (11)
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.
The Wikipedia entry on the Barcan formula states:
Quoting 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?
Quoting Snakes Alive
You mean, that all formulae are evaluated with respect to the actual world?
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.
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?
No.
What do you mean?
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?