Seems to me the best way to proceed is by differentiating Combinatorialism and Abstractionism, and at the core the difference is that while Abstractionism sets up possible worlds in terms of states of affairs, Combinatorialism sets it up by combinations of individuals, relations and universals. Trouble is that Combinatorialists go on to talk about states of affairs. But if we are to make sense of the distinction those states of affairs for Combinatorialists consist in combinations of individuals and relations, but for Abstractionists they are fundamental. — Banno
I wrote a whole freakin' essay.
:grimace:
Modal logic's touchstone is the way we think about the world around us. Simple stuff like: "What if I'd never been born?" That's the theme of a famous Christmas movie called "It's a Wonderful Life" starring Jimmy Stewart and Donna Reed:
In the movie, an angel shows the protagonist what the world would be like without him. He does this by literally putting the character into this alternate world, where he walks around learning what's happened to people he wasn't there to help. Some died. Some became alcoholics. Some took over the town and turned it into a dark hellhole.
Why is it so easy to follow the events of the movie? Why don't we become profoundly confused? Apparently it's because we routinely think this way. We look back and imagine a multitude of paths leading up to the singular present, and from there, we imagine a multitude of futures. Time is shaped like an hour glass in our minds. We're at that place in the middle where grains fall one at a time.
The old question appears, though. What is the relationship between the way we think and the way things really are? The first recorded philosopher to testify that we can't know the answer to that was Socrates in Plato's
Crito. What is the role of the logician here? Is she supposed to answer the question that Socrates himself warned can't be answered?
I think abstractionism, concretism, and combinatorialism are three ways of exploring how extravagant we want to get with answering the question.
Concretism: I think this version forgets the original touchstone: the way we think. In the movie
It's a Wonderful Life, that's not an alternate Jimmy Stewart. The whole point of the movie is that
our Jimmy learns what the world would be like without him. If it turns out that that's a different Jimmy, then we really would become confused and turn the movie off. For all its advantages, I have to nix this one.
Abstractionism: This is a modest approach that enjoys roots in Frege. It gets thumbs up from philosophy of math. It says alternate worlds are figments of thought. How does that relate to the way the world really is? We don't know. We talk about sets, propositions, states of affairs, etc. because it's handy to use those ideas. When God Almighty steps in and reveals the true nature of Everything to us, we'll modify as needed.
Combinatorialists Some people say dreams are just memories that have been jumbled and recombined. Combinatorialists are saying the same thing about possible worlds. A possible world is just components of the actual world pulled apart and put back together in a new way. Is that true? They seem to be saying that I can't dream up anything truly new. I'm not fired up to argue about that. If an orbiting satellite wasn't really something new, it was just the same old stuff reorganized, then ok. It seemed new when they first thought of it, though.