bigideas

The idea of “possible worlds” is a sort of metaphor for talking about modality. The modality of a statement is to do with whether it’s possible for the statement to have been wrong. Given some statement x like “grass is green”, modal logic deals with statements like “x, but only by accident” and “it’s necessarily true that x” and “x is impossible”. (Disclaimer: there are other kinds of modality too, but I’ll ignore them in this post).

It turns out that grass is green. It also turns out that 1 + 1 = 2. I can imagine a parallel universe in which grass isn’t green, but I can’t imagine one where 1 + 1 isn’t 2. The possible worlds metaphor tells us that there are possible worlds in which x is false, but no possible worlds in which 1 + 1 = 2 is false, because it’s impossible for this to be false. There’s a reason why we call them “possible” worlds — impossible ones are ruled out. For historical reasons, philosophers tend to use “world” to refer to what today we might call a “universe”.

Things that are true in all possible worlds are called “necessary” truths; “necessary falsehoods” are true in no possible worlds. “Contingent truths” are true in our world (the “actual” world, as it’s called) but not in others; contingent falsehoods are also true in some but not all worlds, and our happens to be one where they’re not true. All this just adds up to a nice way of thinking and talking informally about modality, and in fact it’s close to the way we spontaneously do talk about such things. Of course it can be formalised, which is what modal logic is for.

There are all kinds of interesting things to think about here. One is the assumption that the set of all possible worlds is well-defined. It certainly seems plausible that there’s a possible world in which there’s no shrimp; that is, in which the species we call shrimp never evolved. But could there be a universe in which there’s only shrimp — no water, plankton or anything else? Would a creature that could survive in such a place still be a shrimp? It doesn’t seem likely. (Yes, I nicked the example from Buffy the Vampire Slayer; I don’t have the citation handy). If you’re not sure about that example, what about a universe without atoms, or where time worked completely differently? What counts as “possible” is by no means well-known.

In analysing real problems, people often specify a possible world by saying: “it’s like our world, except x”, where x is something like “there are no shrimp”. But things are intricately interconnected. For example, if there were no shrimp, the things that eat shrimp would need something else to eat, and the things shrimp eat would have to have their populations controlled some other way. The people there would presumably have no word for shrimp, and no concept of it. Or they might, but for them it would be a mythological creature. There would be quite a few differences between that world and ours. How similar two possible worlds can possibly be looks like an intractable question in general (it’s also a modal question, inviting regress or circularity).

Another question, and one I’ll come back to, is that of “transworld identity”. Say I’m wondering whether my day would have gone better if I’d had porridge for breakfast. In modal terms, I’m asking “are there any possible worlds in which I had porridge for breakfast, and if there are did my day go better in most of them?”. But who is this “I” in the other possible world? Not me — I’m here, in the actual world. Suddenly the whole intuitive idea that we can identify the “same thing” or the “same person” across possible worlds seems extremely shaky. Kripke’s famous Naming and Necessity is one very influential treatment of this problem.

So possible worlds are, if you haven’t met them, a useful way to talk about things like possibility and contingency (although not, I don’t think, probability). But they also reveal all kinds of interesting problems with our ideas about what’s possible, or what might have happened, that we might not have thought about otherwise. More on this to come, inevitably.