Ways It Could Have Gone

You could have missed the train. That sentence is true, and nothing in this world makes it true, because the train was caught. Claims about what must be, what might be and what would have been are everywhere in ordinary speech and in every science, and for most of the history of logic there was no rigorous way to handle them at all.

The apparatus that changed this is deceptively simple. Imagine the complete set of ways things could have gone: possible worlds. Then necessity means true in all of them, possibility means true in at least one, and a counterfactual means true in the nearest worlds where its antecedent holds. Modal claims become ordinary claims about a domain, quantification does the work, and a century of technical progress follows. That the machinery works is not in dispute. What the worlds are is the entire philosophical argument, and it is a real one.

The deflationary answer is that they are a manner of speaking: a useful fiction, or at most sets of sentences describing how things might be. This is comfortable and it makes the success of the machinery slightly mysterious, in the way that any very effective fiction is mysterious.

David Lewis took the other road as far as it goes. Other possible worlds are exactly as real as this one. They are not abstract, not constructions, not sets of sentences: they are concrete worlds with donkeys and rainstorms in them, spatiotemporally isolated from ours. And 'actual', he argued, is indexical, like 'here' or 'now'. It picks out the speaker's own world rather than marking a privileged one. The inhabitants of other worlds are just as entitled to call theirs actual, and they are right. Lewis defended this for decades on the grounds that it does more work at lower theoretical cost than any rival, and he recorded the standard response with some amusement as the incredulous stare, noting that a stare is not an argument. It remains the most admired and least believed position in modern metaphysics.

Saul Kripke's contribution runs alongside and has been more consequential outside philosophy. A rigid designator is a term that picks out the same individual in every world where that individual exists. Names do this. There is no possible world in which Aristotle is somebody else, though there are many in which he never taught Alexander, so 'the teacher of Alexander' is not rigid and 'Aristotle' is. From this a startling result follows. If 'Hesperus' and 'Phosphorus' both rigidly designate the same planet, then the identity holds in every world, so it is necessary: even though it took astronomy to discover it.

The same argument gives you that water is necessarily H2O. This broke an assumption so old that most philosophers had not noticed it was an assumption: that the necessary and the knowable-in-advance are the same category. Kripke pulled them apart. There are necessary truths that only experiment can reveal, and contingent ones that can be known without investigation. Necessity turns out to be about how things are, not about the limits of what we can imagine, and imagination, which had been doing duty as the test of possibility, turns out to be a poor guide.

There is a practical version of all this in every risk model ever built. A team runs a thousand simulated scenarios and reports failure in three per cent of them. What they have done is sample from a distribution they wrote down, which means the worlds they visited are the worlds their model can represent. A failure arriving by a route nobody encoded is not rare in that model; it is absent from it, and the reported three per cent is silent about it. This is precisely the problem of distinguishing what is genuinely possible from what someone found it easy to conceive, wearing a spreadsheet. It is also why the tails of such models are so reliably wrong, and why the people who build them are usually the least surprised by that.