On Ch. 4 of Lewis's book Counterfactuals (1973) and the essays “Scorekeeping in a Language Game” (1979) and “Truth in Fiction” (1978).
What makes counter-factual statements true? If you think "I might have grown up in Cleveland" is true, then what thing about the world makes that "might" statement true? Or by contrast, "I might have been a round square" is not only obviously false, but it can't be true. We could say that it's true that "it's impossible for a round square to exist," or to put the same point another way, "it's a necessary truth that nothing can be both round and square." Some philosophers going back to Leibniz have described these modal notions of possibility and necessity in terms of possible worlds. Something is necessary (e.g. maybe 1+1=2) if the proposition expressing it is true in all possible worlds. Something is possible (might have been) if it's true in at least one world.
This idea was formalized (meaning converted to logical symbols) by a different Lewis, C.I. Lewis, near the beginning of the twentieth century, and further developed by Rudolf Carnap, Saul Kripke, and others. David Lewis is perhaps best known for taking this notion metaphysically seriously, saying that possible worlds aren't just a metaphor but are metaphysically real. Matt Teichman from the Elucidations podcast joins Mark, Wes, and Dylan to figure out what this might mean. Clearly Lewis doesn't mean that they're part of the "actual" world, i.e., our world. They're merely possible. If you were living in one of those possible worlds (and technically, you couldn't, i.e., the actual you; at best a counterpart of you could exist in a possible world), then you'd consider that world actual and ours merely possible. So while ordinary language considers "real" and "actually existing" to be synonymous, Lewis is separating those.
We do our best to use the work of our previous episodes to make sense of all of this. In considering first Quine's "On What There Is" in ep. 66 and then Carnap's response in "Empiricism, Semantics, and Ontology" in ep. 191, we came across the idea that "to be is to be the value of a bound variable." This means that when we talk, we use expressions like "everything," and we should then look at what "things" are covered by that "everything" to decide what our ontology (the list of types of things that we think exist) is. So if you want to make statements about all numbers (and most mathematicians do!), then in some sense numbers have to be in your ontology, or maybe you have to engage in some elaborate reduction to show that (as an empiricist like Quine would prefer), no, numbers are just abstractions from macroscopic things in the actual world.
Lewis is just applying this insight about numbers to possible worlds. To do math, we need to talk about numbers. To use modal concepts like "possible" and "necessary," we need to talk about possible worlds (or more precisely, talking about possible worlds makes sense of the common-sense modal intuitions that result in us using these terms). Lewis considers various ways that possible-world talk could be reduced to other sorts of talk (maybe a possible world is just a consistent set of propositions), but he finds those alternatives more problematic than just talking about possible worlds.
But what is it to insist that talk of these worlds is not just irreducible to some other kind of talk, but possible worlds themselves are real? What does "real" add to this? Reflecting on our series from 2018 on the notion of truth (starting with ep. 194), we decide that at least at this stage of Lewis's thinking, maybe we can say that saying it's "real" doesn't actually add anything to saying that it's an irreducible kind of talk. This is a deflationary theory of what it is to be real (or true). For Tarski (and further, back to Frege), saying "it is raining" and "it is true that it is raining" are the same; "it is true that" adds nothing. So "we need to talk about possible worlds to make sense of our modal intuitions" and "we need to talk about possible worlds to make sense of our modal intuitions, and furthermore, possible worlds are real" are two sentences with the same logical content in them, even though they look different.
Note that in order to find possible-world talk useful, you don't have to agree with Lewis about their metaphysical status. In part two of our discussion, we'll get into how this possible-world talk applies to the philosophy of language. Don't wait for it; get the full, ad-free Citizen Edition now. Please support PEL!
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Image by Solomon Grundy.