David Lewis’s ‘Possible Worlds’ (1986)

i) Quantifying Over Anything

ii) Quine, Lewis and Meinong's Jungle

iii) Necessity

iv) Possible-worlds Realism

v) Existence and Actuality

vi) The Point of Possible Worlds

This is an account of the 'Possible Worlds' chapter of David Lewis's book Counterfactuals (1973).

Quantifying Over Anything

It can be assumed that most people will accept that

“there are many ways things could have been besides the way they actually are”.

However, the American philosopher David Lewis (1941 - 2001) believed that this sentence involves an existential quantification. Why did he believe that? Surely you can only existentially quantify over that which exists. That’s why it’s existential. “Ways things that could have been” don't actually exist. There could have been three-headed snakes; though there aren’t. Therefore we can’t quantify over three-headed snakes. As W.V.O. Quine put it: “To be is to be the value of a bound variable.” Things that could be can’t be the values of variables... Actually, if the philosopher or logician wants to, he can quantify over everything and anything – over literally everything in some cases (as well as nothing, in the case of the dialetheist philosopher Graham Priest).

Lewis qualified his argument by saying that people who believe in possibilities “believe in the existence of entities”. What is Lewis’s argument for this move from belief (in possibilities) to existence? Believing in ways things could have been doesn't entail (or imply) their existence. So if these ways things could have been are possible worlds (or parts thereof), then possible worlds exist?

Why does belief in possibilities entail (or imply) existential quantification? Again, David Lewis himself might have been a bricklayer; though David Lewis the bricklayer didn't and still doesn’t exist. That is, we can’t quantify over a bricklaying David Lewis (unless it’s just someone with the same name).

Lewis, however, preempts these problems by asking the following question:

“If our modal idioms are not quantifiers over possible worlds, then what else are they?”

Was Lewis asking us where the bricklaying David Lewis is if he isn’t at a possible world? Who is it, precisely, that I’m talking about? Is this Plato’s Beard all over again? That is, if we talk about a bricklaying David Lewis, then he must exist in some shape or form. Thus:

Are there different modes of existence (or being), including a mode of existence at possible worlds?

Quine, Lewis and Meinong's Jungle

Quine (in his ‘What There Is’) has provided us with strong arguments against such extravagant Meinongism. (Though was Lewis really an extravagant Meinongian?) This problem itself brings in a whole host of accompanying problems about the references of words and the names of entities that seemingly don’t actually exist.

Yet we can quite happily talk about a round square: does that fact somehow bring about the round square’s existence? I can talk about a Possible Murphy who has three thousand girlfriends. Does my talk alone bring this Possible Murphy into existence? Indeed who is this God, for example who “doesn’t exist”? (This is something Bertrand Russell grappled with way back in 1918 in his 'Existence and Description'.)

However, this is still a fair question:

What is it we're talking about when we talk about “way things could have been”?

Necessity

The same is true, according to Lewis, when we talk about any given x being necessary (rather than merely possible). What are we talking about when we talk about this or that being necessary? What are we referring to? What makes this or that necessary?

Necessity can’t be seen (as it were) in one world – in our own world. Therefore it must be something about (as it were) every possible world. That is one possible expression of Lewis's position.

Thus when we say that

2 + 2 = 4 is necessarily true.

what are we saying? We're saying that this equation is true at every possible world - even in a world made of alcohol seas or one without our own physics. We can only make sense of necessity - in this and in all instances - by believing in the possible worlds that make our statements of necessity true. Without possible worlds, what is it that makes 2 + 2 = 4 necessarily true? After all, it may be true in our world; though how do we know that it's true at all other possible worlds? We know by imagining other possible worlds (of all shapes and forms) and then we quickly realise that 2 + 2 = 4 must be necessarily true at these worlds too. If 2 + 2 = 4 were true only in our world, then it wouldn’t be necessarily true.

Again, why are logical or mathematical truths necessarily true? Because they're true at all possible worlds. Their necessity comes from their being true at all possible worlds. Thus, in order to guarantee (or insure) necessity and possibility, we need possible worlds. That, anyway, is part of Lewis's argument (in this paper at least).

Possible-worlds Realism

So let’s be clear what Lewis believed about possible worlds. Thus:

i) Are possible worlds simply theoretical constructs?

ii) Are they convenient posits which somehow solve a whole host of problematic modal issues?

iii) Are they fictions-for-a-purpose?

iv) Or, in Lewis’s own words, are they “linguistic entities”?

The answer in all cases is: Absolutely not! Lewis was a realist when it comes to possible worlds. That’s what he’s famous for. He wanted to “be taken literally”.

Though precisely what should we take literally?

Well, for a start, “possible worlds are like our world”, according to Lewis. They are, in fact, (often?) very similar to our world. So what’s different about them? Well, different things “go on in them” than go on in our world. Therefore it can be said that - departing a little from Lewis - possible worlds have exactly the same constituents as our world; though those constituents differently configured. (This was D.M. Armstrong's position in his 'The Nature of Possibility'.) This means that possible worlds have legs, buses, atoms, trees, tables, etc; and, presumably, explosions, orgasms, car chases and so on. They also have David Lewises, Houses of Parliaments and so on. However, at one – or more - possible world, David Lewis (his “counterpart” - who's not literally our David Lewis) is a bus conductor. At another world, David Lewis is Prime Minister. In addition, at other possible worlds there are different configurations of atoms, molecules, etc., as well as different laws, constants of nature, etc.

This is where things get complicated.

Existence and Actuality

David Lewis said that all these other possible worlds exist; though they aren't “actual”... What the hell does that mean? Well, for a start, the word “actual” is indexical (like “here”, “there” and “now”). That is, what is and what isn’t actual is dependent upon (or contextual to) the circumstances of utterance. That is, our world is actual to us; and other possible worlds are merely, well, possible. However, at w, it's the case that w is actual. And other worlds, to w, are merely possible. So every possible world is actual according to itself (even if this is a personification); though only possible according to every other possible world.

Can we make sense of this distinction between actual and existent? At a prima facie level, “actual” and “existent” seem to be virtual synonyms. However, as stated, actual and existent aren't synonyms in Lewis’s scheme.

Strangely enough, Lewis actually says that the "unactualised inhabitants [of possible worlds] do not actually exist". That is according to us (i.e., not them), these inhabitants don't exist. Again, actuality is indexical.

Can we make sense of this strange ontology?

Lewis himself was explicit:

"To actually exist is to exist and to be located at our actual world…"

Here Lewis seems to be conflating existence and actuality. That is, surely we can we say that other-worldly persons aren't actual because they don't exist. What “mode of existence” (or being) do they have? (Being and existence aren't the same thing in philosophical literature.) If they "don't exist according to our world”, then what kind of existence do they have? There seems to be a logical contradiction looming here. Other-worldly persons both exist and don't exist. They don't exist (or aren't actual) according to us; though they do exist (or are actual) according to their own worlds.

What's going on here?

To some philosophers, the conclusion can only be that possible worlds don't exist. So what was Lewis's reply to this? In Lewis's own words, it "does not follow that realism about possible worlds is false". He also came out with this Zen-like statement:

“[T]here are more things than actually exist."

So some things that don't exist do actually…well, what, have being?

Again, the word “unactualised” seems to be synonymous with “non-existent”; whereas earlier Lewis offered us a distinction here. However, Lewis - in this paper a least - doesn't offer us a precise account of his ontological position; which would, hopefully, clear away some of these problems. Again, do non-actuals have some kind/mode of, well, existence? If not existence, then some mode of being?

The extent of Lewis's realism about possible worlds can be seen in the following passage. In it he stated:

"[T]here is much about them [possible worlds] that I do not know…"

So possible worlds certainly weren't imaginative creations to Lewis. If they were, then he, presumably, would have known everything about them. Possible worlds are therefore like unknown planets. Thus there are indeed a vast amount of planets out there; though we know precisely nothing about the vast majority of them.

The Point of Possible Worlds

Lewis didn't just believe in possible worlds because he thought that they exist or have being. He also thought that their existence solves various philosophical problems. So his interest (or belief) in possible worlds wasn't entirely contextless (if that's the right word to use).

So what did possible worlds do for Lewis and other possible-worldists? Firstly, they "systematize [our] pre-existing modal opinions". That is, they serve a philosophical purpose over and above the mere fact of their existence... or being.

What are these other worlds like, according to Lewis?

As stated above, although earlier in this paper Lewis wrote that possible worlds are very much like our world (only reconfigured - at least that's a word one can use), he also argued that the physics of some of these possible worlds will be – or are - different to our own. Indeed it follows from a belief in possible worlds that certain possible worlds must have alternative physics.

However, Lewis didn’t accept that any possible world can have an alternative logic or alternative mathematics. And isn't that the primary point (if they need a primary point) of possible worlds? Of course Lewis wasn't talking about specific (or generally-accepted) logical or mathematical systems; only that logical and mathematical truths and realities will be true regardless of our efforts to codify them. Thus Lewis was also a realist (as it were) about logic and mathematics. That is, there may be some logical or mathematical truths (or realities) that we human beings can never - or will never - know or be able to formulate (e.g., Goldbach's conjecture).

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