A Critical Introduction to D. Lewis on Possible Worlds

Possible Worlds

We can all accept that

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

Tony Blair might have been a serial killer. But what does that mean? Could Tony Blair really have been a serial killer? What does that claim actually mean? If Tony Blair might have been as serial killer, then there must be things about Tony Blair that he has here and now, and the same things in this possible world scenario. It therefore immediately becomes obvious that possible-worldists must be committed to essences of some kind. The serial Tony Blair shares an essence with the politician Tony Blair. If they did not share their essences, then we could not even say that Tony Blair

might have been a serial killer.

Blair, at both worlds, must have necessary properties that remain in him, as it were, despite the radically different situations and condition that both Blairs encounter. We now must ask: Are there such things as essences? If not, then it may be the case that Tony Blair at another possible world could not, well, be Tony Blair because there is no essence of Blair to bind Possible Blair with Actual Blair. This must mean, then, that none of Blair’s properties are essential or necessary because in that situation, someone who passes for Blair may not actually be Blair. Another way of putting this is that if we identify Blair by exclusively contingent properties, then it could be the case that this Possible Blair has none of the properties of Actual Blair. And if that is the case, he would not be Actual Blair or even a Blair counterpart. Only an essence would guarantee a degree of uniformity between Actual Blair and Possible Blair.

Lewis thinks that the sentence

Tony Blair might have been a serial killer.

 involves an “existential quantification”. Why does he think that? Surely you can only existentially quantify that which exists. That’s why it’s “existential” and not, say, "possible". Ways things could have been do not actually exist. There could be three-headed snakes, but there aren’t. Therefore we can’t quantify over three-headed snakes. As Quine put it:

To be is to be the value of a variable.

Things that could be can’t be the values of variables. However, Lewis qualifies his argument by saying that people who believe in possibilities “believe in the existence of entities”. Why does Lewis’s argument follow? Believing in ways things could be does not necessitate or imply a belief in their existence. Why has Lewis made that conclusion? If these “ways things could have been” are possible worlds, then possible worlds do not exist. Why does belief in possibilities entail or imply existential quantification? Again,

David Lewis could have been a bricklayer.

But David Lewis the bricklayer doesn’t exist. We can’t quantify over a bricklaying David Lewis (unless it’s just someone with the same name).

Lewis, however, pre-empts my problem and therefore asks:

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

Is he asking here where is the bricklayer David Lewis if he isn’t at a possible world? What is it, precisely, that I’m talking about? Does this simply mean that if we say ‘Lewis could have been a bricklayer’ then at the least we must be imagining something? We must be imagining a bricklaying David Lewis. How can we imagine something that does not in some sense exist – even if it not actual at our own world? Imaginary scenarios must therefore be scenarios of something other that the acts of imagination and the mental items of imagination. Therefore a bricklaying Lewis must exist in some sense. Is that the argument? Is this Quine’s “Plato’s Beard” again? If we talk about bricklaying David Lewis then he must exist in some shape or form. And here we go again:

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

Of course Quine, in his ‘What There Is’, has provided us with strong arguments against such extravagant Meinongism. Is Lewis an extravagant Meinongian? This problem itself brings in a whole host of accompanying problems about the references of words and names of entities that seemingly don’t actually exist. I can quite happily talk about a round square. Does this 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 into existence this possible Murphy? However, it is still a fair question.

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

What are these things ‘that could have been’? Where are they? And if we talk about them, must they exist at some possible world?

The same is true, according to Lewis, when he talks about something being necessary (rather than 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 in one world – in our world, therefore it must be seen at every possible world. When we say that

2+2=4 is necessarily true.

what are we saying? We are saying that this equation is true at every possible world. Even in a world made of alcohol seas or one without our physics. We can only make sense of necessity, in this instance and in all instances, by believing in possible worlds that, as it were, make our necessary statements true. Without possible worlds, what is it that makes 2+2=4 necessarily true? After all, it may be true in our world, but how do we know that it is true at other possible worlds? We know by imagining other possible worlds of all shapes and forms and 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.

Let’s be clear what Lewis believes about possible worlds. Are they simply theoretical constructs to him? Or are they convenient posits which somehow solve a whole host of problematic modal issues? Are they fictions-for-a-purpose? Or, in Lewis’s own words, are they “linguistic entities”? The answer is, of course, in all cases, absolutely not. Lewis is a realist when it comes to possible worlds. That’s what he’s famous for. He wants to “be taken literally”. What should we take literally? Well, for a start, possible worlds are like our own world, according to Lewis. They are, in fact, very similar to our world. What’s different about them? Different things go on in them than go on in our world. We could say, departing a little from Lewis, that possible worlds have exactly the same constituents as our world, but they are differently configured. Possible worlds have legs, buses, atoms, trees, tables and so on. They also have Tony Blairs, David Lewises, Houses of Parliaments and so on. However, at one possible world Tony Blair is a serial killer. At another David Lewis is Prime Minister. And perhaps at others there are different configurations of atoms and molecules (perhaps there is no H² 0 at certain possible worlds).

This is where things get complicated. Lewis says that all these other possible worlds exist, but they are not “actual”. What does that mean? Well, for a start the word “actual” is indexical (like “here”, “there”, “now”). What is and what isn’t actual is dependent or contextual on the circumstances of utterance. Our world is actual to us. And other possible worlds are merely, well, possible. However, in world W¹ it is the case that world W¹ is actual. And our world, to them, is merely possible. Every possible world is actual according to itself; but only possible or existent according to every other possible world. Can we make sense of this distinction between actual and possible/existent? At a prima facie level, actual and existent seem to be virtual synonyms. However, as I’ve said, actual and possible don’t seem to be 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, not them. Again, actuality is indexical. Can we make sense of this strange ontology? Lewis is explicit:

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

Here Lewis seems to be conflating existence and actuality. Otherworldly persons do not exist and they are not actual (because they don't exist?). What sort of existence or being do they have? 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. Otherworldly persons exist and don't exist. They don't exist according to us. But they do exist according to their own worlds. What's going on here? To me, the conclusion can only be that other possible worlds don't exist. In fact, in Lewis's words, it "does not follow that realism about possible worlds is false". What does Lewis say to this? He comes out with this Zen-like statement:

…there are more things than actually exist.

Some things that don't exist do actually…well, what, have being? Exist? Again, unactualised seems to be synonymous with non-existence, whereas earlier Lewis offered us a distinction. However, Lewis, in this paper a least, doesn't offer us a precise account of his ontological position. Again, the non-actual have some kind of, well, existence. If not existence, then what? Being?

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

…there is much about them [possible worlds] that I do not know…

They certainly aren't imaginative creations. If they were, then Lewis, presumably, would know everything about them. Possible worlds are therefore like unknown planets. There are unknown planets out there for sure, but we know precisely nothing about them. Or we can see them vaguely through telescopes, but we still don't know much or anything about them.

However, Lewis doesn't just believe in possible worlds because he thinks that they exist (they are out there?), he thinks that their existence, as it were, solves various philosophical problems. His interest or beliefs in possible worlds are not, as it were, entirely objective (if that's the right word). What do possible worlds do for Lewis and other possible worldists? They

systematize [our] pre-existing modal opinions.

They serve a philosophical purpose over and above the fact of their existence.

What are these other worlds like, according to Lewis? Although earlier in this paper he wrote that they are very much like our world, only reconfigured. However, he does say that the physics of these possible worlds may be different from our own. Indeed doesn't it follow from a belief in possible worlds that certain possible worlds must have alternative physics? It depends, I suppose, on whether or not there are infinite possible worlds, or even just billions. If Lewis confesses to not knowing anything certain about any possible world, then he sure as hell doesn’t know how many there are. He quite happily accepts, as I've said, alternative physics. However, he doesn’t accept that they have alternative logics or mathematics. And isn't that the primary point (if they need a point) of possible worlds? Of course Lewis isn't talking about specific or generally-accepted logical or mathematical systems and truths, only that logical and mathematical truths and realities will be true and real regardless of our efforts to codify them. He is, therefore, a realist rather than an anti-realist about logic and mathematics. There may be some logical or mathematical truths or realities than we human beings can never or will never know or be able to formulate (e.g., Goldbach's theorem). And here I detect a circular argument. Why are logical or mathematical truths necessarily true? Because they are true at all possible worlds. Their necessity comes from their being true at all possible worlds. In order to guarantee or insure necessity, we need possible worlds. The necessary truths of particular other worlds are dependent on their being necessarily true at all other possible worlds.

Nolt explains Lewis’s view in this way. According to Nolt, what brings about the existence of a possible world is the ‘mere consistency of an assertion’. If that assertion is consistent but not true at our world, then it must be true at another possible world. Basically it can only be consistent of there is another possible world at which it could be true. In other words, it could not be consistent unless it could, or is, true at another possible world.

Lewis believes that if an assertion is consistent, then there must be a possible world at which it is not only consistent, but also true. However, Nolt does not see consistency this way. Because there is a possibility that the consistent assertion is true, there must be a world at which it is true. The mere possibility that there could be such a world at which it is true, does not bring that universe or world into existence. Just because there is a possibility that a world could be such and such a world, does not mean that the world actually exists.

Nolt is saying that in order for a statement to be consistent, that consistency would at least require a ‘model’ that exemplified that statement’s consistency. Without such a model, then how would we know that the statement is indeed consistent? If there is always a ‘model’ of a consistent statements, then surely there must be a ‘world’ at which that statement is also true. The obvious question remains: Is a ‘model’ also a ‘world’? Perhaps we can now say that if there is a model, then there must also be a world that exemplifies that model. A consistent statements requires a model and a model requires a world:

Nolt admits the fact that the

consistency of a statement does entail the logical possibility in which the statement is true.

If the statement is genuinely consistent, then it is indeed the case that there is the logical possibility that there is a world in which that consistent statement is also true. There is a logical possibility that there is a possible world at which that statement is true. However, this logical possibility of a world does not itself mean that there is such a world. Nolt, therefore, sticks to his original position: possibility does not entail actuality or existence. More simply, there is the logical possibility that there could be, or that there is, a golden mountain. However, that ‘mere’ possibility does not in and of itself bring about that mountain’s actual existence.

In Lewis’s scheme, the words ‘actual’ and ‘exists’ are distinguished. Things are only ‘actual’ according to as they exist at our world. Possibilia only ‘exist’ at other possible world. According to another possible world, things in their world are also ‘actual’, but only actual to them. That must mean, by hypothesis, that we are not ‘actual’ to them. We merely ‘exist’ to them. However, according to Nolt, these two words, in ‘plain English’, are in fact synonymous.

Hobbits do not exist because they are not actual.

In order for there to be ‘possible Hobbits’ these must be ‘actual’ Hobbits. Lewis, on the other hand, says that possible Hobbits exist, but they are not ‘actual’ to us at a-world.  Of course possible Hobbits will be ‘actual’ at the worlds in which they ‘exist’.

Things ‘might have been different in various ways’ does not mean that these things are different in various at other possible worlds. This means that these ‘various ways’ things might have been are not actual or existent. There need not be possible worlds at which these ‘various way’ are, as it were, instantiated. There are lots of ‘ways things might have been’. This does not mean that these things are at other possible worlds. Tony Blair, for example, might have died as a child. This does not mean that Tony Blair himself, or his counterpart, died as a child as another possible world. (We can also ask here: In what sense would this dead child be Tony Blair?)

Possible worlds, then, determine the truth of our modal statements about necessity and possibility. If

Blair could have been a serial killer.

has a truth-value, then it does so care-of a possible world at which that statement is true. Similarly

Blair must be a person.

 is made a true assertion of necessity because at all the possible worlds in which Blair exists, he is always a person at these worlds. This means that our modal idioms effectively quantify over possible worlds. We could even say that possible worlds provide the truth-conditions for modal statements. In other words, what makes the statement ‘Blair must be a person’ true? It is true because other possible worlds make it true. Blair is a person at all possible worlds. Similarly, what makes the modal statement

Blair might have been a serial killer.

true? It is true because at least one possible world Blair, in that world, is in fact a serial killer. These possible worlds make these modal statement true or false. How else could we establish their truth-value?

It is accepted by the possible-world realist that possible worlds are ‘causally disconnected from us’. In that case, how do we know anything about them? Perhaps the possible-worldist would say that we do not need to be causally connected to possible worlds. We know what happens in the sense that we know what must, and what must not, happen in them. We know a priori what must happen at possible worlds. This means that if a modal statement is in fact true, then there must a possible world that makes it true. Therefore there must be a possible world that does what the modal statement says that it does. If the statement ‘Tony Blair might have been a serial killer’ is true, then there must be a world at which Blair is a serial killer. We know this a priori. We do not need ‘causal contact’ with the worlds at which Blair is a serial killer. There simply has to be such worlds. We know about possible worlds quite simply because we know that they have to exist, and how they exist, by virtue of the nature of our modal statements themselves.

Of course, these are metaphysical claims about possibility and possible worlds. Stalnaker is correct to say that these worlds are ‘unverifiable speculations’. The possible worlds must be, but we cannot verify their existence in the way that we can verify the existence of something in our own world. Of course something that is ‘causally disconnected’ cannot be verified by us. Possible world semantics is about what must be the case and what possibly could be the case about other possible worlds. They are like the philosophical ‘propositions’ in Wittgenstein’s Tractatus. They too cannot be verified in the way that world-directed scientific statements can be verified. However, these philosophical and logical propositions could still tell us what is the case and what must be the case and what could be the case and what couldn’t be the case. They were still, nevertheless, unverifiable. Tractarian propositions tell us about the ‘logical structure of the world’, just as modal statements tell what must be the case for these statements to be either true or false.

Because possible worlds are defined by the way that they are needed to make modal statements true or false, then it will be of no surprise that possible worlds taken in their entirety are seen as 

maximal consistent set of propositions.

In order to make one modal sentence true, there needs to be a situation or thing at another world that makes it true. What of the entire possible world itself? Well now, instead of a single modal statement, we have a ‘set’ of statements or propositions that if taken together, and taken to be true, must be made so because there exists a possible world that makes them true. This means that a ‘world-story’ will make a ‘maximal consistent set of propositions’ true. Not only that, but in order to have a ‘world-story’, or a possible world, the set of statements that makes or needs it will need to be consistent. All the statements in that set must not contradict one another. If one statement contradicted another, then the set to which they belong would not be consistent. And if it were not consistent, then it could not rely on a ‘world-story’ or a possible world. However, there is no mention here of ‘modal’ statements. There are just references to statements. If that is the case, then non-modal statements would not need a ‘world-story’. They would simply need only our own world because they do not claim anything about necessity and possibility.

The set of true and consistent propositions are not actually the possible world itself. The possible world is what will make that set true. That’s why, one presumes, that possible-worldists talk about ‘maximal sets of consistent statements’ being possible worlds. The sets need or require possible worlds in order to be taken as true within modal contexts.

If we use the existential quantifier within a modal context, then the quantifier must change its meaning. Ordinarily, the existential quantifier’s domain includes objects that actually exist. In modal logic, it must also include ‘merely possible objects’. This means that the existential quantifier is quantifying over things that do not exist, but are merely possible. How can we therefore call it the ‘existential’ quantifier if it is also quantifying over possibilia? The verb ‘exists’ therefore seems to lose both its currency and its point. In modal logic, therefore, the existential quantifier now means ‘there is possible’ or ‘there could be’. This must mean that the domain of existential quantifiers will expand indefinitely, perhaps infinitely. Similarly, the universal quantifier must change its meaning within all modal contexts. The universal quantifier no longer means ‘for all…’, where ‘all’ means ‘all that exists’, it must now mean ‘for all possible’. Here again the domain of quantification will expand indefinitely because it will also include possibilia. Again, how can the existential and universal quantifiers quantify over things that do not exist? Is a domain that includes possibilia indefinite in size? And if that’s the case, then the existential quantifier seems to loose its point:

◊ p is true iff $x (x is a (possible) world & p is true in x).

Counterparts

Take the pointlessness of exact duplicates. If we have exact duplicates at other possible worlds, then there is no point in experimenting with possible worlds. One of the points of possible worlds is to see what happens in situations that could have been different or objects that could have been different. This wouldn’t work with duplicates. I would not say that possible worlds “do not contain identical objects”, only that if they did, it wouldn’t be of any use to possible world theorists.

I will play Lewis’s advocate here. Someone says:

Something is necessary if it is true at all possible worlds.

Lewis might have asked:

How do you explain the necessity of this and that, without believing in possible worlds? Where is the necessity in our own world? Point to it. If you can’t point to it, then describe it.

Quine, for example, would say that there is nothing over and above 2+2=4 being true. Where is its necessary truth? Quine, therefore and in most cases, denies necessity. Lewis argues that possible worlds provide an answer. To use Lewis’s own words:

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

Tony Blair could have been a serial killer. Can we show or even prove this without pointing to a serial killer called “Tony Blair”, or perhaps Tony Blair with a different name, at another possible world? What is this thing – Tony Blair being a serial killer? Where is it? What is it? If something could be the case, then something necessarily could be the case. Then how do we show that Tony Blair could have been a serial killer without pointing to Tony Blair at another possible world? In our world Tony Blair couldn’t be or have been a serial killer, because in this world, say, Tony Blair wasn’t violently abused by his dad, etc. But at another possible world, this did happen to Tony Blair. Then we have truth conditions that back up the statement that “Tony Blair could have been a serial killer” (i.e., given certain conditions).

The same goes for essential properties. How does an anti-possible-worldist show or prove to us that certain properties are essential? Tony Blair’s smile may be essential to him in this world, but not at another possible world. Again, without possible worlds, what is this thing – this essence? Show me it. Describe it. Can it be quantified without the help of possible worlds? Again, someone like Quine denies the existence of essences and therefore contingences. Therefore possible worlds provide a lifeline for essentialists (e.g., Plantinga). Without possible worlds, Lewis and Plantinga would argue that there wouldn’t be essences because we couldn’t know if they were indeed essences.

Why are some worlds possible and not others? I can offer a – circular – argument. Some worlds aren’t possible because no other world could instantiate them. At no other possible worlds are non-possible worlds possible. Some may define the possibility of rejected possible worlds by the reality of existent but not actual possible worlds. As to explaining without using the term or concept necessity, this would be a win-win situation for those that deny possible worlds. We are asking the possible-worldist to defend his arguments without the notion of necessity, but necessity is what possible worlds are all about. We are asking him to defend possible worlds with arguments that may reject or deny possible worlds. Therefore we are asking him to argue a position that is self-contradictory. Perhaps this is a virtuous circle, on the possible-worldist’s part.

Lewis agrees! He says:

Our modal opinions do change, and physicists do a lot to change them..

We have indeed limitations on our imagination. And physics does change our notions of what is necessary and what is not. For example, Quine has suggested jettisoning the Law of Excluded Middle in the light of the findings of quantum physics. However, I think that what Lewis would say here is that these are simply epistemological - or philosophy of science - points, not metaphysical ones. What are necessary remain necessary regardless of the findings of quantum physics, etc. This sharply divides metaphysics from epistemology. And of course some philosophers believe that there can’t be such a division.

Possible cases are not actual, but they could be. Surely we will learn a lot by exploring possibilities. And the best and most fruitful of doing so, is by postulating possible worlds at which these possible happenings and beings become actual. Indeed we can actually learn something about the actual by playing games with the possible. It could well be the case that clairvoyance is ‘reliable’, or an ‘intellectual virtue’, at other possible worlds.

And that’s why possible world scenarios are so useful and helpful when it comes to clarifying and explaining our modal notions or intuitions. We need not be realists about possible worlds. Indeed sometimes we don’t even need possible worlds but can make do with possible planets or even possible situations in our own world. And on a smaller less exotic scale, we can even make do with possible situations or counterfactuals. However, counterfactuals are often cashed out in terms of what could happen at our world and according to this world’s natural laws. Sometimes we need to travel to possible worlds in order to enlarge our space of possibilities to include worlds that do not have the same natural laws as our own world. It could be said that clairvoyance does not work in this-worldly counterfactual situations, but it could be reliable at another possible world. And if it is reliable at least one possible world, what would that possible world tell us about clairvoyance that the actual world doesn’t tell us? What would be needed at that world to make clairvoyance a reliable tool of knowledge acquisition? At a more extreme level, if there were a world at which entities were not self-identical, what would it be about that world that made this strange possibility actual?  

In one sense, our counterparts tell us what is essential to us. If all our counterparts are human, then I am essentially human. Similarly, if all my counterparts are ‘corporeal’, then I am essentially corporeal. It follows from this that all the attributes I share with my counterparts are essential attributes. Again, the attributes that I share with my counterparts tell me which of my attributes are essential and which are merely contingent. How do I find my essence? By putting together, as a collection, all my essential attributes. The collection will be, therefore, my essence. This must mean that some of my counterparts will not have my complete essence, but they will share with me certain of my essential attributes. If a counterpart shares all my essential attributes, then it would no longer be my counterpart – it would be me. Also, if a counterpart shared my entire essence, then it would not work as a counterpart because it would be a simply replica or duplicate.

A counterpart is a counterpart because it shares part of our essence. And we get to know our essence by seeing what our counterparts are like. But surely we must define our essence first in order to discover our counterparts. We do not in fact get to know our essence from analysing our counterparts. We get to know our counterparts after we have stipulated our essence. What we do learn from our counterparts, however, is what we would d and what we would be like in other worlds. Even though they have our essence, or part of our essence, they still behave differently in different worlds. Lewis says that we

have just defined the essence of something as the attribute it shares with all and only its counterparts.

This seems to suggest that we discover our essence by seeing what properties we share with our counterparts. But, again, we would not recognise a counterpart as a counterpart if we had not already determined our essence. That determination of essence allows us to find or discover our counterparts at other possible worlds. We class something a counterpart if it shares our essence. We do not discover our essence by analysing our counterparts. I discover that a counterpart shares my essence only after I have already determined what is in fact my essence. And then we can see how our counterparts behave given the fact that they share our essence.