Modality and Possible Worlds
“As the realm of sets is for mathematicians, so logical space is a paradise for philosophers. We have only to believe in the vast realm of possibilia, and there we find what we need to advance our endeavours” – David Lewis
The idea of other possible worlds and universes, especially the idea of the multiverse in theoretical physics, is now prevalent in popular science. Type in “multiverse” into google and you’re sure to find millions of articles about the multiverse hypothesis. There are several different kinds of multiverse that physicists talk about, the distinction between them is made clear in Max Tegmark’s book “Our Mathematical Universe”.
We have one level of multiverse where all the universes are spatiotemporally connected, but they’re so distant now that no light signal could ever travel to one and back – no communication or travel to them is possible.
There’s also a quantum level of multiverse that physicists discuss. If a quantum event occurs, then for each possible outcome of the quantum event, you have a distinct universe in the multiverse in which that quantum event happens. The saying “anything that can happen will happen” is associated with this kind of multiverse.
There are other kinds of multiverse that physicists discuss, but there’s an entirely different kind of multiverse that is discussed by philosophers, not physicists. This is the multiverse of “possible worlds”, and was introduced as a semantics that made modal statements much easier to analyse.
The inspiration for this article comes from a discussion I recently had with a Christian apologist. It was their contention that if the multiverse of the physicists existed then it followed that “Christianity is correct” must be true in one possible world, and since this entails that God exists in one possible world, then God exists in the multiverse and so “Christianity is correct” is true in all worlds.
The fallacy made by the apologist here is equating the physicist’s idea of the multiverse with the philosophers’. As I will detail now, the possible worlds that philosophers speak of are very different.
Possible world semantics was introduced into metaphysics because of the way it made sense of modal statements.
What are modal statements? We make them all the time, whenever we say something like “I could’ve studied History at university instead of Physics”, “I could’ve been born with blue eyes” we make a modal statement. To sum it up, modal statements are statements about the way things could’ve been.
But what does it mean to say something could’ve been otherwise? What fact makes the statement “I could’ve been born with blue eyes” true? Philosophers introduced possible worlds semantics to make sense of modal statements. Here’s an idea of how it works:
- When we say “I could’ve been born with blue eyes” what we’re saying is that there is a possible world in which you exist, and you have blue eyes
- A possible truth is one that is true in at least one possible world
- An impossibility is a statement that is true in no possible world (2+2=5 is a suggestion for an impossibility)
- A necessary truth is one that is true in every possible world
- What makes statements like “I could’ve been x instead of y” true or false is whether there exists a possible world in which you are x instead of y
So far we have made no commitment to the existence of these possible worlds. All we’ve done is come up with a way of talking about modal statements that makes them easier to analyse.
Whether the possible worlds of philosophers actually exist is another question that is hotly debated. It’s another question entirely whether any meaningful identification can be made between the possible worlds of philosophers and the multiverses that physicists talk about.
Modal Realism and Ersatzism
David Lewis is perhaps the most famous name associated with possible worlds semantics. It was his book “On the Plurality of Worlds” that really kickstarted interest in possible worlds in metaphysics. It is critical reading for anyone studying modality at university.
Now David Lewis defends a position known as “modal realism” – that these possible worlds are all real in the same way that our universe is real. Lewis’ realism is radical but has its supporters.
More commonly, philosophers tend to adopt an “Ersatzism” about possible worlds. They claim that this is the only universe that exists, but we can logically construct Ersatz possible worlds which we can use to assign truth values to modal statements.
One proposal for the nature of these Ersatz possible worlds is that they’re sets of consistent sentences. Imagine a list of every sentence that could ever possibly be formulated. Ersatz possible worlds are this list of sentences but with different truth values (true or false) assigned to each sentence in a consistent way.
For example in this world “Donald Trump won the 2016 presidential election” is true, whereas this sentence will be false in other possible worlds.
It should be clear that this kind of possible world semantics is different to the multiverses that physicists speak of. Whereas (unless it’s an impossibility) “Christianity is correct” will be a sentence that is true in some possible world for the philosopher, the other universes that physicists speak of are built up of quantum events and not sentences.
“Everything that can happen, will happen” is a misleading moniker. It does not mean that somewhere in the physicist’s multiverse there is a universe in which Christianity is correct. All it means is that all the possible outcomes of a quantum event are realised in some universe in the multiverse.