Changing How the World Thinks

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Infinite possibilities, infinite worlds

The surprising benefits of a strange theory

21 04 07.Possible worlds

The idea of an infinite number of worlds - each containing all the possibilities presented in our own world - might initially seem bizarre. Certainly David K. Lewis had a hard time convincing his fellow philosophers of his theory. But its application to theories of possibility - and its undeniable similarity to how we already think about time - means that we must make sense of its extraordinary claims, writes Daniel Nolan.

 

David Lewis (1941-2001) was an influential American philosopher of the second half of the twentieth century. His biggest impact in philosophy has been in the field of metaphysics.

One of his views, above all else, struck many of his fellow philosophers as fantastic and hard to believe. Lewis held that, as well as our concrete universe, there also existed infinitely many variations, cut off from our "world" each in their own space and time. These "possible worlds" were not just variants with our fundamental laws of nature but different parameters, they included every way of reassembling the kinds of objects and properties found in our world, plus endless kinds objects and properties not even dreamt of by our physicists.

Each ordinary object is found in only one such possible world, but similar worlds are filled with similar objects. Other worlds thus contain "counterparts" of each one of us, living out their lives in parallel spacetimes. What happens to those counterparts are all the things that are possible for us: since I could have had an older sister (but do not), I have a counterpart with an older sister. Since I could have lived in a castle of gold casting magical spells (in a very generous sense of "could have"), I have a counterpart in another universe living on a golden mountain casting magical spells.

Lewis convinced relatively few other philosophers, but some took his theory very seriously. Lewis's postulation of "concrete" possible worlds, a theory known as "modal realism", provided a clear and straightforward account of how we talk about possibilities and provided an easily understandable background for a number of important applications.

Our ordinary talk seems engaged in talking about merely possible outcomes as well as about actual ones. For example, when we are choosing between actions, the actions that are not eventually performed are in our set of options alongside the ones we eventually choose. Thinking about the possible circumstances captured or excluded by a sentence or belief is fruitful in everyday life and in philosophising. And possible worlds have been fruitful for modelling all sorts of relationships in the theory of knowledge, in ethics, and in the rest of metaphysics.

Possible worlds have been fruitful for modelling all sorts of relationships in the theory of knowledge, in ethics, and in the rest of metaphysics.

This is especially true of counterfactual conditional statements. Sometimes we want to use "if... then..." statements about what would have been rather than what is. "If we had not replaced the electrics, there would have been a fire", or "If the printing press had not appeared in Europe, the Reformation would have been delayed." What does it take for one of these claims to be true or false? Lewis suggested that a counterfactual "If A then C" is true if, in all the possible worlds where A is true and most relevantly similar to our actual world, C is true in those worlds as well.

So, "if we had not replaced the electrics, there would have been a fire" is true provided that in all the possibilities where we did not replace the electrics, and were otherwise most relevantly similar to the actual world, fires break out. The relevant similarities here include not just the laws of nature, but the state of the rest of the system, what kinds of currents flow through the electrics, whether anything flammable is near the wires, etc. etc. Counterfactuals are often difficult to resolve, because it can be unclear what actual circumstances matter, and how much they would have to change in other possibilities for the relevant A to be true there.

Lewis's ‘modal realism’ comes in to establish whether a possible world is relevantly similar to our own. Lewis's theory is far from the last word on counterfactual conditionals, and understanding them and the role they play in our navigating the world is an ongoing challenge for philosophy, cognitive science, and psychology. But most leading contenders today incorporate some of the insights of Lewis's view in one way or another.

Possible worlds theory might initially look absurd. But perhaps it looks less absurd in the light of two analogies.

The first is an analogy with a theory of other times. When we talk about what has happened, or what will happen, we talk as if there are entire realities like our present, filled with many people, objects and events which do not exist now (although some might). Lewis, like many philosophers, wanted to take this at face value. As well as the people and events happening now, there are many people and events elsewhere in time, just as real and concrete as our present day. If we accept that there are other times like ours, we have a straightforward way of understanding sentences like, "There were T. Rexes sixty-seven million years ago": that sentence can be about flesh-and-blood dinosaurs of a certain sort, out there in reality a long time ago. If one does not think that there is any other time it is hard to talk about T Rexes and their behaviour as if they are living creatures.

Just as it makes sense to think there are other times filled with their own events and objects, it makes sense to think that there are other possibilities, likewise equipped with their own objects and events.

A second analogy is with the many worlds postulated by the so-called “many-worlds interpretation” of quantum mechanics.

This holds that we should understand the probability of each different outcome predicted by quantum mechanics as the distribution of a quantity called "intensity" over the range of concrete alternative outcomes.

Suppose we observe an electron arriving at a detector with spin-up, when our theory tells us that there was a 50% chance it would be spin-up, and 50% spin-down. According to many-worlds interpretations of quantum mechanics, there are multiple outcomes, almost exactly like the one we observe, where an electron arrives at a detector with spin-down. We can explain why we observed a determinate outcome when the fundamental laws assign only probability distributions by multiplying observers: since some of our counterparts observed spin-down and we observed spin-up (along with others of our counterparts), there need be no "collapse process" to break the symmetry between the two outcomes to declare one of them the "real" one.

Just as the many-worlds physicist thinks there is no outcome that is the unique outcome, so Lewis thinks there is no one way the universe is: the universe that seems to us to be the one real universe is simply the one in which we happen to be located. Thinking this one has a special privilege is like the mistake of thinking here must be special, on the grounds that all the other places are unlike here in being far away.

While Lewis's conception of possible worlds did not become orthodox, many philosophers are convinced that using possible worlds in our theorising, and more general thinking about the world, is valuable. In fact it is valuable enough that we must be able to make some good sense of the claim, e.g. that there are alternative buildings that could be built on a given site, or that there are possible animals that could have evolved that would have been larger than any actual animal, past, present, or future.

Discovering the limits of possibility, and what, if anything, lies beyond, can be as exciting as piecing together maps of distant lands.

Suppose we did become "modal realists" and accept the existence of all of Lewis's worlds, together with the idea that those worlds are the alternative possibilities for us and our world. How should that change our sense of ourselves and our place in reality? Lewis appeared to think that it should not change very much at all. Others have thought that it would be very revisionary in one way or another.

My own view is that, if we came to think it were true, it might make a few differences. It might make us more aware of the contingency of many of the aspects of the world we face: almost anything that seems fixed and unalterable here is different somewhere else. You may pride yourself on being the first or the fastest or the best: but even if that is true in this world, there will be others out there doing the same things and thinking the same thoughts. All the wonders, and all the horrors, that are even coherent lie out there somewhere. We cannot hope to affect it all, or even change the overall pattern. All we can hope to do is to tend our own gardens, and make the world better for those we find ourselves with. Perhaps that is an attractive lesson in any case.

The effect on me of Lewis's modal realism has been primarily as a puzzle: how can we understand possibility in a way that has most of the advantages of Lewis's framework without its extravagant posits? But I suspect it may have had another influence as well. In Lewis's scheme, trying to work out the bounds of what is possible, and discovering the principles that are necessary in the strictest sense, has some analogies with ancient cartographers trying to construct maps of the furthest reaches of the world and what their limits are. Like ancient map-makers, we cannot just contact a satellite to send us an image of the terrain. Discovering the limits of possibility, and what, if anything, lies beyond, can be as exciting as piecing together maps of distant lands. To feel that excitement, using Lewis's picture as a guiding myth can be as useful as taking it to be the sober truth.

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