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Possible Worlds

The following is a tutorial essay for Knowledge and Reality with Daniel Kodsi. In effect, it is a quick agenda for an hour-long discussion on a guiding question, which for this week was ‘Should we believe that there are possible worlds? If so, should we believe that there are Lewisian possible worlds?’. A free-standing and much more readable version of some of the material may eventually go up on my Substack.

The first section of the original essay was quite bad, and is totally superceded by work in higher-order metaphysics, where the debate really should be taking place. I’ve replaced it with a relevant passage from Peter Fritz’s book.

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I take a Lewisian possible world to be something that, for some possible state of the world, really is that way. Note that this does not automatically require that every Lewisian possible world is spatiotemporally connected; that only follows if ‘island universes’ are impossible (that is, if it’s absolutely impossible for the world to comprise disconnected spacetime regions). But this relaxation makes it only easier to believe that there are Lewisian possible worlds. In the other direction, we set aside the uncontroversial fact that there is something (namely, the world) which really exemplifies a possible world (namely, the way the world is), and so there is a Lewisian possible world. §II argues that we should not believe that there are Lewisian (merely) possible worlds.

I. We should believe that there are possible worlds

[As noted above, the original content of this section is completely superceded. Here’s a representative quote Peter Fritz’s The Foundations of Modality (2023), although the argument is well-known. Essentially, a possible world is a proposition that, for every proposition, strictly entails exactly one of either it or its negation.]

Informally, the argument goes as follows. Consider first the truths (the propositions which are true), and then the proposition that they are all true. Every truth is true, so the claim that they (the truths) are all true is true as well. A universal claim strictly implies every one of its instances, so the claim that they (the truths) are all true strictly implies all of the truths, and so is maximal. Thus there is a true maximal proposition. This line of argument does not depend on any contingent assumptions, so the conclusion should hold necessarily. So, necessarily, there is a true maximal proposition, which is just what Atomicity claims.

II. We should not believe that there are Lewisian possible worlds

I take it that, by default, we should not believe that there are Lewisian possible worlds. I allow that we can be agnostic on the matter; but in the absence of a compelling reason to believe that there are Lewisian possible worlds, we should not believe that there are.

We might make the following argument for believing in Lewisian possible worlds. (Compare Lewis 1986.) First, consider an analogy: the set-theoretic universe is a paradise for mathematicians, so we should admit pure sets into our ontology. That is, ZFC is a remarkably good theory, so we should believe that it’s true. We should believe that there are things which play the postulated theoretical roles, and in particular we should believe in pure sets (the domain of the intended interpretation). We interpret mathematical claims as claims about the pure sets. Similarly, the thought goes, the Lewisian universe is a paradise for philosophers, so we should admit Lewisian possible worlds into our ontology. That is, theories which appeal to ways that the world might be are remarkably good, so we should believe that they’re true. We should believe that there are things which play the postulated theoretical roles, and in particular we should believe in Lewisian worlds (the domain of the intended interpretation). We interpret modal claims as claims about Lewisian worlds.

I grant that modal theories are very fruitful. One example is probability theory as applied (with great success) to the real world, where the sample space is intended to be understood as a set of ways that the world might be, each of which fully determines all of the features we’re interested in. We can also appeal to possible worlds when giving semantics of formal and natural modal languages; this approach has led to a well-established research program in both philosophy and linguistics.

However, I argue against the further claim that we should believe in Lewisian worlds, and understand modal claims in terms of them. Firstly, the most obvious candidate for what plays the theoretical role of possible worlds are just the possible worlds themselves. (What naturally plays the role of the pure sets are just the pure sets themselves.) But perhaps these aren’t really entities in the required sense; one might hold that they’re merely properties of entities. For one reason or another, our theory can’t actually be directly about them; we need representations of them to play the requisite theoretical roles. This opens up a gap: what connects the representations to the possible worlds they represent? The only viable representations, on Lewis’s view, are real things which exemplify the corresponding world (things which are thus of the same sort as us and all of our spatiotemporal surroundings). In particular, it’s not possible for simple abstract entities to somehow represent possible worlds: this would require a suspicious necessary connection between the entity and the possible world.

But there just doesn’t seem to be anything mysterious or magical going on here. (Compare Kripke 1980.) Conventionally, for very basic probability theory, random variables always map to the real line; if the values I’m interested in are, say, what color a traffic light is going to be, I can just arbitrarily let the event X(w) = 1 represent red, X(w) = 5 represent yellow, and X(w) = 4 represent green by stipulation. Lewis is free to ask why it’s that way around, or what makes it so that the elements mapping to 1, rather than 5, are rightly called ‘red’, or what makes it so that the ones mapping to 1 rather than 5 are those necessarily mapped to if and only if the traffic light is red, or how anything can have these necessary connections. But, in this simple setting, these questions just seem totally irrelevant. When we want to represent ways the entire world could be, rather than just ways the traffic light could be, there is no more mystery. Further, it’s not even clear how much better Lewisian possible worlds represent ways that the world could have been. (Compare Stalnaker 2012.) Some other Lewisian possible world being some way doesn’t seem to automatically represent the actual world being that way. (Painting a wall blue doesn’t represent that wall as being blue, let alone represent the wall in front of me as being blue.)

So, although modal theories are fruitful, they only require that we believe that there are other ways that the world could be. If, for one reason or another, we require that the theory works with representations of these ways rather than the ways themselves, we can (as is commonplace) just arbitrarily stipulate that some simple abstracta do the representing.

Now, there might be other ways for believing in Lewisian worlds. One might think that, on the correct interpretation of quantum mechanics, reality has some branching structure; but these ‘many worlds’ would be spatiotemporally connected, and hence part of the same Lewisian possible world. (But see Wilson 2020.) One might think that the existence of Lewisian possible worlds predicts with certainty that I would have the exact experiences I do have, which on other theories this is very surprising, and so I should update massively in favor of Lewisian possible worlds; but as Lewis (1986) notes, more antecedently plausible views ‘might do to meet whatever need there is for an anthropic principle in cosmology’. In any case, we haven’t seen a compelling reason to believe that there are Lewisian (merely) possible worlds; so, we should not believe that there are.

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