# Briefly on Modality and Possibility

Consider statement $\alpha$, ‘McCain could have won the 2008 election.’  What makes statements about what is possible (but not actual) true or false?  You might say that, ‘there exists a way things could have been, such that McCain was the winner of the 2008 election.’  One interpretation of what it is for that to be true is to read, ‘there exists a possible world where McCain wins the 2008 election.’  This raises the question ‘what is a possible world?’  We will discuss two views addressing this, (1) linguistic ersatzism [LE] and (2) modal realism [MR].

A possible world is like a ‘worldbook’; something that describes to the very last details everything that is true of the world.  Think of a worldbook as a maximally complete and consistent set of propositions.  Proposition $\beta$, ‘McCain is the winner of the 2008 election’ is an element of a consistent set of propositions — it cannot include $\neg \beta$, e.g. $\gamma$, ‘Obama is the winner of the 2008 election’, because then the set would be inconsistent.  So the  complete and consistent set that includes $\gamma$ must be different than the set that includes $\beta$, and so each set must be describing a different possible world.  In contrast, saying that ‘it is necessary that Obama wins the election’, means that in every possible world Obama wins the election — though this is likely false.

LE sits nicely with this.  An ersatz possible world is an abstract formulation of a possible world, namely a set of propositions (abstract like the set of natural numbers).  To define a set of propositions, a world making language is used, e.g. the lagadonian language.  Let each object and property in the actual world be name for itself, e.g. if there is a grey table, then it also represents the proposition ‘the table is grey.’  We can recombine objects and properties in conceivable ways (like ‘the table is blue’), each recombination defining a possible world.  So all possible worlds will be some recombination of the objects and properties of our actual world, to be identified with abstract, complete, and consistent sets.

On LE, to say $\alpha$ means that there exists a complete and consistent set of propositions which contains $\beta$.  Crucially, there is no commitment to the abstract set actually being instantiated somewhere in reality.

MR, championed by David Lewis, maintains that the possible worlds must be real, concrete entities, as opposed to abstract sets.  (With ersatz possible worlds being the mere abstractions of the concrete possible worlds.)  Lewis cannot conceive of our actual world as a mere set of consistent sentences; consequently, he cannot conceive of possible worlds as being mere abstractions.  This is prima facie parsimonious: we are not asked to believe in any strange, new kind of thing, but rather just an infinity of things of exactly the same kind of thing as our own universe.  On this view, each possible world is as real as our own, and each is causally and spatiotemporally isolated from the other.  ‘Possible’ is to be contrasted to ‘actual’ insofar as ‘actual’ is treated as an indexical.  That is, ‘the actual world’ refers to this world, the one occupied by us.  When a person in a different world says ‘actual’ they are referring to their world.  A possible world is the same kind of thing as the actual world, but with varying degrees of differing facts.

On MR, when I say $\alpha$, I am saying that there exists a possible world where a counterpart to the John McCain in the actual world wins the 2008 election.  A counterpart is an entity in a possible world bearing the relevant similarity relation to the entity-in-question in the actual world.  Relevant similarity is dependent on the context of the modal statement, for the similarity between any two objects is dependent on the aspect of their comparison.  So $\alpha$ means there is a possible world where a counterpart McCain wins the election — the actual McCain and the counterpart being united by their relative similarities insofar as, e.g., being a senator, a war vet, or such-and-such age.  But if I say that $\neg \alpha$, then any would-be counterpart of McCain who does win the election is not a genuine counterpart, because for me the relevant similarity relating them is not just that he is a senator, but also that he loses the election.  So on MR, what makes it possible that $\phi$ could be $\psi$ is that there exists a possible world, just as real as the actual world, where a counterpart-$\phi$ is in fact $\psi$.

Neither MR nor LE, however, is palatable.  Analyzing modal statements in terms of possible worlds is unintuitive and a mistake.

Here’s why.  Intuitively, when we say ‘$\phi$ could have been $\psi$‘ we are stating a (modal) fact about this world that we inhabit.  We are trying to evaluate something about the potentialities of our universe; we are not trying to evaluate the truths of other worlds, but rather about our world (what is possible for it).  On both LE and MR, our modal statements will not be about our world at all — and this is why they are unsatisfying.  According to MR, saying $\alpha$ is just to say ‘in another spatiotemporally/causally isolated world, $\beta$.’  So a modal statement in our world is not actually about our world at all — rather, it states a fact about some other world, failing to say anything insightful about our world.  Knowing that something is true in a possible world does not entail that that thing is possible in our world, for the spatiotemporal and causal isolation between worlds makes it such that there cannot be a meaningful relation between worlds.  So facts in one world entail nothing about facts in another world, the mere fact that $\phi$ in world $\Gamma$ entails nothing about $\phi$ in world $\Delta$.  Intuitively, that $\phi$ is a possibility for our world is a fact about our world.  Enumerating the facts of other worlds can tell us nothing about our own.

This applies equally to LE.  When I want to know whether something is possible, I do not want to know whether it is part of an abstract, consistent, and complete set.  Rather, I want to know whether events in this world could have unfolded such that some other thing could have occurred.  We may be able to define a complete and consistent set where the gravitational constant is $1/g&bg=e7e5e3$ (instead of $g&bg=e7e5e3$) — but this does not entail that that is a genuine possibility for this world.  In this way, LE equivocates conceivability and possibility.  But we seem to be saying something different when we say something like ‘it is possible that $\phi$‘ versus ‘it is conceivable that $\phi$‘.  The latter does not entail the former.

So how do we think of $\alpha$ without the aid of possible worlds?  Prima facie, $\alpha$, if true, suggests there was a time in this world where things could have turned out such that $\beta$.  But what does it mean for $\alpha$ to be true in this world, where $\neg \beta$ obtains?  What facts, without possible worlds, make something like $\alpha$ true?

Interested in other thoughts.  May update with my own.