The Thesis of Modal Realism

A few post ago I was talking about formal systems.  As an example I talked a little about Hofstadter’s example of the MIU system and promised to talk about decision procedures.  I would hate to be a liar and so I do plan on returning to this matter.  However, it seems appropriate to me to take a diversion into the philosophical foundations of Tegmark’s view before delving into the more mathematical aspects.  For this reason, and in keeping with the announcement of my previous post, I am going to interact a bit with David Lewis’ work On the Plurality of Worlds.

So, what is Modal Realism?  From what I gather, the name was actually coined by Lewis, though he expresses certain regrets for calling it this based on some ambiguity in the term ‘realism’ and what it has come to mean in academia.  As one who is less familiar with the larger body of literature on realism, I find the name perfectly appropriate and satisfying.

The term ‘modal’ comes from modal logic which analyses the notions of necessity and possibility.  G.E. Hughes and M.J. Cresswell summarize this discipline similarly:

Modal logic can be described briefly as the logic of necessity and possibility, of ‘must be’ and ‘may be’.

‘Realism’ as Lewis intends to use it deals with ontology.  Put together, modal realism is

… the thesis that the world we are part of is but one of a plurality of worlds, and that we who inhabit this world are only a few out of all the inhabitants of all the worlds.

In other words, modal realism takes possible worlds semantics quite seriously as well as literally.  Upon reading this description, one may be tempted to think of modal realism as a multi-verse theory and indeed it is (we’ll see that it corresponds to Tegmark’s Level IV multiverse), but not in the sense often portrayed in popular literature.  The worlds of modal realism are not some distant universes located some vast, albeit finite, distance away.  Nor are they located in some alternate dimension of this reality.  As Lewis puts it,

They are isolated; there are no spatiotemporal relations at all between things that belong to different worlds.  Nor does anything that happens at one world cause anything to happen at another.

One should liken this to the way in which the vector space $\mathbb{R}$ is isolated from the finite field $\mathbb{Z}_{7}$, to sneak in some mathematics.

Lewis goes on to say,

The difference between this and the other worlds is not a categorial difference.  Nor does this world differ from the others in its manner of existing.  I do not have the slightest idea what a difference in manner of existing is supposed to be. [emphasis mine]

Thank you!!!  I expressed this very sentiment in A Philosophical Interlude.  It always feels amazing when one’s own thoughts are legitimized by world renown experts.  Okay, enough tooting my own horn.  The idea, here, is that some things exist, say, on Earth, while other things exist elsewhere and this is a difference in location of existing things (not a difference in any mode of existence).  Similarly, though somewhat more controversial, some things exist in the past, others now and still others in the future.  This is a temporal difference (we will deal with the nature of time in another post).  To extend this further, it seems reasonable that the same could be said for worlds.  Some things exist in this world and other things exist in other worlds and this is still a difference between existing things as opposed to a difference in any mode of existing.

For those not familiar with the language of possible worlds, I should hasten to point out that a world need not be a synonym for a universe (though it might be).  Rather, a world is a complete state of affairs, an entire reality.  Thus, in our world, if there is a God who created the universe, then clearly our world is more than just our universe.  Alvin Plantinga in his book The Nature of Necessity defines a possible world to be a maximal state of affairs and a maximal state of affairs $S$ is one such that for every state of affairs $S'$, $S$ includes $S'$ or precludes $S'$.  Note the similarity of this definition with that of completeness for a mathematical system:

A system is complete if, for every statement $p$, we can find a proof of $p$, or a proof of not-$p$.

Here “proof” refers to a demonstration within the system in question using the axioms and the rules of inference. In other words, a “proof”, here, of a statement $p$ within a system $S$ “consists of a sequence of statements, each of which is either an axiom or a logical consequence of certain preceding statements in the list, such that the last statement in the list is $p$.”

At this point, we needn’t get bogged down in technicalities.  The basic idea is that modality is best understood by actually taking possible worlds semantics as more than just semantics.  According to modal realism, all possible worlds are actual worlds, where actuality is taken to be indexical.

11 comments on “The Thesis of Modal Realism”

1. akismet-d742a703e2ea28d6b6032af5f1a20f3c says:

“Nor does anything that happens at one world cause anything to happen at another.”

Consider:

1. It is the case that in a particular possible world “W23”, Louis does not comment on this blog post tonight.

If (1) is true, then it is true in every world (since it is world-indexed). Thus my not commenting on this blog post in W23 tonight causes it to be the case in another world, indeed in every other world, that I did not comment on this post in W23 tonight.

Now, consideration of (1) was critical to my decision to write this post in the actual world tonight. Therefore it is the case that something that happened (or in this case, something that didn’t happen) in one world caused something to happen in another.

2. akismet-d742a703e2ea28d6b6032af5f1a20f3c says:

“…some things exist, say, on Earth, while other things exist elsewhere and this is a difference in location of existing things (not a difference in any mode of existence)”

I take it that possible worlds are not worlds that differ in their modes of existence at all, since existence is binary (an object can’t “kind of” exist). It is simply that possiblia are of a different genus altogether than actualia. So a possible world exists just as much as the actual world does. However the fact that a wooden duck and a live duck both exist equally as much as one another (it is not as if the wooden duck “kind of” exists), it does not mean they are ontological equals. Similarly, the actual world exists as an actuality, while possible worlds, though existent, are not actual.

The ontological difference between being possible and being actual cannot be overstated.

3. Ryan says:

This is definitely an interesting potential counter example, though, admittedly it depends on what one means by “causation”, which I didn’t define. I might respond that it wasn’t so much anything in W23 itself that “caused” you to comment in $\alpha$, it was your own understanding of something about W23 in $\alpha$ that caused you to comment in $\alpha$. There certainly exist logical relations between possible worlds, which allows content about other worlds to be apart of our world $\alpha$ (and any other world).

4. Ryan says:

Existence is certainly binary with respect to any possible world $W$. The question, though, seems to be about how something exists. What does it mean to only exist as possibility and for something else to be both possible and possess some strange quality of actuality? It is exactly the genus notion that I am questioning. As of right now, actuality seems best understood (if not only understood) as indexical. Otherwise, it simply remains as some mysterious “genus”, which can only be described in some kind of Heideggerian terms of “thereness”. I find this woefully inadequate.

…the actual world exists as an actuality, while possible worlds, though existent, are not actual.

I could actually agree to this, except that I would say that possible worlds are not actual in $\alpha$.

5. akismet-d742a703e2ea28d6b6032af5f1a20f3c says:

“The question, though, seems to be about how something exists.”

Whether my contention with this is simply a matter of phrasing or something more substantive, I want to be clear that I am trying to say that the issue is not in fact about _how_ worlds exist, but about _what_ worlds _are_.

“What does it mean to only exist as possibility and for something else to be both possible and possess some strange quality of actuality?”

I would rather us say that possible worlds _exist only_ as possibilities than that possible worlds _only exist_ as possibilities.

Here are the definitions I propose:

The broadest domain of possibilities is “logical”. A proposition is logically possible if it is not self-​​contradictory and if it does not otherwise violate a rule of logic.

Inside this domain of possibilities is “metaphysical possibility”. A proposition is metaphysically possible if it is logically possible and it does not violate the rules of metaphysics.

Inside (at least hopefully inside) this latter domain of possibility is “epistemic possibility”. A proposition is epistemically possible for a person A if it is logically and metaphysically possible, and it is unknown to A whether it is true in the actual world.

We often rely on domains of possibility within the metaphysical but not congruent with the epistemic. For example, one might argue that it was historically possible for Gore to win the election instead of Bush. This would mean that it was not only metaphysically possible, but also that the initial conditions, constants, quantities, and laws of the actual world and all of the antecedent conditions leading up to a given moment in history did not sufficiently determine that Bush would win the election.

A possible world is a maximally specific set of metaphysically possible propositions.

So on these definitions, for a possible world to exist only as a set of possibilities simply means that its propositions may not be true. For example it is not true that I did not comment on this blog on the 15th of August, 2012. While you might counter that it is true in some possible world, I would simply say that such would only mean that my not commenting on this blog on August 15th would not violate the laws of logic or metaphysics. It does not mean, nor does it entail, that there is a whole world out there, being as vividly experienced by sentient beings as the actual world, in which I do not comment on this blog (never mind that it couldn’t truly be me in such a world).

Wielding “possible” and “actual” like predicates frames the discourse in a way that makes it seem like an object may be possible or both possible and actual. However it seems to me that for an object to be possible but not actual would mean that such an object does not exist at all! What would exist however, would be proposition that stipulates that the existence of the object in question would not violate the laws of logical or metaphysics. To say that the object “exists in a possible world” is merely a façon de parler.

For you to disagree with this and insist that possible worlds are actual for their inhabitants would result in a view according to which I would say (and have said), “possible worlds don’t exist”.

“[On your ersatzist view], [actuality] simply remains as some mysterious “genus”, which can only be described in some kind of Heideggerian terms of “thereness”. I find this woefully inadequate.”

The strange quality of actuality (or as I would say “existence”) may be difficult to understand or put into words, but so are many features of reality. Consider that even on modal realism the actual world—in fact every possible world—contains some objects (which would be both possible and actual) _but not other possible objects_ (which would not be actual). What is the mysterious distinction between _those_ sets of sets of objects?

6. akismet-d742a703e2ea28d6b6032af5f1a20f3c says:

*would be a proposition that stipulates

7. Louis says:

*laws of logic or metaphysics

8. Ryan says:

What are the rules of metaphysics?

9. Louis says:

An example from Roderick Chisholm is that an object may not be opaquely red all over and green all over at the same time. This impossibility turns out to be neither logical nor physical, but metaphysical.

10. Ryan says:

Not sure I buy it. Why wouldn’t that be logical?

11. Louis says:

Because redness and greenness themselves are not features of logic and their properties, such as that each excludes the other, cannot be derived from the laws of logic. Only after one understands what redness is and sees that it excludes greeness can logic help one see that they cannot be simultaneously present in an object.