Why Talk of 'Possible Worlds'?

 This from a commenter:

I have a question about a tangential matter, in case you care to respond to it. You say [in your discussion of divine simplicity and modal collapse] that you don't need talk of possible worlds. I don't think I find such talk puzzling, but I've never understood the vogue for it. Since many absolutely first-rate philosophers seem to insist on using it, I assume there must be some great advantage to doing so, and not seeing what that is I assume that there is something important I don't understand. If you care to explain I'd be interested.

The notion of possible worlds dates back at least to G. W. Leibniz (1646-1716) but the current vogue began roughly in the middle of the 20th century when philosophers and logicians applied themselves to the formal semantics of the different systems of (alethic) modal logic. Now this is a highly technical topic but the technicalities can be avoided for present purposes.  I will assume the S5 axiom set. 

Assumption: reality has a modal structure

I will also assume that reality has a modal structure, that modality is somehow ingredient in extramental reality. Thus modality is not a merely epistemic/doxastic matter.  For example, Hillary could have won in 2016. It was really possible for her to have won. Had she worked harder and smarter, kept her trap shut about the 'deplorables,' etc., then she probably would have won.  Things really could have gone otherwise, and this possibility is not parasitic upon our ignorance of all the factors involved in her losing. 

The utility of talking the talk

As I see it, the utility of 'possible worlds' talk is that it allows for an especially  perspicuous representation of modal relationships in extensional terms.  And it seems to me that one can talk the talk without walking the walk. That is, one can  make use of 'possible worlds' (PW) jargon without taking on too many heavy-duty ontological commitments. What do I mean? One thing I mean is that one can employ PW jargon without buying into David Lewis' extreme modal realism. For Lewis, possible worlds are maximal mereological sums of concreta. One can surely talk the talk without walking that walk. How?

Sketch of an abstractist approach to possible worlds

A much saner way of thinking about possible worlds is as follows. If the Lewisian way is concretist, the following way is abstractist: possible worlds are abstract objects, maximal Fregean propositions on one abstractist approach.

0) The actual world is the total way things are. A merely possible world is a total way things could have been or could be. Let that be our intuitive starting point.

The actual world is the total way things are, but not the things that are that way. Thus the actual world is not the same as the universe, whether physical or physical plus any nonphysical items there  are.  Surprised? Think about it!

1) The actual world is a possible world. This is because everything actual is possible. But of course the actual world is not merely possible. Mere possibility and actuality are mutually exclusive.

2) There is a plurality of possible worlds. This is because the possible outruns the actual: the set of actualia is a proper subset of the set of possibilia. So if there are possible worlds at all, there are many of them. If you say that there is only one possible world, the actual world, then that leads to the collapse of modal distinctions, or, to put it less dramatically, the extensional equivalence of the possible, the actual, and the necessary. This view, call it modal Spinozism, cannot be dismissed out of hand. But I will not here argue for the reality of modal distinctions. That is something we are now presupposing.

3) There is and can be only one actual world. This follows from the maximality property of worlds. Whatever one's exact conception of a world, worlds are all-inclusive totalities. (So much is built into the very word, 'world.') If a world is an abstract state of affairs, as A. Plantinga maintains, then it must be a maximal state of affairs: one that includes every state of affairs with which it is logically consistent. If a world is a (Fregean) proposition, then it must be a maximal proposition: one that entails every proposition with which it is logically consistent. These maximal objects are so big that, to employ a chemical metaphor, they are 'saturated': adding another member to them would 'precipitate' a contradiction. So there cannot be two or more actual worlds.

4) There must be an actual world. It cannot be the case that every world is merely possible. If every world were merely possible, then that would be the case, actually the case, which implies that the total way things are would include its actually being the case, which implies that there would be, after all, an actual world. So it cannot be the case that every world is merely possible. Think about it.

5) Possibilities come in world-sized packages: necessarily, if state of affairs S is possible, then there is a world W such that W includes S. This amounts to a denial of 'isolated' or 'worldless' possibilities. I am now blogging, but I might have been now sleeping, where both occurrences of 'now' pick out the very same time. Let S = BV's sleeping now. Had S been actual now, everything would have been different in a few major ways and in an infinity of miniscule ways. So if I had been sleeping now a world different from the world that is actual would have been actual.

6) Actuality is absolute, not world-relative. If by #2 there is a plurality of possible worlds, and by #3 there is only one actual world, then there is a distinction between merely possible worlds and that privileged possible world that is the actual world. Although every world is actual at itself, only one world is actual simpliciter, actual period.

Compare: although every time is present at itself, only one time is present simpliciter. This comparison of course assumes (controversially) that the B-theory of time is false, the theory according to which time is exhausted by McTaggart's B-series, the series of events ordered by the relations earlier than, later than, and simultaneous with. I am assuming that in addition to the B-relations there are also the monadic A-properties of pastness, presentness, and futurity, and that these properties are instantiated.

'Now' of course is an indexical expression: it picks out the time of its tokening. Tokened at midnight, it picks out midnight, at noon, noon. But is 'actual' an indexical? Does its reference depend on the context of utterance so that, tokened in this world it refers to this world, tokened in another, to that other? That's what David Lewis maintains, but I say 'actual' is not an indexical. When I say that this world, our world, is actual, I mean to ascribe to it the monadic property of actuality, a property which only one world can have.

There are many possible worlds, but only one is actual. Furthermore, the one that is actual might not have been actual. So the one that is actual is contingently actual. If that were not the case, the merely possible worlds would not be possible. For whatever is possible, is possibly actual. The worlds that do not bear the privilege of actuality could have borne it.

7) X exists in/at world W =df were W actual, X would exist.  

8) X is a contingent being =df X exists in some but not all possible worlds. It follows from this definition that something, Pegasus say, can be a contingent being even if it does not actually exist. If the word 'being' throws you, substitute 'item.'

9) X is a necessary being =df X exists in all possible worlds.

10) X is an impossible being =df X exists in no possible world.

11) X is actual =df X exists in the actual world, the one world that happens to be actual.

12) Puzzle: It looks as if, on the one hand, 'The actual world is not actual' is a contradiction. On the other hand, it is surely the case that the actual world might not have been actual. The puzzle is solved by distinguishing two uses of  'the actual world.' It can be used as a Kripkean rigid designator that picks out one particular world, this world, our world, and does so in every possible world. Used in this way, 'The actual world is not actual' is possibly true. But 'the actual world' can also be used as a definite description that applies to whichever world happens to be actual. Used in this second way, 'The actual world is not actual' is a contradiction.

13) But what exactly is a possible world? I take an abstractist line. Worlds are maximal (Fregean) propositions or maximal (abstract) states of affairs. They are not maximal mereological sums of concreta, pace David Lewis. If worlds are propositions, then actuality is truth. That is one interesting consequence. Another is that worlds are abstract objects which implies that the actual world must not be confused either with the physical universe (the space-time-matter system) or with that plus whatever nonphysical concreta (minds) that there might be. And if worlds are abstract objects then they are necessary beings. (See #9 above.) So every possible world exists in every possible world.

If actuality is truth, and individuals cannot be true (in the exact sense in which a proposition can be true), then perhaps there is a problem with #11 above.

14) If worlds are maximal Fregean propositions, then no concretum such as Socrates can exist in any world in the manner of a constitutent. This is because concreta are not among the constituents of Fregean propositions. Therefore, to say that there is a possible world in which Socrates exists but dies in battle, is to say that there is a maximal proposition according to which Socrates dies in battle. 

Restriction to alethic modalities

The concern here is with alethic modality, not deontic or epistemic modality. By alethic modalities I understand the modalities of truth, of existence, and of property-possession.

Truth

It is necessary that 2 is a prime number, impossible that 2 is an an odd number, and contingent that 2 is the number of my cats. In PW jargon: 

Every metaphysically possible world w is such that *2 is prime* is true in w.
No metaphysically possible world w is such that *2 is odd* is true in w.
Some (but not all) metaphysically possible worlds are such that *2 is the number of my cats* is true in w.

If we quantify over possible worlds, we can understand the modal terms 'necessary,' 'impossible,' and 'contingent' by analogy with the quantifiers of standard, first-order predicate logic: 'every,' 'no,' 'some.'  And we can then set up a modal square of opposition in analogy to the standard square of opposition.

 

Isn't that neat? The modal relationships fairly jump out at you. Necessarily p entails possibly p. Of course. What is true is true in every world is true in some world, but not conversely.

When I say that the PW representation of modal propositions and inferences is extensional, all I mean is that the representation involves quantifying over possible worlds assumed as given.

Existence and Property-Possession

A necessary being is one that exists in all worlds; an impossible being one that exists in no worlds; a contingent being is one that exists in some but not all worlds. If x has a property essentially, then x has the property in every world in which x exists; if x has a property accidentally, then x has it in some but not all of the worlds in which x exists. If a necessary being has a property essentially, we can say that it has the property necessarily in that there is no world in which it does not have the property. Thus the number 7 is necessarily prime and God is necessarily omniscient.  Socrates, by contrast, is essentially human but not necessarily human.

An important Euthyphro-type question

Now let's dig a little deeper.

God is a necessary being. He exists in every world. But does he exist in every world because he is necessary, or is he necessary because he exists in every world?  I say the former.  His metaphysical necessity grounds and thus explains his existence in every world.  He exists according to every maximal proposition because he is metaphysically necessary.  But what grounds the divine necessity? The divine simplicity: existence and essence are one in God.

Now take Socrates. He is a contingent being: he exists in some but not all possible worlds.  But does he exist in some but not all worlds because he is contingent, or is he contingent because he exists in some but not all worlds? I say the former. Only some world-propositions say he exists because he is contingent.  But what makes him contingent? One answer is that he is contingent because there is in him and in all contingent beings that actually exist a real distinction between essence and existence.

Answering the reader's question

The reader asked about the advantage of PW talk.  My answer is that such talk allows for an especially perspicuous representation of modal propositions and relationships.   

If I am right, the patois of PW is a dispensable manner of speaking: we can make every point we want to make without engaging in PW talk.  What I just said is not perfectly obvious and there may be counterexamples. I have one in mind right now. Stay tuned.