PHIL2109 Contemporary Metaphysics
Week 7: Possible Worlds

Situations and worlds

  1. Last week we looked at the property of being possible (and the related properties of being necessary and being contingent). We adopted the view that being possible is primarily a property of situations (or states of affairs), and only secondarily a property of other kinds of things (propositions, beings, etc.). So too for the properties of being necessary and being contingent.
  2. We considered the idea that situations vary in their degree of maximality: some are less than maximal, some are maximal. A situation s is maximal iff for all propositions p: either p is true in s or p is false in s. Maximal situations are typically called worlds. Maximal possible situations are typically called possible worlds.
  3. If we like, we can simplify things and take it that all situations are maximal (i.e. worlds), even if we sometimes only specify them partially. Let's do that.
  4. The main question for this week is: What exactly are possible worlds?

Two ways of talking

  1. Rather than talking in the first way below, philosophers often talk in the second way:
  2. (It might be helpful to compare this with the following two ways of talking, a famous example due to Gottlob Frege:

  3. It is sometimes said that the second way of talking makes it more perspicuous what we mean by the first.
  4. It is sometimes said that the second way of talking gets rid of the modality in favor of straightforward quantification.
  5. Some are wary of the second way of talking, claiming it to be too ontologically committed, and prefer the first way of talking, because it is not so ontologically committed.
  6. Perhaps the second way of talking is just a heuristic device: helpful, but not meant to be literally true. Then it is like talking as if my car has a mind: "my car is trying to kill me" - helpful, but not meant to be literally true.
  7. Perhaps the second way of talking is not even meant to be meaningful. The term 'possible world' is a meaningless symbol whose manipulation is helpful device. Just like the beads on an abacus are meaningless things whose manipulation can be helpful.
  8. Perhaps the second way of talking is fictional, and possible worlds are fictional characters (this is modal fictionalism).
  9. If it turns out that the second way of talking is after all a synonymous paraphrase of the first, then to understand our modal claims it seems that we need to understand what possible worlds are.

Possible worlds as sets

  1. One common suggestion is that worlds are maximal sets of propositions, and that possible worlds are maximal consistent sets of propositions.
  2. What is it for a set of propositions to be consistent?
  3. Another common suggestion is that worlds are maximal sets of sentences, and that possible worlds are maximal consistent sets of sentences.
  4. Here is one more issue for these approaches: if the actual world is a possible world, then does that mean that the actual world is a set of propositions (or sentences)?

Lewis's modal realism

  1. David Lewis gives the following argument that there are such things as possible worlds ('Possible Worlds', p. 182):
  2. Lewis famously holds the following view about possible worlds:
  3. Objection: The view is far too ontologically unparsimonious.

    Reply: Lewis distinguishes two kinds of parsimony: qualitative and quantitative. He agrees that his account is quantitatively unparsimonious, but he seens no reason to be concerned about that.

  4. Objection: Why is this a fact about how I could have been? How could it make any difference to me whether or not such worlds even existed, given that they are causally disconnected from this world? Things in this world would still have the same modal properties. Also, it raises some epistemological concerns. And does it help us to understand modal talk?
  5. Objection: We need to be told more about what other possible worlds are like before we can believe in such things. How many are there? How can they be different? How must they be the same?

    Reply: Lewis says that since he is a realist about possible worlds, he cannot make up the details as he choses - there are many things about other possible worlds knowledge of which he does not have, and does not know how to get. We must rely on science to learn about what is possible and what is not.

Stalnaker's moderate realism

  1. Bob Stalnaker argues (in 'Possible Worlds') that "there is a coherent thesis about possible worlds which rejects extreme realism, but which takes possible worlds seriously as irreducible entities, a thesis that treats possible worlds as more than a convenient myth or a notational shortcut, but less than universes that resemble our own".
  2. Stalnaker agrees with Lewis that there are such things as ways things might have been, and is happy to go along with Lewis in calling them 'possible worlds', but only as long as we are not thereby misled into thinking that they are the same kind of thing as the actual world. He believes that there is just one world. The claim that the actual world alone is real cannot, he thinks, be sensibly denied, because 'the actual world' means the totality of everything there is.
  3. He argues: If possible worlds are ways things might have been, then the actual world is the way things are. The way things are is a property or state of the world, so ways things might have been (i.e. possible worlds) are also properties or states of the world.
  4. It might be argued that for each way things might have been, a property, there must be a world that has that property, because properties cannot exist uninstantiated.

    But Stalnaker takes it that properties can exist uninstantiated, so it may be that all these properties (ways things might have been) exist uninstantiated in the actual world there need be no more worlds than the actual world for all these properties to exist.

  5. Stalnaker's account is thus a version of actualism. According to actualism, everything that exists actually exists. According to possibilism, the denial of this, some things that exist do not actually exist. Lewis's modal realism is a version of possibilism: my counterparts, for example, all exist but do not actually exist.

Iterated modalities and accessibility

  1. It is plausible to think that the first claim below is false, but the second is true:
  2. In the language of possible worlds:
  3. If we want to use the language of possible worlds, but allow that the second claim is true while the first claim is false, then we need to allow that what possible worlds there are varies from possible world to possible world.
  4. What we can say is that each world has a set of accessible worlds. And we can speak in the following ways:

    Now the first comes out false and the second comes out true, as long as (a) there is no possible world that is accessible to the actual world in which I give birth, and (b) there is a possible world that is accessible to the actual world which has a possible world that is accessible to it in which I give birth.

  5. We can talk of an accessibility relation between possible worlds, call it R: w stands in R to w' iff w' is accessible to w.
  6. Note that in order to get the first to come out false and the second to come out true we need the accessibility relation to not be transitive. Why?
  7. There are interesting relationships between properties of the accessibility relation and entailments between modal claims:
    R is reflexive iff p entails possibly p
    (i.e. necessarily p entails p)
    R is symmetric iff possibly necessarily p entails p
    (i.e. p entails necessarily possibly p)
    R is transitive iff possibly possibly p entails possibly p
    (i.e. necessarily p entails necessarily necessarily p)