PHIL2109 Contemporary Metaphysics
Week 6: Possibility and Necessity

Possibility

  1. Some things are possible, and some things are not:
  2. So there is the property of being possible, which some things have and some things do not.
  3. What kinds of things have this property? In the first example above it is a situation (or state of affairs) that has the property of being possible.
  4. It sometimes said that other kinds of things are possible:

    Perhaps these things do indeed have the property of being possible, but plausibly it is because some situation has the property of being possible. In the first case, because there is a possible situation in which I drink too many martinis tomorrow night. In the second case, because there is a possible situation in which there is a three-legged dog.

    So perhaps being possible is ultimately (or primarily) a property of situations, and only derivatively (or secondarily) a property of other kinds of things.

    (Interestingly, it has been argued (by Saul Kripke) that unicorns are not possible beings. Why not? Because they are fictional characters.)

  5. Every actual situation is a possible situation. But the converse is not true: some possible situations are not actual situations (there is a possible situation in which there are no kangaroos in the U.S., but it is not actual). Such situations are said to be merely possible situations.
  6. Every actual being is a possible being. But the converse is not true: some possible beings are not actual beings (six headed people are possible beings, but they are not actual). Such beings are said to be merely possible beings.

Situations

  1. What is a situation? More about this question next week, but a few things to note now.
  2. Not all situations are possible: some are impossible. Any situation in which I drink both fewer than two and more than three martinis is not a possible situation.

    An alternative to saying that this situation is not possible is to say that there is no such situation. On this view, all situations are possible. But this risks making the property of being possible a bit uninteresting.

  3. It is sometimes said that some situations are partial (or incomplete, or sub-maximal), and some are total (or complete, or maximal):
  4. Typically, total situations are called worlds, and total possible situations are called possible worlds.
  5. Lowe seems to think that something like the identity of indiscernibles holds for possible worlds: if w1 and w2 are distinct possible worlds, then there is some proposition that is true in one but not the other. But should we accept this? Perhaps, if possible worlds are just sets of maximally consistent propositions. More about this next week.

Necessity

  1. There is also the property of being necessary, which some things have, and some things do not:
  2. The three things above that are necessary are situations. It is sometimes said that certain beings are necessary:

    Perhaps these things do indeed have the property of being necessary, but plausibly it is because some situation has the property of being necessary. In the first case, because it is necessary that God exists. So perhaps being necessary is ultimately a property of situations, and only derivatively a property of other kinds of things.

  3. Here are some controversial examples of necessary situations:

Duality

  1. There is a close connection between the property of being possible and the property of being necessary: they are dual properties. That is:

    (These are logically equivalent: each entails the other.)

  2. This relies on the notion of the negation of a situation. The negation of a situation s is itself a situation - the situation in which s does not obtain.

Contingency

  1. Some things are contingent:
  2. In general:

Kinds of possibility (and necessity)

  1. There are thought to be different kinds of possibility (and necessity):
  2. There is also: conceptual possibility, bouletic possibility, ....
  3. We are mostly interested in logical possibility, also called metaphysical possibility.
  4. All this raises the question: Is possibility a property, as we have been taking it, or is it a relation to something, such as a body of laws? At least if we fix on a single kind of possibility we can take it to be a property.

The necessity of identity

  1. Many people think (having been convinced by Kripke) that since Hesperus is identical to Phosphorus, Hesperus is necessarily identical to Phosphorus. In general:
  2. Is there a possible situation in which Hesperus is not Phosphorus?
  3. Here is a famous argument that if a is identical to b then a is necessarily identical to b:
    1. For all x: necessarily, x is identical to x. (The necessity of self-identity)
    2. For all x and y: if x is identical to y then whatever is true of y is also true of x. (Leibniz's law)
    3. Suppose that a is identical to b.
    4. Necessarily, b is identical to b. (From 1)
    5. So it is true of b that: necessarily, it is identical to b.
    6. So, it is true of a that: necessarily, it is identical to b. (From 2, and the supposition that a is identical to b)
    7. So a is necessarily identical to b.
    8. So if a is identical to b, then a is necessarily identical to b.
  4. So what? If this result is true, then it is thought by many to show that there are necessary truths that are knowable only a posteriori: e.g. that Hesperus is identical to Phosphorus.

    (Many think there are also contingent truths that are knowable a priori: e.g. that I am here now.)

  5. It also has implications for various identity theories - it can and has been used to argue against them. According to one theory, for example, a person is his or her body. So I am my body (I am identical to it). But if identity is necessary, then that means that I am necessarily my body (my actual body, call it b), so it is not possible that I am not b. But this seems wrong: it seems possible for me to exist without b existing (perhaps I have another body, perhaps I have no body), and thus not be b. So it seems possible for me to not be b. So I am not b.
  6. A possible objection to the proof:
  7. Objection: my favourite number is six, but it might not have been six - it might have been nine. So here is an example of contingent identity. But the question is not whether some other thing could have had the property of being my favourite number. Rather, it is whether the thing that is not my favourite number, six, could have not been six. We get these apparent counterexamples whenever we use an expression to contribute an identifying property, rather than a thing directly (e.g. a definite description, but also a name).