Section 1.1: Explaining the Possibility of the Impossible

Logical and Causal Possibility

To think about the notion of possibility and impossibility (both of which come in a variety of different flavors!) it is helpful to first start out with a conception of what are called "possible worlds".

What is a possible world? Well, if you've seen the TV show "Sliders", then you're halfway there. On the TV show, a group of people travel from one alternate universe to another. The cool thing about each universe is that if something was logically possible in the original universe (the one they started from), then there was an alternate universe that represented that possibility, but in reality. Since there are literally an infinite number of different logical possibilities in this world, there are an infinite number of "possible worlds".

Ex. I drive a silver Honda Accord. That's a fact. Much as it is a fact, it is also clearly logically possible that my car could have been blue. It isn't blue, but it's logically possible that it could have turned out that way. How do we know it is logically possible?

Simple: if there is no contradiction involved in such a "state of affairs" then it is logically possible. Since there's no contradiction involved in the proposition "A blue Honda Accord exists", it is logically possible. So:

Logical possibility = df. "X is causally possible in any possible world if and only if X is not self-contradictory".

Now let's think of the other notion of possibility. Is it causally possible that my car could have been blue? Causal possibility works a little differently than logical possibility. In short:

P1= It is not the case that all logically possible events are causally possible.

BUT

P2 = It is the case that all causally possible events are logically possible.

So as a concept, "logical possibility" is wider in scope than "causal possibility".

This doesn't answer the question about my car, however. As it turns out, my car being blue is in fact an event that is causally possible.

Causal possibility = df. "X is causally possible in Wn if and only if X is not inconsistent with the natural laws in Wn" (where X is some state of affairs and Wn is some possible world).

Think of my car. In this universe, natural laws are set up in a certain way. Gravity works in a certain fashion, E = mc2 is true (it could be false in a world with different causal laws). When you think of all of the causal laws that govern this universe, none of them are inconsistent with a blue Honda Accord. So that state of affairs is causally possible in this world.

According to P2, since it is causally possible, my car being blue is also logically possible (logical possibility is not "indexed" to a world like causal possibility is -- if X is logically possible, then it is logically possible in any possible world).

How about travelling faster than the speed of light? As it turns out, this is causally impossible in this world. The way in which this world is constituted (the natural laws in it) it is not causally possible that something move faster than the speed of light. Is it logically possible to travel faster than the speed of light? Sure. There's no contradiction in the notion of faster than light travel. Since it is logically possible, there must be some possible world where it is actually the case (where it turns out to be causally possible).