Possible Worlds

One solution to the modal logic problem presented in my last post is that such statements as this are meaningless:

(1) If I were president, I’d appoint Noam Chomsky to my cabinet.

You can just say, “Nope, the logic breaks down, so there’s no semantic content there.”  That’s an answer you can give.  I’m not president, and so anything following that arrow is nonsense.  Ip -> Cn is exactly equivalent to

(2) If I were president, I’d turpulate the gorganza bang.

This solution fails to save the appearances, though.  I’d really like to think that (1) means something, because when I say (1) people might say “Oh, no you wouldn’t,” or “he’d never accept the position” or “yeah, me too!”  If I say (2) I hope they’d rush me to the emergency room so they could see what just happened to my Wernicke’s area.

There’s another solution, and that’s that we can assess the P part of P -> Q according to possible worlds, and that the modal buried in if-statement signals us to search possible worlds for a world in which P is true (and it also implicates that P is not in fact true, in this world, which we’ll call the “actual” world, and later, for reasons that might make sense, the “indexical world.”).

So (1) means that we look through our imagination for possible worlds, and find one in which I’m president, and then see if I appoint Noam to my cabinet in that world, or if I tap Bernie Sanders instead.

Some worlds are not possible.  I don’t mean highly improbable — me being president is already pretty unlikely.  Possible worlds include anything I can say before an if-statement containing a modal that makes logical sense.  Logical sense isn’t used in its colloquial and loose meaning here, but means isn’t self-contradictory.  So:

(2) If I were a woman, I would wear a bra.

(3) If I didn’t eat meat, I’d go mad.

(4) If I were King of France, I’d wear a toupee.

And so on.  All of those imply possible worlds, in which I’m a woman, a vegetarian, and the King of France (which in our world doesn’t even exist, but we can imagine a logically consistent world in which the King of France does exist).

An impossible world would be something like this:

(5) If I were a man and not a man I’d be a dancer.

I can’t be both a man and not a man.  You can’t have A & ~A.  Just can’t.  One or the other.  So such a world isn’t possible.  I had to sit and think for a long time to come up with an example, by the way, because there are countless, countless possible worlds.

Now, here’s where things get weird — when I say “there are countless possible worlds,” I’m not speaking metaphorically.  There are countless possible worlds.  They exist.  In fact, they’re real.

And I ain’t just saying that ’cause I’m a crazy wizard.  This is an actual position of some logicians, because it solves a lot of problems with modal logic all in one fell swoop.

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2 Responses to “Possible Worlds”

  1. Picky point: (5) is an implication (if-then statement), and therefore trivially true if the antecedent (in this case, “X and not X”) is false.

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