Something I thought of today.
Suppose three logically possible worlds. Each world is identical except for the colour and shape of your gem.
World 1: The gem is blue and oval
World 2: The gem is not-blue and oval
World 3: The gem is not-blue and not-oval
Suppose that world 1 is the actual world while world 2 and world 3 are possible worlds.
Intuitively, it seems that world 2 is closer to world 1, the actual world, than world 3, because world 2 is different from world 1 only with respect to the colour of the gem, while world 3 is different from world 1 with respect to the colour and shape of the gem. In the space of logical possibilities, then, the proximity of world 1 and world 2 seems greater than world 1 and world 3. That is, world 1 and world 2 are closer or more alike than world 1 and world 3 … at least in English.
Suppose, instead, we spoke Inglish.
In Inglish, something is ‘bluval’ if it’s blue and oval or not-blue and not-oval; and something is ‘not-bluval’ if it’s not-blue and oval or blue and not-oval. After translating our three worlds into Inglish, we get:
World 1: The gem is blue and bluval
World 2: The gem is not-blue and not-bluval
World 3: The gem is not-blue and bluval
The words ‘blue’ and ‘not-blue’ exist in Inglish, but the words ‘oval’ and ‘not-oval’ don’t. In Inglish, something is ‘oval’ if it’s blue and bluval or not-blue and not-bluval, while something is ‘not-bluval’ if it’s not-blue and bluval or blue and bluval. Anything you can say in English can also be said in Inglish. To the English speaker, ‘bluval’ is derivative of ‘blue’ and ‘oval’, but to the Inglish speaker, ‘oval’ is derivative of ‘blue’ and ‘bluval’.
Now, by describing our three worlds in Inglish rather than English, world 3 is now closer to world 1, the actual world, than world 2. In the space of logical possibilities, the proximity of world 1 and world 3 seems greater than world 1 and world 2. That is, world 1 and world 3 now appear closer or more alike than world 1 and world 2 … at least in Inglish.
It seems to me this has important ramifications for possible world semantics: the proximity of possible worlds is a function of the ontological prejudices of each language. It would seem, then, that if we conceive of possible worlds as purely logical constructs, then there is no such thing as a possible world that is closer to the actual world than any other. All possible worlds, including the actual world, are equidistant from each other.
Anyone encountered this argument before? I admit, it’s not all that original, because I’m borrowing from arguments about verisimilitude that I read once (from Miller?), but I haven’t known them to be brought against the idea of close possible worlds.