Thursday, August 29, 2013

Merging Lewisian worlds

According to Lewis, any pair (or, more generally, plurality) of concrete (he doesn't even restrict it this way) of objects has a mereological sum. Now, suppose that x and y are concrete objects in worlds w1 and w2 respectively. Let z be the mereological sum of x and y. According to Lewis, worlds are maximal spatiotemporally connected sums of objects. Now, here are some plausible principles:

  1. Spatiotemporal connection is transitive and symmetric.
  2. If a is spatiotemporally connected to a part of b, then a is spatiotemporally connected to b.
Consider any concrete objects a and b in w1 and w2, respectively. Then a is connected with x, since all objects in a world are connected. And y is connected with b. Moreover, by 2, a is connected with z since x is a part of z. And by 2, b is connected with z. Thus, by 1, a is connected with b. Thus, all objects in w1 and w2 are mutually connected, and so by Lewis's account of worlds, there is only one world. Which is absurd.

5 comments:

Jonathan D. Jacobs said...

For Lewis, spatio-temporal connection is neither necessary nor sufficient for being worldmates.

Not sufficient: x and y are worldmates only if every part of x is spatio temporally connected to every part of y. (Lewis says about this that it "avoids difficults that might be raised concerning partial spatiotemporal relatedness of trans-world merelogical sums. . . .")

Not necessary: spirits can be world mates, for Lewis, so long as they are interrelated by something *analogous* to spatio temporal relations. Whatever such analogous relations are, for Lewis they must be 1) natural, 2) pervasive, 3) discriminating, and 4) external.

Alexander R Pruss said...

Good catch. I forgot this part of Lewis.

But I don't think the "every part" thing avoids the difficulty. For every part of a is connected with z and every part of b is connected with z, so every part of a is connected with every part of b, it seems.

Padruig said...

I'm pretty sure the "every part" thing does avoid the conclusion that there is only one world, since every part of a is not connected with every part of z (it's only connected with x, after all) and every part of b is not connected with every part of z. So z is not a worldmate of a nor of b, and thus there's no reason to think of a and b as worldmates.

Further, spatio-temporal connection is plausibly transitive and symmetric, but it's also plausible that a's being connected to only a part of z and not the whole of it will cause transitivity to fail in the sort of case your pursuing.

Another response Lewis could give is that there's spatio-temporal connection and there's trivial spatio-temporal connection, where the latter is defined as the sort of connection two things a and b have when they're connected to an object z but not to each other. He could then qualify 1. or 2. in terms of this distinction and admit that all things are trivially connected but deny that they're connected. I don't think this would have to be an ad hoc solution.

Richard Davis said...

The 'non-trivial' reading might be 'being connected by a continuous path in space-time'. Then the trivial reading could be the transitive closure of the non-trivial reading.

If 'spatiotemporal connection' is understood to mean 'being connected by a continuous path in spacetime', then it's not obvious to me that premise (1) is true. Alternatively, if it is understood in any other way, then I don't see why premise (2) should be true.

Alexander R Pruss said...

Padruig:

If we maintain 1 and 2, then every part of a is connected with every part of z. For a is connected with every part of x, and hence by 2 it is connected with z. Moreover, z is connected with b, so by 1, a is connected with b. But b is connected with every part of y. So a is connected with every part of y by 1.

But if a is connected with every part of x, and a is connected with every part of y, then surely a is connected with every part of x+y.