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:
- Spatiotemporal connection is transitive and symmetric.
- If a is spatiotemporally connected to a part of b, then a is spatiotemporally connected to b.
5 comments:
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.
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.
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.
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.
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.
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