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Concretists about possible worlds say that possible worlds are concrete entities (usually some kind of mereological sum of concrete individuals). Abstractionists say that worlds are abstract things: Properties, states of affairs, propositions, sets of propositions or what have you.

Most of those philosophers who think there's some interesting work for possible worlds consider concretism to be absurd and abstractionism to be the viable option, since it allegedly fits better with our metaphysical intuitions.

But is that really true? After all, for every possible world w it is possible that w is the actual world. The actual world is, well, the universe, a very, very big concrete thing. So, for every world w it is possible that w is concrete. So, according to abstractionism, there are abstracta that are possibly concrete. In other words abstractionists have to hold that abstractness is a contingent property of worlds. But many modal metaphysicians tell us that our intuitions tell us that abstractness is a necessary property of whatever has it. Can abstractionists do without the contingently non-concrete?

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For the abstractionist, possible worlds don't (necessarily) have the properties they represent certain possibilities as having--- they merely represent.

If you're a concretist, like David Lewis, you can claim that a possible world represents a certain possibility by simply being that possibility. So, to represent itself as being concrete the world just needs to be concrete. Similarly, if a world is to represent the possibility of a talking donkey, it will do so by containing a talking donkey as a part.

For the abstractionist all possible worlds--- even the actual world ---are abstract. They represent possibilities in different ways. David Lewis lays out three different types of abstractionism (he terms the view "ersatzism" and the worlds "ersatz worlds"; that terminology has stuck in the literature, imo) based on how the worlds represent possibilities (See On The Plurality of Worlds, ch. 3).

  1. Linguistic Ersatzism: This is the version defended by Robert M. Adams (will have to dig for a citation later) and holds that possible worlds represent by saying a possibility is a certain way. One version of this view holds that possible worlds are maximal consistent sets of propositions, completely specifying some way the world might be. The actual world is represented by a maximal consistent set of propositions describing the way the world actually is.
  2. Pictorial Ersatzism: Possible worlds represent by isomorphism, like a picture or map. A map of the USA represents the USA in virtue of depicting 50 states in the right spatial arrangement, etc. This is how possible worlds represent, they're like pictures.
  3. "Magical" Ersatzism: Possible worlds represent by magic. This is what Lewis calls views, like the property view of Robert Stalnaker, that don't explain--- and, Lewis claims, leave mysterious ---how worlds represent.

The point here is that whereas a concretist can identify the actual world with this concrete thing we inhabit, an abstractionist will generally (always?) have an abstract surrogate for even the actual world. None of the abstractionist's worlds are (or could be) concrete, though many, if not all, represent possibilities involving concrete objects. Remember that not even "the actual world" is concrete for an abstractionist--- though it certainly represents a concrete possibility (ours!).

TL;DR Your argument contains a false assumption: abstract worlds could not possibly be concrete, they just represent possibilities involving concrete individuals.

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