Recombinations, Alien Properties and Laws of Nature

A recombinationist like the earlier Armstrong (1989) claims that logically possible worlds are recombinations of items found in the actual world, with some items reduplicated if need be and others deleted. An immediate consequence of this is that if an alien property is a property that could only be defined in terms of fundamental properties that are actually uninstantiated, then it is logically impossible that an alien property be instantiated as no recombination of the items in the actual world can yield a world with an entity having such a property. Recombinationism immediately implies that S5 is false. To see this, suppose for simplicity, as I will throughout this paper, that electric charge is a fundamental property--otherwise, a different example would have to be used. Then, let w be a possible world lacking any charged objects. At w, then, it is true that it is logically impossible that there be a charged particle since no recombination of the entities in w yields a charged particle. Therefore, contrary to S5, what is possible at w differs from what is possible at the actual world, since charged particles are actual and hence logically possible at the actual world. While this argument may make one sceptical of recombinationism, the recombinationist will say that it is not surprising that if we follow out the Aristotelian intuition that possibility is to be grounded in actually existing entities, then what is possible will depend on what is actual. Henceforth I will no longer assume S5, and so logical possibilities will have to be relativized to worlds if recombinationism is true: it is logically possible at the actual world for charged particles to exist, but at a world at which there are no charged particles it is logically impossible for charged particles to exist...
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