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By Henry Bradford Smith

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First released in 2004. Routledge is an imprint of Taylor & Francis, an informa corporation.

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The answer is that they all have exactly the same representational significance, but we need many of them in order to represent the way in which maximal propositions have the potential to be further refined. This potential is reflected in higher-order propositions about propositions and in the iterated modal propositions that were the basis of McMichael's challenge to what he called "atomistic actualism:' Intuitively, one may think of the points as representations of possibilities, one of which would be maximal if the partition cell of which they are members had been realized.

But now the attentive reader may be inclined to cry foul, complaining that she has been subjected to a bait and switch. 1 started by asking what possible worlds are and answered that they are properties that a universe might have-maximal properties or, equivalently (1 proposed), maximal consistent propositions. I also promised a vindication of orthodox possible-worlds semantics, but now I am saying that the entities that are the "possible MERELY POSSIBLE POSSIBLE WORLDS 33 worlds" in the models of our orthodox semantics are different from the maximal propositions that I began by identifying with possible worlds.

And he seems to be assuming that while prop· erties of the latter kind may exist contingently. purely qualitative properties will be necessary existents. Perhaps there are some very abstract properties that exist necessarily. but I would argue that qualitative properties such as color and shape. like the things that exemplify them. exist only contingently. But my most important disagreement with Adams is that he holds that a metaphysical view that accepts the contingency of propositions and possible states of the world requires.

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A primer of logic by Henry Bradford Smith

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