Saturday, March 04, 2006

Characterising Modal Spaces

To clarify my earlier post, note that a space of possible worlds is typically characterised in terms of its breadth of content. For example, the nomologically possible worlds include everything consistent with our laws of nature, whereas the logically possible worlds include all this and more, so are immediately seen to be "more spacious". Now, if you propose a third class of worlds, say "metaphysically possible worlds", philosophers are apt to ask for a characterisation in terms of its spaciousness. (They might ask, for example, whether you mean a space of worlds more encompassing than the nomological, yet more restricted than sheer logical possibility.) But that's not what I mean by the term at all. The way to characterize the sort of modality I have in mind is not (antecedently) in terms of its content, but rather in terms of its brute modal nature.

I'm interested in the worlds that really could have been actual, and merely missed out through "the luck of the draw" (or divine decisions, or whatever is the reason why this universe exists rather than some other one -- say, filled with unicorns and pegasi).

Now, this space of metaphysically possible worlds must have some or other breadth, and so be specifiable in terms of restrictions on content. Perhaps it includes all the logically possible worlds. Or perhaps it includes only the actual world, as would be the case if things never really had any genuine opportunity to be different. Whatever. (If all else fails, one could simply give an exhaustive specification of each and every world that it includes, and say that their disjunction is the content restriction.) Any of these "spatial" properties are prima facie consistent with the concept I'm trying to point to, because its fundamental character lies in a different dimension.

Unlike the other (so-called) modal concepts, we don't immediately characterize it in terms of the breadth or restrictions on content. The criterion for a world's inclusion in this space is instead its brute modal nature. We don't ask: "Does this world contain anything which violates restrictions R?" Instead we ask: "Is this a world that had the opportunity to be actual?" This is an irreducibly modal question. (The former, by contrast, isn't.)

Once we have a grasped metaphysical modal space by way of the above question, we can go on to ask questions about the space's breadth and content. I will do just that in future posts. But for now I emphasize that the concept must be initially grasped in these brutely modal terms. You cannot begin by characterizing metaphysical modal space in terms of its contents, because those are not included in the concept as it initially presents itself to us. If you begin with them, you are really grasping a different concept altogether. After all, for any space of worlds characterized in terms of their content, one can still coherently ask: "but might they really have been actualized?" It remains an open question, unless one begins by characterizing the space of worlds in terms of their modal properties, as described above.


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