Aristotle on Impossible Worlds

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Shortly before David Lewis died, he was at the Metaphysical Mayhem conference that we were at the time holding in Syracuse. In a talk by Kit Fine about something like coincident entities views, Lewis made a comment about allowing talk of impossible worlds. Of course these things don't exist in the way that all possible worlds do, according to Lewis, but somehow we need to be able to talk about them for a complete view of modality. These were just suggestions, but I found it intriguing.

Yesterday morning I happened upon a passage in Aristotle's Eudemian Ethics that seems to rely on exactly the thing Lewis said we need. He was talking about humans need to be the starting-point of their own action for moral responsibility in a way similar to how modern libertarians talk (though Aristotle was probably more like a compatibilist, and the common compatibilist description of the line of causation running through the agent may be closer to what he had in mind here). Here's the stuff about impossible worlds:

Since, as in other things, the starting-point is a cause of those things that are or come about because of it, we must understand it as we do in the case of demonstrations. For if it is necessary, if a triangle contains two right angles, that a quadrilateral has four, it is clear that the cause of this is that the triangle has two. If the triangle is different, the quadrilateral must be different too; if the triangle has three right angles, the quadrilaterial has six, and if the triangle has four, the quadrilateral eight. And if a triangle is of such-and-such a character, and could not be different from that, the other must also be of such-and-such a character. It is evident from the Analytics that what we are attempting to show is necessarily the case... [II.6.29-39 (1222b) from J.L. Ackrill, ed., A New Aristotle Reader]

The idea here seems to be that a triangle's angles add up to 180 degrees, and a quadrilateral's add up to 360 and that this relationship is of necessity. Even if a triangle's angles added up to 270, the ration with the angles of a quadrilaterial would remain 2:1, and its angles would add up to 340. The ratio is necessary. But aren't the sums of the angles necessary also? Why does Aristotle raise this question when you can't really consider such an impossible situation? His analogy ends up being problematic because causal necessity depends on laws of nature that aren't metaphysically or logically necessary. You can talk about what would be the case with different laws, which is required for free willy discussions. You can't do that with mathematical truths without some sense of how to discuss the absolutely impossible. Apparently Aristotle thought he could do that, which is what connected this in my mind with what David Lewis was saying. Aristotle believed in talking about impossible worlds as a guide to modality. I guess Lewis was 2500 years behind on this one.

What do you get when you cross David Hume with Gottfried Leibnitz? Not Gottfried Heim; David Lewitz. -- David Chalmers, "David Lewis: In Memoriam" 8 February 2002

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