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Thursday, October 14, 2010

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"What Black's example seems to show is that there can be numerical difference without property-difference"
Say, we name the 2 spheres A and B (and use these names rigidly). Now there is at least one property they don't share "being 10 meters distant from B". Am I wrong?

Thanks for your comment, but to answer your question, Yes.

First of all, the spheres are not labeled, and there are no observers or language users in Black's world. If they were labeled, then of course there would be a property difference.

Second, being 10 meters from B is an impure property.

I may be a bit confused. If you can say "each has the property of being ten meters from an iron sphere"
while "each" stands for a single sphere why can't I use A and B rigidly in the same way? If we are not observers inhabiting Black's world, we are still observers of Black's possible world and we can refer to its insividuals rigidly, i.e. without involving us as observers.
Then you say "being 10 meters from B" is an impure property. Agreed, but why shouldn't I cansider also "being 10 meters from an iron sphere" an impure property or something that presupposes an impure property? After all isn't true that the sentence "A is 10 meters from B and B is 10 meters from A" and the sentence "each has the property of being ten meters from an iron sphere" are made true by the same portion of reality?

But 'each' does not refer to one sphere rather than the other.

Ex hypothesi, the spheres are not labeled, and there is no one to label them. Being ten meters from an iron sphere is common to both, and so can't distinguish them.

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