Are Fundamental Properties Intrinsic?
This is a problem that cropped up several times in my thesis on Lewis, but which I never seriously discussed.
Lewis argues, or rather, stipulates, that all fundamental ("perfectly natural") properties are intrinsic. I agree that fundamental extrinsic properties would be strange. For if a thing x's being F depends on the existence and the properties of other things, it seems that F-hood should be reducible to intrinsic properties (and relations) of all the things involved. Moreover, fundamental properties are supposed to be the basis for intrinsic similarity between things, and they could hardly be if they were themselves extrinsic.
On the other hand, if fundamental properties are intrinsic, they can't be identified by their theoretical role. Hence whether a certain class of things in some possible world is in the extension of a certain fundamental property, say spin, is completely independent of the role these things play in their world. Hence Lewis: "We can distinguish our world from one in which, say, one of the quark colours has traded places with one of the flavours" (Plurality, p.162).
This has many strange consequences. For example, there are also worlds where quark colour and flavour are switched only in some, but not all things. But does it really make sense to wonder whether somewhere in China the properties that occupy the role of quark colours are in fact quark flavours?
Next, imagine a world where physicalism is false because there are immaterial Cartesian spirits instantiating some alien perfectly natural property X. If X is intrinsic then there is another world just like ours but where X has traded places with one of the quark flavours. On Lewis' account, this is not a physicalistic world. This is strange because the physicalists in that world are in exactly the same position as the physicalists in our world. How do we know our world is not one of those? (Or is "physicalism" indexical and both worlds are physicalist worlds from their own point of view but not from the point of view of the other world?)
Finally, consider the world where our quark flavour occupies the X-role. This world is indistinguishable from the world of Cartesian spirits, and yet, on Lewis' account, it is a physicalist world!