Intrinsicness and the Duplication Account

Last Friday, Maya Eddon presented a paper ("Intrinsicality and Hyperintensionality") arguing against the adequacy of the duplication account of intrinsicality (where, intuitively, intrinsic properties are those that objects possess solely in virtue of the way the objects themselves are).

Granting, for purposes of spelling out a duplication account, that there is a privileged set of (perfectly) natural properties, we can define what it is to be a duplicate: an object x is a duplicate of object y if and only if x is like y with respect to the instantiation of all perfectly natural properties.

So, the duplication account of instrinsicality is:
DUP: A property P is intrinsic if and only if it never divides duplicates.

One purported problem for the account is identity properties (being David Lewis, for instance). Since there could be a world with two duplicates of David Lewis, but there cannot be a world with two things that are David Lewis, at most one of those duplicates can have the property of being David Lewis, and thus, the property of being David Lewis divides duplicates. Thus, the duplication account treats the property of being David Lewis as not an intrinsic property, but, intuitively, it is an intrinsic property. In other words, the objection maintains that: never dividing duplicates is not a necessary condition for intrinsicality.

Another purported problem comes from necessary properties (being such that 2 plus 2 equals 4, for instance). Since every object is (necessarily) such that 2 plus 2 equals 4, that property never divides duplicates. Consequently, on the duplication account, every necessary property is intrinsic. But, intuitively, being such that 2 plus 2 equals 4 is not intrinsic. In other words, the objection maintains that: never dividing duplicates is not a sufficient condition for intrinsicality.

After the talk, I thought of a possible variation to the duplication account. It doesn't do anything to help with the objection from identity properties, but it does help out with necessary properties. If one is willing to bite the bullet on identity properties, this would be an adequate replacement account (if one is not willing to bite the bullet, one could at least extract a sufficient condition for intrinsicness from the revised account).

DUP*: A property P is intrinsic if and only if it ever divides duplicates from non-duplicates.

Here is how this minor revision helps. Consider a necessary property like being such that 2 plus 2 equals 4. This property never divides duplicates from non-duplicates, because every non-duplicate will possess it. Now consider a paradigmatic intrinsic property, like, having such-and-such shape. Since some object lacks that property, but no duplicate of something possessing the property will lack the property, it does divide duplicates from non-duplicates.

Some things worth noting:
a) As already mentioned, this does not help at all with identity properties.
b) DUP* is incompatible with treating any necessary properties as intrinsic.
c) Eddon's paper is concerned with responding to a number of attempted evasions of these objections, and I haven't discussed any of those. I don't mean to be taking a stand here as to whether any of those ways of evading the objections work.
d) Eddon's broader dialectical purpose is to argue for hyperintensional properties, and I obviously haven't sketched how she pursues that conclusion, but it is pretty clear that, on an intensional conception of properties, there is only one necessary property, and it will have to either be intrinsic or extrinsic, so hyperintensionality is clearly necessary if one wants both intrinsic and extrinsic necessary properties.