A sentence or statement or proposition that ascribes intrinsic properties to something is entirely about that thing … A thing has its intrinsic properties in virtue of the way that thing itself, and nothing else, is … The intrinsic properties of something depend only on that thing … If something has an intrinsic property, then so does any perfect duplicate of that thing … (Lewis 1983a, p. 197) I once offered a definition that was meant to capture the notion expressed by the intuitive descriptions in this quote from Lewis.¹ The basic idea is that F is an intrinsic property of an item x just in case x's having F consists entirely in x'sha ving certain internal properties, where an internal property is one whose instantiation does not consist in one's relation to any distinct items (items other than oneself and one's proper parts). I still think that this relational analysis is largely correct, and here I wish to provide additional support for it and defend it against some objections that have been raised. In the process I aim to make the account somewhat more precise, especially by contrasting it with a grounding approach to defining the intrinsic/extrinsic distinction.
In Favor of a Hyperintensional AccountConsider those properties that must be exemplified by any item that exists. Following Weatherson and Marshall (2013), let's call them "indiscriminately necessary" properties. Being self-identical is an indiscriminately necessary property. Unlike the property of being identical with Dennett, being self-identical is a property that cannot go unexemplified by anything. In addition to being indiscriminately necessary, the property of being self-identical also seems to be intrinsic; having this property does not seem to be a matter of how an item relates to anything distinct from itself. While this one seems intrinsic, some indiscriminately necessary properties (INPs) appear to be extrinsic. Assuming that numbers exist and exist necessarily, the property of coexisting with the number 9 is an INP. Given realism about numbers, our coexisting with 9 consists in our relation to something distinct from ourselves, which seems to make it an extrinsic feature of you and me. See Francescotti (1999).