Consider this anti-self-referentiality (ASR) thesis about properties:
- There is no property P and relation R (complex or not) such that a component (say, a conjunct or disjunct) of P is the property of being R-related to P.
Suppose ASR is true. Then we may well get the following consequences:
- Property-identity forms of divine command theory are in trouble. On these theories, being obligatory is identical with being commanded by God. But being commanded by x is a complex property one component of which is being intended by x have obligatoriness. And that's a way of being related to obligatoriness. And hence property-identity forms of divine command theory likely violate ASR.
- For the same reason, property-identity forms of legal positivism and moral prescriptivism are in trouble. For in both cases, we identify a species of obligation with a species of being commanded, and it is plausible that the property of being commanded in the relevant way will include a relation to obligation.
- The property of being asserted (requested, commanded, etc.) by x is not identical with any complex property that includes a conjunct like being intended to be taken as asserted (requested, commanded, etc.) by x. Thus various accounts of illocutionary force fail.
- No property P is identical with being taken to have P, being properly taken to have P, being felt to have P, etc. All sorts of projectionist views are in trouble.
A fair amount of work would be needed to substantiate the inference from ASR to the above claims.
I suspect quite a bit of other stuff is ruled out by ASR. For instance, no property P can have a component of being R-related to Q while Q has a component of being S-related to P.
I don't know if ASR is true. I suspect it is.