Saturday, September 24, 2011

Self-referential properties

The following is even rougher than is usual for posts.  It's notes to self mainly.

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:  
  1. 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.
  2. 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.
  3. 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.
  4. 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.

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