My notion of a function “for itself” is supposed to be that the functional mechanism somehow benefits the thing of which it’s a part. (Of course hammers can benefit carpenters, but we don’t tend to think of the hammer as a part of the carpenter, only a tool the carpenter uses. But I must confess that where that line is I don’t know, given complications like the “extended mind” hypothesis.)
Putting this in utility-theoretic terminology, you are saying that “for itself” telos places positive expectation on its own functional mechanism, or perhaps stronger, uses significant bits of its decision-making power on self-preservation.
A representation theorem along these lines might reveal conditions under which such structures are usefully seen as possessing beliefs: a part of the self-preserving structure whose telos is map-territory correspondence.
Putting this in utility-theoretic terminology, you are saying that “for itself” telos places positive expectation on its own functional mechanism, or perhaps stronger, uses significant bits of its decision-making power on self-preservation.
A representation theorem along these lines might reveal conditions under which such structures are usefully seen as possessing beliefs: a part of the self-preserving structure whose telos is map-territory correspondence.