Kind relative predication

It is a broadly Aristotelian doctrine that many predicates apply to individuals in a kind-relative way. Call such predicates k-predicates. (We can stipulatively say that God is the sole member of a kind membership in which is identical with himself, or something like that.) For a k-predicate F, what exactly it is for an x to be F depends on what kind of an entity x is. If it is the same thing for x to be such that Fx as for y to be such that Fy, then kinds of x and y are either the same or have something in common (e.g., a higher genus).

Examples of k-predicates are easy to find. To determine whether a given individual "has legs", we first have to see what counts as legs for an individual of that kind. Thus, Peter has legs in virtue of a particular pair of limbs. Which limbs count as legs? That is defined in part by his human nature, or maybe more generally his nature as a member of Tetrapoda. What it would be for an amoeba to have legs is a different, and more poorly defined, question. What it is for a table is fairly well defined in terms of the nature of the table (we could imagine a table with four upward projecting horns at the corners; the nature of a table being to stand on solid ground on its legs, if it has any, would prevent these from counting as legs).

Whether an entity is n inches tall is even more clearly kind-relative. It depends on which axis counts as the "vertical" axis—remember that the entity might be lying on its side for much of the day.

Another kind of predicate is an r-predicate. An r-predicate is a predicate that can only be had by members of one particular (perhaps higher level) kind. Thus, "is a mammal" is an r-predicate, since it can only be had by mammals. And "is Socrates" is also an r-predicate, since it can only be had by a human.

We can perhaps form complex predicates that are neither k- nor r-predicates. Thus, "is not Socrates" is not an r-predicate (all horses and chairs, and most humans satisfy it) and may not be a k-predicate either. Though on the other hand, it may a k-predicate: maybe for non-humans, it holds in virtue of kind difference, while for humans, it holds in virtue of numerical difference within a kind.

There are also some non-contentful predicates, like "is a substance" or "is self-identical" that are neither k- nor r-predicates.

Thesis: All simple, contentful predicates are either k- or r-predicates.

I don't know if the thesis is true. There seem to be counterexamples. Having a particular shape does not seem to be a k- or r-predicate. Likewise, having a certain mass does not seem to be such, either. I suspect such apparent counterexamples can be overcome—but that may be matter for another post.