What if we call the relation "Brotherhood", and each of the mappings
between or among the tuples of the relation [from the tuple Tim to the
tuple John and vice versa] constitutes a role that one entity in the
relation plays with respect to one or more other entities in that relation.
John plays the brother role/is a brother of Tim and Tim plays the brother
role/is a brother of John. But there's still this type called "Brotherhood"
that is a relation. It exists eternally in the land where types live.
There's also the particular instance of the brotherhood relation that
exists between Tim and John. It came into existence at the moment [given
one of the two males, John or Tim, already existed and] the second of the
two was born (assuming other criteria such as the same genetic parents or
an equivalent legal surrogate of that condition, such as represented by an
adoption). Technically speaking, when one or the other of Tim or John
dies, that instance of the brotherhood relation won't exist anymore, except
in a historical or hypothetical context.
---I think this is beside the point. The point of the linguistic test is not to prove that there is no sensible way to view an instance/tuple of a relatoin as an instance of a type. Rather , the point, it seems to me, is that the linguistic test genuinely distinguishes relation tuples (for which the answer to the isa question is NO, from instances of non-relation (i.e ordinary) types.
ALthouhg you may think you are arguing, it is not clear to me that you disagree on anything substantial.
Mike Uschold