The phrase "a relation holding" is correct and usable in written English.
It can be used in contexts involving mathematics, logic, or discussions about relationships between entities or concepts.
Example: "In this mathematical framework, a relation holding between two sets can determine their interaction."
Alternatives: "a relationship existing" or "a connection maintained".
On this relational view of touch, all immediate tactual perception involves a relation holding between our body and objects in contact with it.
The most important of these are the following: (a) prehension is a relation holding between a type of experience and particulars of such kind that adjectives like "red" and "hot" can be predicated of them; (b) it is logically possible that a particular that was prehended as having a certain quality could have had that quality regardless of whether anyone ever prehended it.
Some (Armstrong 1991, Dretske 1977) think that the framework supports the idea that laws play a special explanatory role in inductive inferences, since a law is not just a universal generalization, but is an entirely different creature — a relation holding between two other universals.
An Armstrongian state of affairs (or fact) exists "if an only if a particular (at a later point to be dubbed a thin particular) has a property or, instead, a relation holds between two or more particulars.
Note that this actually involves two relations to an object: (i) a reference relation, holding between the subject term of the judgment and the object the judgment is about (its object); and (ii) a correspondence relation, holding between the predicate term of the judgment and a property of the object.
The American philosopher Eli Hirsch has provided an elegant definition of "natural class," using a resemblance relation holding among trios one thing's being more similar to another thing than the latter is to some third thing.
If there is a default version of the predicate view, it's that the predicate expresses a binary relation holding between facts (Audi 2012; Rosen 2010).
For another example, it has been argued that singular causal statements cannot be analyzed in terms of a causal connective (essentially for reasons having to do with the above-mentioned slingshot argument) but rather require that causation be treated as a binary relation holding between individual events [Davidson 1967b].
One might also respond that even if one is acquainted with one's being appeared to 48-speckledly, one might fail either to have the right sort of thought or fail to be directly aware of a correspondence relation holding between this fact and the corresponding thought.
Here the idea (for monadic properties at least) is that instantiation is a three-place relation holding between an object, a property, and a region.
The intentionality of a thought comes about because there is an actual relation holding between the thought and its object.
