Vast piles of mathematics exist without any relational objects, and not exclusively in the intuitionistic sense either. Geometers say it's about rigidity. Number theorists say it's about generative rules. To a type-theorist, it's all about injective maps (with their usual sense of creating new synonyms for everything).
The only thing these have in common is that they are properties about other properties.
But that thing the property is from is called a number, isn't it?
You just said the same thing as GP, but it sounds like you’re trying to argue with them about it.
Perhaps there’s a math formula to describe the relation between your messages’ properties.