Without an auxiliary premise identifying the bearer of a property with the property instance itself, the inference commits the Bradley regress error of conflating relata with relations.
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F.H. Bradley(the philosopher whose argument is referenced)
A 19th-century British philosopher who argued that our everyday understanding of relations and things doesn't actually hold up under logical scrutiny.
Property instance(as used in metaphysics)
A single occurrence of a property in a particular object—like the specific redness of one red apple, as opposed to the general idea of redness.
Relata(in philosophy of relations)
The individual things that a relation connects—for example, in 'Alice loves Bob,' Alice and Bob are the relata (the things being related).
Relations
A relation is a way of describing how two or more things are connected or related to each other. For example, "is the parent of," "is taller than," or "is friends with" are all relations that show how people or objects link together. In everyday terms, it's simply a pattern or connection that shows how one thing depends on, compares to, or associates with another.
inference(Nyāya epistemology)
A component of epistemology in Nyāya philosophy; a veritable inference yields knowledge about the world and must have premises that are themselves known