Original argument appearring in Chapters II and III of [1] (1893), and S.E.P. commentary here:
Bradley notes that there appears to be such a thing as ‘a lump of sugar’, and this thing appears to have qualities such as whiteness, sweetness, and hardness.
But what is this “thing” that bears properties?
On the one hand, it’s odd to assume that there is something to the lump of sugar beside its several qualities
So, postulating a property-less bearer of properties is incoherent.
On the other hand, he notes that the lump cannot merely be its qualities either, since the latter must somehow be united.
For Bradley, unity or “coexistence” of qualities presupposes relations.
But the ontology of relations is prone to the following infinite regress:
We postulate the relation \(C\) that relates properties \(A\) and \(B\)
We then need a relation to relate \(C\) to \(A\) (and to \(B\)).