In this interesting post at Maverick Philosopher, Bill Vallicella explores critically the metaphysical theory that all properties in the world are tropes, which are ontologically simple building blocks (technically speaking, abstract particulars). In other words, trope theory is a one-category ontology. The key question is, then, how do these tropes come together to make things? The advocate of the view would need to propose a compresence relationship which binds tropes, but still is itself a trope of the same ontological variety. Vallicella then argues that this leads to problems, particularly a vicious regress. If the compresence trope ‘C’ links tropes ‘R’ and ‘S’ together, then what links C to both R and S? If it is another trope C*, you can see the regress. It made sense to me, although I imagine philosophers who have developed different varieties of trope theories would have a response. In any case, the arguments are carefully constructed, and I refer you to the post itself and the SEP entry on tropes for further reading.
For me, this discussion lends support to my previously held belief that a single simple ontological building block cannot account for the diversity of natural entities. A second relation is needed – a property which binds and actualizes, but is itself not in need of binding in the same way. At first, this may seem to make for a less appealingly simple or monistic ontology; however, when the property complexes that result are cast as events rather than things, the dual aspect seems to me elegant and not ad hoc, as I argued in this recent post.