I've posted a new version of my paper "Fundamental and derivative truths". The new version notes a few more uses for the fundamental/derivative distinction, and clears up a few points.
As before, the paper is concerned with a way of understanding the---initially pretty hard to take---claim that tables exist, but don't really exist. I think that that claim at least makes good sense, and arguably the distinction between what is really/fundamentally the case and what is merely the case is something we should believe in whether or not we endorse the particular claim about tables. I think in particular that it leads to a particularly attractive view on the nature of set theory, since it really does seem that we do want to be able to "postulate sets into existence" (y'know how things form sets? well consider the set of absolutely everything. On pain of contradiction that set can't be something that existed beforehand...) The framework I like lets us make sober sense of that.
The current version tidies up a bunch of things, it pinpoints more explicitly the difference between comparatively "easy cases"---defending the compatibility of set theoretic truths with a nominalist ontology----and "hard cases"---defending the compatibility of the Moorean corpus with a microphysical mereological nihilist ontology. I've got another paper focusing on some of the technicalities of the composition case.
This project causes me much grief, since it involves many many different philosophically controversial areas: philosophy of maths, metaphysics of composition, theory of ontological commitment, philosophy of language and in particular metasemantics, and so forth. That makes it exciting to work on, but hard to present to people in a digestible way. Nevertheless, I'm going to have another go at the CSMN workshop in Olso later this month, focusing on the philosophy of language/theory of meaning aspects.