I put forward a semantic theory of untyped propositions satisfying the equivalence schema. Propositions are well-founded in a clear sense but are also allowed to exhibit a non-vicious kind of self-reference. Moreover, they satisfy a fine-grained identity criterion closed under certain (but not all) logical transformations that preserves many shared intuitions. Time permitting, I will explore a somehow natural extension of this framework to properties.
See the seminar webpage http://users.ox.ac.uk/~philmath/pomseminar.html for titles and abstracts of other speakers when available.
Philosophy of Mathematics Seminar Convenors: Daniel Isaacson and Volker Halbach