Now that I have some genuine philosophers reading my blog and commenting I guess it would be good to get some of my thoughts on what might turn into my dissertation to see if I can get any feedback on them.
One of the problems I've been thinking about has to do with coming into or going out of existence. I had thought I had identified a problem with a view that I've never really liked much, the view that posits coincident entities to explain the puzzles of change. Since a statue and a clay have different persistence conditions (the clay can go on existing once the statue has been melted down), they must not be the same thing, by Leibniz's Law. That means there's a statue and a piece of clay both existing at the same time in the same place, one constituting the other.
Coincident entity theorists have trouble when they admit to something taking time to come into existence. For example, Judith Jarvis Thomson's famous paper on abortion presents what's now the standard view, among philosophers anyway, about fetuses and personhood. A fetus isn't a person from conception but is by birth (or some say even not yet then but by age 2). The process of becoming a person is not immediate, because 'person' is a vague term, admitting of borderline cases. The problem with saying this is that coincident entity theorists believe some genuinely new thing has come into being once the person exists, just as a genuinely new thing has come into existence when the clay has been fashioned into a statue. Views that say that a fetus has literally become a person (i.e. it has a new property) but isn't a new thing don't face this problem at this point. An ontology that allows a new thing to come into existence out of exactly the same parts as something else that's there is going to have trouble with that thing taking time to come into existence, though, since there's a problem specifying whether the new thing exists during the transitional time. It's neither exists nor fails to exist, just as someone with a certain small enough number of hairs isn't quite bald but isn't quite not bald or some color right in the area between red and pink, say, might not be red but also isn't not red.