So, I am a student in mathematics and physics with no formal training in philosophy whatsoever, although I enjoy reading popular discussions of philosophical questions. However, my question is bound to be vague and badly phrased, for which I apologise in advance.
There is one thing about the debate on the existence of free will that always bothers me. I get that if you consider a human being from a physics perspective, that is, as a sum of physical processes, whether deterministic or not, then it doesn't may not make much sense to attribute to said organism such a thing as free will. However, in that case it doesn't make much sense to me to talk about the organism as having an identity at all - talking about that particular organism would just be a short-cut to talk about the underlying processes. On the other hand, once you assume that "you" is actually an existing thing, then of course it makes sense to talk about free will as well - on the level where "you" exists, so do emotions, thoughts, decisions and free will. The different levels here appear quite important to me: both world-views are equally 'true', but sometimes it's useful to talk at one level and sometimes to talk about the other.
To make an analogy with physics: as long as you see a room filled with gas as a collection of molecules flying around, then notions such as pressure and temperature don't make sense. However, on the macro scale they do and are useful in understanding the world.
So, the point I try to make: to me it seems like the existence of free will and the existence of an "I" are very much intertwined. Assume the existence of one and you get the other, and any argument against the existence of free will applies equally well as an argument of the existence of you.
(The follow-up of this argument for me would be to argue, with I suppose Decartes, that a world-view in which I do not exist is much more unreasonable than a world-view that is not supported by my perception).
I never see this link being made in popular discussions on free will. Does the argument have any merit? Can you recommend any readings that explore this?