Dear Russell Smith , I'm a bit rusty on the delta function, but from what i remember it's that little switch to something out of nothing, right? I think, as you seem to be pointing out there, that there is a big problem with point particles which in turn infects many things within physics: zero extension, zero width, zero mass, all of mass on one point (black holes) etc., etc. I always felt that this is a bit of cheating, and then basing your whole theory on this idea is going to lead you astray. but this starts way back with the beginning of calculus and d anything (dt, etc).
Haris Shekeris I agree. There are many logical mistakes within physics that lead to the correct result for the the wrong reason. The delta function on point particles is one of them. Here is a link if you want more details. Thanks for your comment. Preprint The Laws of Existence and the Structure of Our Universe
wow, audacious effort, though I would refrain from trying to prove god through science (i think science is just another religion and the only place i'd look for laws within science wouldn't be classical logic but history).