although I admit I was expecting a more concise one ;)
First, let me say that on the topic of philosophy of science I understand your points about the limitations of 'empirical science' (hypotheses, models, experiments, etc) and I agree with your views.
I'm also confident I have a pretty good understanding of limits and probability theory.
My question is this: what is this connection you refer to between probability and limits? To me, limits are not probabilistic at all - they are totally deterministic. You can think of it as a process, moving in time, with a particle getting closer and closer to a point but that's just a 'physical metaphor'.
Sorry if I am being a nuisance - I'm just curious about the mental link you have made there.