I don't know about physics specifically but there is a significant amount of discussion in the Philosophy world about the class of problems that you are describ

I don't know about physics specifically but there is a significant amount of discussion in the Philosophy world about the class of problems that you are describing. http://plato.stanford.edu/entries/vagueness/ http://plato.stanford.edu/entries/vagueness/ http://plato.stanford.edu/entries/sorites-paradox/ http://plato.stanford.edu/entries/sorites-paradox/