Developing a mathematical theory of computability which speaks the language of levels

In this paper, we use the modern systems theory to retrace the history of some of the important and interesting philosophical problems. And, based on the discussion, it is shown that the multilevel structure of the nature can be approached by making use of the general systems theory approach started by Mesarovic in the early 1960s. Two difficulties appearing in modern physics are listed, and studied in terms of a new mathematical theory. This theory reflects the characteristic of multilevels of the nature. Some elementary properties of the new theory are listed. Some important and fruitful leads for future research are posed in the final section.