From principles of mechanics to quantum mechanics - a survey on fuzziness in scientific theories

In this paper we discuss the principles of two fundamental theories of physics: mechanics and quantum mechanics. First, we consider two philosophical positions of the German physicist Heinrich Hertz. He established one of the both in the introduction of his well known Principles of Mechanics. This view - Hertz\´s "picture" concept - which has a long tradition in philosophy, particularly with regard to physics and later to other empirical sciences, serves as the starting point of an interpretation of the relationship between real systems and theoretical structures of modern science using the concept of fuzziness. This "fuzzy view" on philosophy of science gives particularly an interpretation of Hertz\´s earlier lecture on The Constitution of matter. Second we consider some principles of quantum mechanics, particularly Werner Heisenberg\´s uncertainty relation of subatomic object\´s position and momentum, and Max Born\´s probabilistic interpretation of the quantum mechanical wave function. These principles are parts of the so-called Copenhagen interpretation of quantum mechanics. Third, we argue that the "fuzzy approach" is fruitful for a "fuzzy" interpretation of quantum mechanics because fuzziness fills the gap between systems and phenomena in reality and the scientific theory of quantum mechanics - as every other scientific theory.