Although Theoretical Physics, System Theory, Philosophy of Science and other branches deal a lot with very sophisticated mathematical structures trying to create a general image of what systems really are, including their sets of states and the physical quantities correlated to them, this book tries to show that ultimately we do not know what physical quantities are. It tries to go beyond the concept of the influence of the observer on the experiment, seeking to analyze the relationship between the thinker and the systems he is exploring. An important step of doing this is to mark out the significance attributed to the system by the exploring mind and to launch the question if there should be taken into consideration an objective, hidden significance to any system, in particular to physical systems. The book is addressed to those who are interested in Philosophy of Science and Cognitive Theory. As it contains also mathematical details, it is split into two parts : the first one is trying to formulate problems in general terms, while the second one introduces some rigor and deals also with mathematical tools.