  There is nothing wrong in principle with these dogmas. However, there are phenomena that are difficult to deal with in the standard framework. Such a phenomenon is non-wellfoundedness, especially circularity, where we may have consequences without transmission of truth and provability. Another phenomenon are substructural distinctions, where it is crucial to include the structuring of assumptions from the very beginning. Moreover, and this is most crucial, we might define things in a certain way without knowing in advance of whether our definition or chain of definitions is well-founded or not. We do not first involve ourselves into the metalinguistic study of the definition we start with, but would like to start to reason immediately. This problem does not obtain if we restrict ourselves to the case of logical constants, where the defining rules are trivially well-founded.  But the problem arises immediately, when we consider more complicated cases that go beyond logical constants.