"The subject of a science is never well circumscribed and there is little use sharpening its definition. However, nobody will deny that physics deals with nature and sociology with human society in some of their aspects. With logic, it is another matter. Logic is usually understood nowadays as a study of certain formal systems, though in former times there were philosophers who held that the subject matter of logic was the formal rules of human thought. In the latter sense it would be an empirical rather than a formal science, though its empirical subject matter would still be fundamentally different from that of psychology of thinking. One interpretation of logic does not exclude the other. Formal approaches are often easier than empirical ones, and for this reason one can understand why logic as a study of formal systems has till now made more progress than logic as a study of the formal rules of thought, even if restricted to scientific thought."

“striking a subtle balance between the freedom of inventing and the force of guiding, between allowing the learner to please himself and asking him to please the teacher. Moreover, the learner’s free choice is already restricted by the “re” of “reinvention”. The learner shall invent something that is new to him but well-known to the guide.”

“Vertical mathematising is the most likely part of the learning process for the bonds with reality to be loosened and eventually cut.”

“Science should be distinguished from technique and its scientific instrumentation, technology. Science is practised by scientists, and techniques by ‘engineers’ — a term that in our terminology includes physicians, lawyers, and teachers. If for the scientist knowledge and cognition are primary, it is action and construction that characterises the work of the engineer, though in fact his activity may be based on science. In history, technique often preceded science.”

“consciously experience, describe and justify the cyclic process of development and research so that it can be passed on to others in such a way that they can witness and relive the experience.”

“Learners should be allowed to find their own levels and explore the paths leading there with as much and as little guidance as each particular case requires.”

“Educational technique needs a philosophy, which is a matter of faith rather than of science.”