Phenomenology (philosophy)

"Our mathematical concepts, structures, ideas have been invented as tools to organise the phenomena of the physical, social and mental world. Phenomenology of a mathematical concept, structure, or idea means describing it in its relation to the phenomena for which it was created, and to which it has extended in the learning process of mankind, and, as far as this description is concerned with the learning process of the young generation, it is didactical phenomenology, a way to show the teacher the places where the learner might step into the learning process of mankind."

"The goal to be reached is the mind’s insight into what knowing is. Impatience asks for the impossible, wants to reach the goal without the means of getting there. The length of the journey has to be borne with, for every moment is necessary, ... because by nothing less could that all-pervading mind ever manage to become conscious of what itself is — for that reason, the individual mind, in the nature of the case, cannot expect by less toil to grasp what its own substance contains."

"Hegel’s lack of charity toward the instrument metaphor is not arbitrary. It represents his disenchantment with the assumption that knowledge is power and that method is the means to this end. ... Descartes’ conception of method, like Bacon’s, is linked to this idea of knowledge as an instrument of power. ... The same could be said of Locke. Hegel can rightly claim that the instrument metaphor pervades the epistemological tradition he is seeking to transcend."