Lecture III

Going back a few centuries, perhaps to the fourteenth century, and observing how people conceived of things mathematical, we find that in regard to numbers they still had an echo of inward feelings. In an age in which numbers had already become an abstract ads they are today, people would have been unable to find the names for numbers. The words designating numbers are often wonderfully characteristic. Just think of the word “two.” (zwei) It clearly expresses a real process, as when we say entzweien, “to cleave in twain.” Even more, it is related to zweifeln, “to doubt.” It is not mere imitation of an external process when the number two, zwei, is described by the word Entzweien, which indicates the disuniting, the splitting, of something formerly a whole. It is in fact something that is inwardly experienced and only then made into a scheme. It is brought up from within, just as the abstract three-dimensional space-scheme is drawn up from inside the mind.