Note 1 — I

Of course, if we comprehend in our view only elementary geometrical and algebraical science, it is easy to show that they do demand both axioms and intuitions. Take, e.g. Euclid I. i., where in the construction it is necessary to employ intuition for the assertion that the arcs really cut one another. There is no logical certainty that they do; in fact, in some other conditions, e.g. in those of other space dimensions, they might not.