Generality is, indeed, an indispensable ingredient of reality; for mere individual existence or actuality without any regularity whatever is a nullity. Chaos is pure nothing.

I think of consciousness as a bottomless lake, whose waters seem transparent, yet into which we can clearly see but a little way.But in this water there are countless objects at different depths; and certain influences will give certain kinds of those objects an upward influence which may be intense enough and continue long enough to bring them into the upper visible layer. After the impulse ceases they commence to sink downwards.

It is terrible to see how a single unclear idea, a single formula without meaning, lurking in a young man's head, will sometimes act like an obstruction of inert matter in an artery, hindering the nutrition of the brain and condemning its victim to pine away in the fullness of his intellectual vigor and in the midst of intellectual plenty.

It is impossible not to envy the man who can dismiss reason, although we know how it must turn out at last.

It is a common observation that a science first begins to be exact when it is quantitatively treated. What are called the exact sciences are no others than the mathematical ones.

Mathematics is purely hypothetical: it produces nothing but conditional propositions.

The real, then, is that which, sooner or later, information and reasoning would finally result in, and which is therefore independent of the vagaries of me and you. Thus, the very origin of the conception of reality shows that this conception essentially involves the notion of a COMMUNITY, without definite limits, and capable of a definite increase of knowledge.