Order, unity, and continuity are human inventions, just as truly as catalogues and encyclopedias.

Zeno was concerned with three problems... These are the problem of the infinitesimal, the infinite, and continuity.

A democrat need not believe that the majority will always reach a wise decision. He should however believe in the necessity of accepting the decision of the majority, be it wise or unwise, until such a time that the majority reaches another decision.

I often long to . . . give up my life to love of my neighbour. This is really a temptation.

Philosophy, though unable to tell us with certainty what is the true answer to the doubts which it raises, is able to suggest many possiblities which enlarge our thoughts and free them from the tyranny of custom. Thus, while diminishing our feeling of certainty as to what things are, it greatly increases our knowledge as to what the may be; it removes the somewhat arrogant dogmatism of those who have never travelled into the region of liberating doubt, and it keeps alive our sense of wonder by showing familar things in an unfamilar aspect

Calculus required continuity, and continuity was supposed to require the infinitely little; but nobody could discover what the infinitely little might be.

I remain convinced that obstinate addiction to ordinary language in our private thoughts is one of the main obstacles to progress in philosophy.