While the dogmatist is harmful, the sceptic is useless ...; one is certain of knowing, the other of not knowing. What philosophy should dissipate is certainty, whether of knowledge or of ignorance. Knowledge is not so precise a concept as is commonly thought. Instead of saying 'I know this', we ought to say 'I more or less know something more or less like this'. ... Knowledge in practical affairs has not the certainty or the precision of arithmetic.
At the Egyptian city of Naucratis there was a famous old god whose name was Theuth; the bird which is called the Ibis was sacred to him, and he was the inventor of many arts, such as arithmetic and calculation and geometry and astronomy and draughts and dice, but his great discovery was the use of letters.
It is by now proverbial that every proverb has its opposite. For every Time is money there is a Stop and smell the roses. When someone says You never stand in the same river twice someone else has already replied There is nothing new under the sun. In the mind's arithmetic, 1 plus -1 equals 2. Truths are not quantities but scripts: Become for a moment the mind in which this is true.
Some of our problems can no more be solved correctly by majority opinion than can a problem in arithmetic and there are few problems that cannot be solved according to what is just and right without resort to popular opinion.
The importance of infinite processes for the practical exigencies of technical life can hardly be overemphasized. Practically all applications of arithmetic to geometry, mechanics, physics and even statistics involve these processes directly and indirectly.
I do know the sorrow of being ordinary, and that much of our life is spent doing the crazy mental arithmetic of how, at any given moment, we might improve, or at least disguise or present our defects and screw-ups in either more charming or more intimidating ways.
Lucy, dear child, mind your arithmetic. You know in the first sum of yours I ever saw there was a mistake. You had carried two (as a cab is licensed to do), and you ought, dear Lucy, to have carried but one. Is this a trifle? What would life be without arithmetic, but a scene of horrors.