Chapter 16, Infinity, part 1

You remember the angel who looks like this, −1. Now I am going to introduce you to another angel. It is called “Infinity.” When you come to it, remember what I told you before—Angels are messengers from the great world of the “As-Yet-Unknown.” They never gossip about their private affairs, or those of other angels. They come to tell you either about what you are to do next, or about something you had better not do next; and if you ask them impertinent questions about things that do not concern you for the time being, they will give you headaches and make your head spin: just to teach you to mind your own business. This particular angel always comes with a message about a broken link or a loosened chain. It comes, when an hypothesis has been fully worked out, to tell you that you are now free from the bonds of that hypothesis and at liberty to start experimenting on a fresh one. But its message is never: “You have got out of that particular house of bondage and therefore you may, for all the rest of your life, run riot, and eat, and drink, and do, whatever you please.” Its message always is: “You have outgrown that master; now you may take a holiday and have a fling before you go into a higher class; but, just because you are set free, look out for danger traps; and mind your Ten Commandments.”

You will understand Infinity's messages better if you will read carefully what is written about it in Chapter XV. of “The Logic of Arithmetic.” It brought the answer to the question: “How many children could pass through a school-room without the apples all being eaten up, supposing that none of the children ate any?” Let us go over that ground again. Suppose there is a cake on the table. How many children can go through the room without the cake being all eaten up?