One circle cannot touch another circle on the outside at more points than one. For, if it be possible, let the circle ACK touch the circle ABC at the points A, C. Join AC. Then because the two points A, C are in the circumference of the circle ACK the line which joins them falls within that circle. But the circle ACK is without the circle ABC. Therefore the straight line AC is without the circle ABC. But because the two points A, C are in the circumference of ABC therefore the straight line AC falls within that circle. Which is absurd. Therefore one circle cannot touch another on the outside at more points than one.
All thoughts, as well as all passions, all delights
votum, timor, ira, voluptas—
whatsoever, in short, engages man’s activity of soul or body, may be deemed the subject of literature and is transformed into literature by process of recording it in memorable speech. It is so, it has been so, and God forbid it should ever not be so!
Now this, put so, is (you will say) so extremely, obvious that it must needs hide a fallacy or at best a quibble on a word. I shall try to show that it does not: that it directly opposes plain truth to a convention accepted by the Ordinance, and that the fallacy lies in that convention.
A convention may be defined as something which a number of men have agreed to accept in lieu of the truth and to pass off for the truth upon others: I was about to add, preferably when they can catch them young: but some recent travel in railway trains and listening to the kind of stuff men of mature years deliver straight out of newspapers for the products of their own digested thought have persuaded me that the ordinary man is as susceptible at fifty, sixty, or even seventy as at any earlier period of growth, and that the process of incubation is scarcely less rapid.
I am not, to be sure, concerned to deny that there may be conventions useful enough to society, serving it to maintain government, order, public and private decency, or the commerce on which it must needs rest to be a civilised society at all— commerce of food, commerce of clothing, and so on, up to commerce in knowledge and ideas. Government itself—any form of it—is a convention; marriage is a convention; money of course is a convention, and the alphabet itself I suppose to contain as many conventions as all the old Courts of Love and Laws of Chivalry put together, and our English alphabet one tremendous fallacy, that twenty-six letters, separately or in combination are capable of symbolising all the sounds produced by an Englishman’s organs of speech, let alone the sounds he hears from foreigners, dogs, guns, steam-engines, motor-horns and other friends and enemies to whom we deny the franchise. Also of course it ignores the whole system of musical notes—another convention—which yet with many of the older bards could hardly be separated from the words they used, though now only the words survive and as literature.