August 24. 1831
Truths and Maxims
The English public is not yet ripe to comprehend the essential difference between the reason and the understanding—between a principle and a maxim— an eternal truth and a mere conclusion generalized from a great number of facts. A man, having seen a million moss roses all red, concludes from his own experience and that of others that all moss roses are red. That is a maxim with him—the greatest amount of his knowledge upon the subject. But it is only true until some gardener has produced a white moss rose,— after which the maxim is good for nothing. Again, suppose Adam watching the sun sinking under the western horizon for the first time; he is seized with gloom and terror, relieved by scarce a ray of hope that he shall ever see the glorious light again. The next evening, when it declines, his hopes are stronger, but still mixed with fear; and even at the end of a thousand years, all that a man can feel is a hope and an expectation so strong as to preclude anxiety. Now compare this in its highest degree with the assurance which you have that the two sides of any triangle are together greater than the third. This, demonstrated of one triangle, is seen to be eternally true of all imaginable triangles. This is a truth perceived at once by the intuitive reason, independently of experience. It is and must ever be so, multiply and vary the shapes and sizes of triangles as you may.
It used to be said that four and five make nine. Locke says, that four and five are nine. Now I say, that four and five are not nine, but that they will make nine. When I see four objects which will form a square, and five which will form a pentagon, I see that they are two different things; when combined, they will form a third different figure, which we call nine. When separate they are not it, but will make it.