“I do not need to give any reasons for it. I am satisfied to know what I know.” I saw that I could not get the better of her in this way, so I said-- “Will you have the kindness to imagine this stone to be a pumpkin?” “Well, Mr Mulligan!” she answered, “if this gives you pleasure, I shall imagine it to be a pumpkin.” “Now take a bite of it, my darling,” I said. “I can’t, and you ought not to ask me anything so absurd.” “But why can’t you?” “Because it is too hard.” “Exactly!” I exclaimed. “And now as you have discovered that it is too hard for being a pumpkin, you have a scientific right to infer that it is not a pumpkin and may possibly be a stone; _quod erat demonstrandum_.” This way of making a simple thing very complicated, according to the strict rules of exact science, pleased the princess very much and amused her greatly. It now became necessary to show to her how we may arrive at a knowledge of universals by drawing logical inferences from particulars. For this purpose I told her that we must never trust to our reason, but only put faith into our method of reasoning. Pointing to the stocking which the princess was just knitting, I asked her what it was. “A stocking,” she said. “I thought you knew that much already.” “Who is going to wear it?” “I.” “And what are you?” “A princess of this kingdom.” “Do all the princesses of this kingdom wear stockings?” “All those whom I know.” “Very well!” I replied. “The consequence is that all the people who wear stockings are princesses of the kingdom of the gnomes.” This seemed strange to Adalga, but she could not prove that it was not so, and I proceeded to explain to her that the power to draw logical inferences was the highest power which a scientist could possess, and that by means of logic almost anything could be proved, be it true or false. Thus I proved to her by way of an illustration, first, that white was black; secondly, that black was white; and thirdly, that there was no colour at all. “White, my dear!” I said, “is, as everybody knows, no colour at all; for it is produced by a combination of all the prismatic colours in the same proportion as they exist in the solar ray, where each colour neutralises the other. Now, if there is no colour, there can be no light, and where no light exists everything is as black as night, and if everything is black, white must be black also, and consequently white is black.” “Very strange!” exclaimed Adalga. “If white is black,” I continued, “it follows that black is white, because if there is no difference between two things they must be identical. Moreover, everybody knows that black is no colour at all, but the negation of colour, and it follows that if a thing has no particular colour of any kind, it must necessarily be white.” “Incredible!” exclaimed the princess.