The "Gedankenexperimente," upon which so much weight has been laid by Mach[125] and Heymans,[126] had already been investigated by the White Queen,[127] who, however, seems to have perceived that the results of such experiments are not always logically valid. The psychological founding of logic appears to be not without analogy with the surprising method of advocates of evolutionary ethics, who expect to discover what _is_ good by inquiring what cannibals have _thought_ good. I sometimes feel inclined to apply the historical method to the multiplication table. I should make a statistical inquiry among school-children, before their pristine wisdom had been biassed by teachers. I should put down their answers as to what 6 times 9 amounts to, I should work out the average of their answers to six places of decimals, and should then decide that, at the present stage of human development, this average is the value of 6 times 9. FOOTNOTES: [125] See, e.g., _E. u. I._, pp. 183-200. [126] _G. u. E._, vol. i. [127] See Appendix T. APPENDIXES A. LOGIC AND THE PRINCIPLE OF IDENTITY. _T. L. G._, p. 45: "'Contrariwise," continued Tweedledee, "if it was so, it might be; and if it were so, it would be: but as it isn't, it ain't. That's logic." * * * * * _S. B._, p. 159: The Professor said: "The day is the same length as anything that is the same length as _it_." * * * * * _S. B._, p. 161: Bruno observed that, when the Other Professor lost himself, he should shout: "He'd be sure to hear hisself, 'cause he couldn't be far off." B. SYNTHESIS OF CONTRADICTORIES. _T. L. G._, p. 71: "'What a beautiful belt you've got on!' Alice suddenly remarked.... 'At least,' she corrected herself on second thoughts, 'a beautiful cravat, I should have said--no, a belt, I mean--I beg your pardon!' she added in dismay, for Humpty-Dumpty looked thoroughly offended, and she began to wish she hadn't chosen that subject. 'If only I knew,' she thought to herself, 'which was neck and which was waist!'" C. EMPIRICAL PHILOSOPHERS AND MATHEMATICS. _T. L. G._, p. 79: "'... Now if you had the two eyes on the same side of the nose, for instance--or the mouth at the top--that would be _some_ help.' "'It wouldn't look nice,' Alice objected. But Humpty-Dumpty only shut his eyes and said: 'Wait till you've tried.'" * * * * * _T. L. G._, p. 72: "'And if you take one from three hundred and sixty-five, what remains?' "'Three hundred and sixty-four, of course.' "Humpty-Dumpty looked doubtful. 'I'd rather see that done on paper,' he said." D. NOMINAL DEFINITION. _T. L. G._, p. 73: "'When _I_ used a word,' Humpty-Dumpty said in rather a scornful tone, 'it means just what I choose it to mean--neither more nor less.' "'The question is,' said Alice, 'whether you _can_ make words mean different things.' "'The question is,' said Humpty-Dumpty, 'which is to be master--that's all.'"