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THREE:

THREE:But the shell-fire of the French overtook them then, as they were retreating, while many others were killed by bombs from French aeroplanes, which were in action in great numbers. The retreat had not stopped before the Germans arrived in Cambray, where the thousands of wounded could at last be put in long trains and sent to Aix-la-Chapelle. A great many bombs from aeroplanes also hit these trains and killed a great many; my own train was everywhere pierced by fragments of those bombs. Within the carriages it was unendurable; the wounded men and their malodorous bandages had occupied them such a long time that the atmosphere was simply insupportable. Happily there was a corridor, where I stood all the time, with the little girl, in the company of some German military men who were sent home, not on account of wounds, but because of internal complaints.

THREE:399Such a view was essentially unfavourable to the progress of science, assigning, as it did, a higher dignity to meagre and very questionable abstractions than to the far-reaching combinations by which alone we are enabled to unravel the inmost texture of visible phenomena. Instead of using reason to supplement sense, Aristotle turned it into a more subtle and universal kind of sense; and if this disastrous assimilation was to a certain extent imposed upon him by the traditions of Athenian thought, it harmonised admirably with the descriptive and superficial character of his own intelligence. Much was also due to the method of geometry, which in his time had already assumed the form made familiar to us by Euclid��s Elements. The employment of axioms side by side with definitions, might, indeed, have drawn his attention to the existence and importance of judgments which, in Kantian terminology, are not analytic but synthetic��that is, which add to the content of a notion instead of simply analysing it. But although he mentions axioms, and states that mathematical theorems are deduced from them, no suspicion of their essential difference from definitions, or of the typical significance which they were destined to assume in the theory of reasoning, seems ever to have crossed his mind; otherwise he could hardly have failed to ask how we come by our knowledge of them, and to what they correspond in Nature. On the whole,385 it seems likely that he looked on them as an analysis of our ideas, differing only from definition proper by the generality of its application; for he names the law of contradiction as the most important of all axioms, and that from which the others proceed;277 next to it he places the law of excluded middle, which is also analytical; and his only other example is, that if equals be taken from equals the remainders are equal, a judgment the synthetic character of which is by no means clear, and has occasionally been disputed.278

THREE:Suddenly the silence was broken by a laugh. It was the croaking kind of laugh that could only have proceeded from the lips of an old man. But there was pleasure in it. It came strangely after the note of tragedy that had dominated the evening. A door opened somewhere, and the laugh came once more.