TWO:
THREE:It is not assumed that shaded elevations should not be made, nor that ink shading should not be learned, but it is thought best to point out the greater importance of other kinds of drawing, too often neglected to gratify a taste for picture-making, which has but little to do with practical mechanics.
THREE:Such 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 Euclids 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 syntheticthat 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:Were this intellectual despondency to issue in a permanent suspense of judgment, it would be bad enough; but practically its consequences are of a much more mischievous character. The human mind is so constituted that it must either go forward or fall back; in no case can it stand still. Accordingly, the lazy sceptic almost always ends by conforming to the established creeds and customs of his age or of the society in which he lives; thus strengthening the hands of authority in its conflict with the more energetic or courageous enquirers, whose object is to discover, by the unaided efforts of reason, some new and positive principle either of action or of belief. And the guardians of orthodoxy are so well aware of the profit to be reaped from this alliance that, when debarred from putting down their opponents by law or by public opinion, they anxiously foster false scepticism where it is already rampant, and endeavour to create it where it does not exist. Sometimes disinterested morality is the object of their attack, and at other times the foundations of inductive science. Their favourite formula is that whatever objections may be urged against their own doctrines, others equally strong may be urged against the results of free thought; whereas the truth is that such objections, being applicable to all systems alike, exactly balance one another, leaving the special arguments against irrationalism to tell with as much force as before. And they also lay great stress on the internal dissensions of their assailantsdissensions which only bring out into more vivid relief the one point on which all are agreed, that, whatever else may be true, the traditional opinions are demonstrably false.
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