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THREE:Ever since the age of Parmenides and Heracleitus, Greek thought had been haunted by a pervading dualism which each system had in turn attempted to reconcile, with no better result than its reproduction under altered names. And speculation had latterly become still further perplexed by the question whether the antithetical couples supposed to divide all Nature between them could or could not be reduced to so many aspects of a single opposition. In the last chapter but one we showed that there were four such competing pairs��Being and Not-Being, the One and the Many, the Same and the Other, Rest and Motion. Plato employed his very subtlest dialectic in tracing out their connexions, readjusting their relationships, and diminishing the total number of terms which they involved. In what was probably his last great speculative effort, the Timaeus, he seems to have selected Sameness and Difference as the couple best adapted to bear the heaviest strain of thought. There is some reason for believing that in his spoken lectures he followed the Pythagorean system more closely, giving the preference to the One and the Many; or he may have employed the two expressions indifferently. The former would sooner commend itself to a dialectician, the latter to a mathematician. Aristotle was both, but he was before all things a naturalist. As such, the antithesis of Being and Not-Being, to which Plato attached little or no value, suited him best. Accordingly, he proceeds to work it out with a clearness before unknown in Greek philosophy. The first and surest of all principles, he declares, is, that a thing cannot both be and not be, in the same sense of the words, and furthermore that it must either be or not be. Subsequent340 logicians prefixed to these axioms another, declaring that whatever is is. The three together are known as the laws of Identity, Contradiction, and Excluded Middle. By all, except Hegelians, they are recognised as the highest laws of thought; and even Hegel was indebted to them, through Fichte, for the ground-plan of his entire system.235

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THREE:Whatever may have been the errors into which Socrates fell, he did not commit the fatal mistake of compromising his ethical doctrine by associating it indissolubly with his metaphysical opinions. Religion, with him, instead of being the source and sanction of all duty, simply brought in an additional duty��that of gratitude to the gods for their goodness. We shall presently see where he sought for the ultimate foundation of morality, after completing our survey of the dialectic method with which it was so closely connected. The induction of Socrates, when it went beyond that kind of analogical reasoning which we have just been considering, was mainly abstraction, the process by which he obtained those general conceptions or definitions which played so great a part in his philosophy. Thus, on comparing the different virtues, as commonly distinguished, he found that they all agreed in requiring knowledge, which he accordingly concluded to be the essence of virtue. So other moralists have been led to conclude that right actions resemble one another in their felicific quality, and In that alone. Similarly, political economists find, or formerly found (for we do not wish to be positive on the matter), that a common characteristic of all industrial employments is the desire to secure the maximum of profit with the minimum of trouble. Another comparison shows that value depends on the relation between supply and demand. Aesthetic enjoyments of every kind resemble one another by including an element of ideal emotion. It is a common characteristic of all cognitions that they are151 constructed by association out of elementary feelings. All societies are marked by a more or less developed division of labour. These are given as typical generalisations which have been reached by the Socratic method. They are all taken from the philosophic sciences��that is, the sciences dealing with phenomena which are partly determined by mind, and the systematic treatment of which is so similar that they are frequently studied in combination by a single thinker, and invariably so by the greatest thinkers of any. But were we to examine the history of the physical sciences, we should find that this method of wide comparison and rapid abstraction cannot, as Francis Bacon imagined, be successfully applied to them. The facts with which they deal are not transparent, not directly penetrable by thought; hence they must be treated deductively. Instead of a front attack, we must, so to speak, take them in the rear. Bacon never made a more unfortunate observation than when he said that the syllogism falls far short of the subtlety of Nature. Nature is even simpler than the syllogism, for she accomplishes her results by advancing from equation to equation. That which really does fall far short of her subtlety is precisely the Baconian induction with its superficial comparison of instances. No amount of observation could detect any resemblance between the bursting of a thunderstorm and the attraction of a loadstone, or between the burning of charcoal and the rusting a nail.Near Lanaeken I met suddenly a Belgian soldier, who did not trouble me after I had shown him my papers. I was quite astonished to find that man there all by himself, whilst so many Germans were only a few miles away. When I asked whether he knew this, he answered:

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THREE:Leaving out problems of mechanism in forging machines, the adaptation of pressing or percussive processes is governed mainly by the size and consequent inertia of the pieces acted upon. In order to produce a proper effect, that is, to start the particles of a piece throughout its whole depth at each blow, a certain proportion between a hammer and the piece acted upon must be maintained. For heavy forging, this principle has led to the construction of enormous hammers for the performance of such work as no pressing machinery can be made strong enough to execute, although the action of such machinery in other respects would best suit the conditions of the work. The greater share of forging processes may be performed by either blows or compression, and no doubt the latter process is the best in most cases. Yet, as before explained, machinery to act by pressure is much more complicated and expensive than hammers and drops. The tendency in practice is, however, to a more extensive employment of press-forging processes.CHAPTER XI. SHAFTS FOR TRANSMITTING POWER.

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