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THREE:IN LIèGE AND BACK TO MAASTRICHT

THREE:5. Every part laid down has something to govern it that may be termed a "base"—some condition of function or position which, if understood, will suggest size, shape, and relation to other parts. By searching after a base for each and every part and detail, the draughtsman proceeds upon a regular system, continually maintaining a test of what is done. Every wheel, shaft, screw or piece of framing should be made with a clear view of the functions it has to fill, and there are, as before said, always reasons why such parts should be of a certain size, have such a speed of movement, or a certain amount of bearing surface, and so on. These reasons or conditions may be classed as expedient, important, or essential, and must be estimated accordingly. As claimed at the beginning, the designs of machines can only in a limited degree be determined by mathematical data. Leaving out all considerations of machine operation with which books have scarcely attempted to deal, we have only to refer to the element of strains to verify the general truth of the proposition.

THREE:We have seen how, for the antithesis between Form and Matter, was substituted the wider antithesis between Actuality and Possibility. Even in this latter the opposition is more apparent than real. A permanent possibility is only intelligible through the idea of its realisation, and sooner or later is certain to be realised. Aristotle still further bridges over the interval between them by a new conception—that of motion. Motion, he tells us, is the process of realisation, the transformation of power into act. Nearly the whole of his Physics is occupied with an enquiry into its nature and origin. As first conceived, it is equivalent to what we call change rather than348 to mechanical movement. The table of categories supplies an exhaustive enumeration of its varieties. These are, as we have already mentioned, alteration of quality or transformation, increase or decrease of quantity, equivalent to growth and decay, and transport from place to place. Sometimes a fourth variety is added, derived from the first category, substance. He calls it generation and destruction, the coming into existence or passing out of it again. A careful analysis shows that motion in space is the primordial change on which all others depend for their accomplishment. To account for it is the most vitally important problem in philosophy.By cutting up some of the longer essays into parts, Porphyry succeeded, much to his delight, in bringing the whole number up to fifty-four, which is a product of the two perfect numbers six and nine. He then divided them into six volumes, each containing nine books—the famous Enneads of Plotinus. His principle of arrangement was to bring together the books in which similar subjects were discussed, placing the easier disquisitions first. This disposition has been adhered to by subsequent editors, with the single exception of Kirchhoff, who has printed the works of Plotinus according to the order in which they were written.418 Porphyry’s scrupulous information has saved modern scholars an incalculable amount of trouble, but has not, apparently, earned all the gratitude it deserved, to judge by Zeller’s intimation that the chronological order of the separate pieces cannot even now be precisely determined.419 Unfortunately, what could have been of priceless value in the case of Plato and Aristotle, is of comparatively small value in the case of Plotinus. His280 system must have been fully formed when he began to write, and the dates in our possession give no clue to the manner in which its leading principles were evolved.420

THREE:It is evident that when the parts of a machine are joined together, each piece which has contact on more than one side must have specific dimensions; it is farther evident that as many of the joints in a machine as are to accommodate the exigencies of construction must be without space, that is, they represent continued sections of what should be solid material, if it were possible to construct the parts in that manner. This also demands specific dimensions.The foregoing analysis will enable us to appreciate the true significance of the resemblance pointed out by Zeller153259 between the Platonic republic and the organisation of mediaeval society. The importance given to religious and moral training; the predominance of the priesthood; the sharp distinction drawn between the military caste and the industrial population; the exclusion of the latter from political power; the partial abolition of marriage and property; and, it might be added, the high position enjoyed by women as regents, chatelaines, abbesses, and sometimes even as warriors or professors,—are all innovations more in the spirit of Plato than in the spirit of Pericles. Three converging influences united to bring about this extraordinary verification of a philosophical deal. The profound spiritual revolution effected by Greek thought was taken up and continued by Catholicism, and unconsciously guided to the same practical conclusions the teaching which it had in great part originally inspired. Social differentiation went on at the same time, and led to the political consequences logically deduced from it by Plato. And the barbarian conquest of Rome brought in its train some of those more primitive habits on which his breach with civilisation had equally thrown him back. Thus the coincidence between Plato’s Republic and mediaeval polity is due in one direction to causal agency, in another to speculative insight, and in a third to parallelism of effects, independent of each other but arising out of analogous conditions.

THREE:"And what happened after that?"