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THREE:The social studies through which we have accompanied Plato seem to have reacted on his more abstract speculations, and to have largely modified the extreme opposition in which these had formerly stood to current notions, whether of a popular or a philosophical character. The change first becomes perceptible in his theory of Ideas. This is a subject on which, for the sake of greater clearness, we have hitherto refrained from entering; and that we should have succeeded in avoiding it so long would seem to prove that the doctrine in question forms a much less important part of his philosophy than is commonly imagined. Perhaps, as some think, it was not an original invention of his own, but was borrowed from the Megarian school; and the mythical connexion in which it frequently figures makes us doubtful how far he ever thoroughly accepted it. The theory is, that to every abstract name or conception of the mind there corresponds an objective entity possessing a separate existence quite distinct from that of the scattered particulars by which it is exemplified to our senses or to our imagination. Just as the Heracleitean flux represented the confusion of which Socrates convicted his interlocutors, so also did these Ideas represent the definitions by which he sought to bring method and certainty into their opinions. It may be that, as Grote suggests, Plato adopted this hypothesis in order to escape from the difficulty of defining common notions in a satisfactory manner. It is certain that his earliest Dialogues seem to place true definitions beyond the reach of human knowledge. And at the beginning of Plato��s constructive period we find the recognition of abstract conceptions, whether mathematical or moral, traced to the remembrance of an ante-natal state, where the soul held direct converse with the transcendent realities to which those conceptions correspond. Justice, temperance, beauty, and goodness, are especially mentioned as examples263 of Ideas revealed in this manner. Subsequent investigations must, however, have led Plato to believe that the highest truths are to be found by analysing not the loose contents but the fixed forms of consciousness; and that, if each virtue expressed a particular relation between the various parts of the soul, no external experience was needed to make her acquainted with its meaning; still less could conceptions arising out of her connexion with the material world be explained by reference to a sphere of purely spiritual existence. At the same time, innate ideas would no longer be required to prove her incorporeality, when the authority of reason over sense furnished so much more satisfactory a ground for believing the two to be of different origin. To all who have studied the evolution of modern thought, the substitution of Kantian forms for Cartesian ideas will at once elucidate and confirm our hypothesis of a similar reformation in Plato��s metaphysics.

THREE:It is generally useless and injudicious to either expect or to search after radical changes or sweeping improvements in machine manufacture or machine application, but it is important in learning how to construct and apply machinery, that the means of foreseeing what is to come in future should at the same time be considered. The attention of a learner can, for example, be directed to the division of labour, improvements in shop system, how and where commercial interests are influenced by machinery, what countries are likely to develop manufactures, the influence of steam-hammers on forging, the more extended use of steel when cheapened by improved processes for producing it, the division of mechanical industry into special branches, what kind of machinery may become staple, such as shafts, pulleys, wheels, and so on. These things are mentioned at random, to indicate what is meant by looking into the future as well as at the present.Turning from sense to reason, Carneades attacks the syllogistic process on grounds already specified in connexion150 with the earlier Sceptics; and also on the plea that to prove the possibility of syllogism is itself to syllogise, and thus involves either a petitio principii or a regress ad infinitum.235 Such a method is, of course, suicidal, for it disproves the possibility of the alleged disproof, a consideration which the Stoics did not fail to urge, and which the later Sceptics could only meet by extending the rule of suspense to their own arguments against argument.236 Nevertheless the sceptical analysis detected some difficulties in the ordinary theory of logic, which have been revived in modern times, and have not yet received any satisfactory solution. Sextus Empiricus, probably copying an earlier authority, it may be Carneades himself, observes that, as the major premise of every syllogism virtually contains the minor, it is either superfluous, or assumes the proposition to be proved. Thus we argue that Socrates is an animal because he is a man, and all men are animals. But if we do not know this latter proposition to be true in the case of Socrates, we cannot be sure that it is true in any case; while if we know it to be true in his case, we do not need to begin by stating it in general terms. And he also attempts to show the impossibility of a valid induction by the consideration, since so often urged, that to generalise from a limited number of instances to a whole class is unsafe, for some of the unknown instances may be contradictory, while the infinite, or at least indefinite multiplicity of individuals precludes the possibility of their exhaustive enumeration.237