FORE:The principal business of reason is, as we have seen, to376 form abstract ideas or concepts of things. But before the time of Aristotle it had already been discovered that concepts, or rather the terms expressing them, were capable of being united in propositions which might be either true or false, and whose truth might be a matter either of certainty or of simple opinion. Now, in modern psychology, down to the most recent times, it has always been assumed that, just as there is an intellectual faculty or operation called abstraction corresponding to the terms of which a proposition is composed, so also there is a faculty or operation called judgment corresponding to the entire proposition. Sometimes, again, the third operation, which consists in linking propositions together to form syllogisms, is assigned to a distinct faculty called reason; sometimes all three are regarded as ascending steps in a single fundamental process. Neither Plato nor Aristotle, however, had thought out the subject so scientifically. To both the framing, or rather the discovery, of concepts was by far the most important business of a philosopher, judgment and reasoning being merely subsidiary to it. Hence, while in one part of their logic they were realists and conceptualists, in other parts they were nominalists. Abstract names and the definitions unfolding their connotation corresponded to actual entities in Naturethe eternal Ideas of the one and the substantial forms of the otheras well as to mental representations about whose existence they were agreed, while ascribing to them a different origin. But they did not in like manner treat propositions as the expression of natural laws without, or of judgments within, the mind; while reasoning they regarded much more as an art of thinking, a method for the discovery of ideas, than as the Systematisation of a process spontaneously performed by every human being without knowing it; and, even as such, their tendency is to connect it with the theory of definition rather than with the theory of synthetic propositions. Some approach to a realistic view is, indeed, made by both. The377 restless and penetrating thought of Plato had, probably towards the close of his career, led him to enquire into the mutual relations of those Ideas which he had at first been inclined to regard as absolutely distinct. He shows us in the Sophist how the most abstract notions, such as Being, Identity, and so forth, must, to a certain extent, partake of each others nature; and when their relationship does not lie on the surface, he seeks to establish it by the interposition of a third idea obviously connected with both. In the later books of the Republic he also points to a scheme for arranging his Ideas according to a fixed hierarchy resembling the concatenation of mathematical proofs, by ascending and descending whose successive gradations the mind is to become familiarised with absolute truth; and we shall presently see how Aristotle, following in the same track, sought for a counterpart to his syllogistic method in the objective order of things. Nevertheless, with him, as well as with his master, science was not what it is with us, a study of laws, a perpetually growing body of truth, but a process of definition and classification, a systematisation of what had already been perceived and thought.
THREE:A learner will no doubt wonder why sand is used for moulding, instead of some more adhesive material like clay. If he is not too fastidious for the experiment, and will apply a lump of damp moulding sand to his mouth and blow his breath through the mass, the query will be solved. If it were not for the porous nature of sand-moulds they would be blown to pieces as soon as the hot metal entered them; not only because of the mechanical expansion of the gas, but often from explosion by combustion. Gas jets from moulds, as may be seen at any time when castings are poured, will take fire and burn the same as illuminating gas.On the other hand, conservatives like Aristophanes continued to oppose the spread of education with acrimonious zeal. Some of their arguments have a curiously familiar ring. Intellectual pursuits, they said, were bad for the health, led to irreligion and immorality, made young people quite unlike their grandfathers, and were somehow or other connected with loose company and a fast life. This last insinuation was in one respect the very reverse of true. So far as personal morality went, nothing could be better for it than the change introduced by Protagoras from amateur to paid teaching. Before this time, a Greek youth who wished for something better than the very elementary instruction given at school, could only attach himself to some older and wiser friend, whose conversation might be very improving, but who was pretty sure to introduce a sentimental element into their relationship equally discreditable to both.70 A similar danger has always existed with regard to highly intelligent women, although it may have threatened a smaller number of individuals; and the efforts now being made to provide them with a systematic education under official superintendence will incidentally have the effect of saving our future Hloises and Julies from the tuition of an Ablard or a Saint-Preux.
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