FORE:"Charlton's white set face as he pressed against the panes."--Page 124The 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 Nature��the eternal Ideas of the one and the substantial forms of the other��as 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 other��s 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.

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FORE:The reformed system of education was to be not only moral and religious but also severely scientific. The place given to mathematics as the foundation of a right intellectual training is most remarkable, and shows how truly Plato apprehended the conditions under which knowledge is acquired and enlarged. Here, as in other respects, he is, more even than Aristotle, the precursor of Auguste Comte. He arranges the mathematical sciences, so far as they then existed, in their logical order; and his remarks on the most general ideas suggested by astronomy read like a divination of rational mechanics. That a recommendation of such studies should be put into the mouth of Socrates is a striking incongruity. The older Plato grew the farther he seems to have advanced from the humanist to the naturalistic point of view; and, had he been willing to confess it, Hippias and Prodicus were the teachers with whom he finally found himself most in sympathy.Moulders generally rap patterns as much as they will stand, often more than they will stand; and in providing for draught it is necessary to take these customs into account. There is no use in making provision to save rapping unless the rapping is to be omitted.

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