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of the principal objects of this work is to vindicate the truth and the supreme utility of Logic as anciently conceived, it is also contemplated to supply the radical defect I have alluded to, and, at the same time, to incorporate with the old Logic the approved results of modern research; some of which are of great importance.

It remains to add a few words as to the method and style with which the subject of the work is treated. Logic is admittedly a demonstrative or apodictic doctrine, and should therefore be treated by the method appropriate to subjects of that nature. This consists in the accurate formulation of our premises, and in reasoning rigorously from them, as in geometry. But this method demands the use of a style altogether different from that in common use; which may be called the popular or rhetorical. For it is the peculiar characteristic of the logical style that it must be accurate or aphoristic, i. l., that it must express the exact truth without any admixture of error. For the same truth holds good in ratiocination, as in nature generally, that hybrids are unprolific; and hence the slightest admixture of error in our premises will render them altogether useless for logical inference. Our method will therefore demand the exact analysis of the terms we use and the formal statement of our propositions; which to the general reader is distasteful. For while the logical style admits, and even requires, great brevity of expression, - so that, in general, volumes of ordinary disquisition inay, by means of it, be compressed into a brief space,-yet it demands a degree of attention and independent thought that only a few highly trained or exceptionally gifted minds are willing to give, or perhaps without great exertion are capable of giving. But this is nevertheless essential to the fruitful study of Logic, as of apodictic science generally. There is no royal road to Logic any more than to Geometry

The best type of this style is found in the Mathematics, and especially in the writings of Euclid and the geometers, whose style and method I have sought to emulate,—with what success remains to be judged. I trust, however, I may, without vanity, say of the result, with Hobbes, that while there is nothing I distrust more than my elocution, nevertheless I am confident, excepting the mischances of the press, it is not obscure."

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LOS ANGELES, February 26, 1900.

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