20 Feb. 1815

Didacologia

10

Ch. Art & Science Division

'. Use

Take any object at pleasure: and at the same time take any property at pleasure, to that same object either that same property does belong, or it does not. This property belongs to that object - this property does not belong to that object. The two propositions are, with reference to each other, termed contradictory ones. To whatsoever object applied, both of them cannot be true; one or other of them is sure to be so.

{Hence may be seen the convenience of that plan of division, according to which, in one or other of the two compartments or condivident portions into which, at each step, the dividend is divided, every particular contained under the name of the dividend is sure to be found. If the dividend thus assumed be that one object by which the whole field of art and science is occupied and covered, proportioned to the number of operations which, under this plan of division, can be performed with truth, the nature of everything contained in that field is gradually developed; and in proportion as it is developed, clearly and thoroughly expressed and made known.}

This being the case, the consequence is - that in so far as the observations, in pursuance of which the properties in question have been ascribed to the object in question, are correct, truth will be the property of every proposition by which an object is referred, to any one of the heaps and correspondent compartments thus formed. At every step, be the individual or other particular object what it may, so it does but belong to the universal, all-comprehensive aggregate, which stands at the top of the system, to one or other of the heaps or compartments thus formed, it cannot but belong, and at the same time it cannot belong to both of them. Hence it is, that so long as the divisional process proceeds upon this plan, so long it is that of the whole contents of the universal, all-comprehensive aggregate, no one item is omitted; which, in other words, is as much as to say, that the plan of division is all-comprehensive and exhaustive; that the whole stock of materials contained under the appellative by which the universal aggregate is designated, is all along exhausted to furnish the matter on which the operations are successively performed.

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