date

20 Feb. 1815 Didacologia 7
20 Feb. 1815

Didacologia

7

Ch. Art & Science

'. Use

Thus in the case above /instance already/ mentioned. On the occasion of the first divisional operation, the dividend taken in hand was the aggregate composed of all bodies whatsoever. By the first operation performed on it as above, it was divided into two condivident portions, to one of which all bodies in which the property of life is to be found were referred, to the other all bodies in which that property is not to be found.

Take then any individual body for example. It being referred to the aggregate, distinguished by the adjunct animated, if that adjunct be with truth and propriety applied to it, what we learn thereby is, that it is possessed of all those properties the aggregate of which is designated by the term of life.

Proceed now and perform an ulterior, viz. the next ulterior divisional operation. Taking for the dividend that one of the two condivident portions for the designation of which, on the occasion of the first divisional operation, the word animated was employed. For the principle or source of division, take, on this occasion, the property designated by the word sensation; on this, as on the former occasion, dividing the aggregate into two portions or heaps, throw into the first heap all such individuals in which this ulterior property is to be found, leaving for the second heap all those in which it is not to be found.

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  • Title: [20 Feb. 1815 Didacologia 10]
    Description: 20 Feb. 1815

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    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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  • Title: [21 Feb. 1815 Didacologia 11]
    Description: 21 Feb. 1815

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    Instead of bifurcate, two-pronged, suppose the plan of division, for example, trifurcate, three-pronged. So long as it remains in this state, the test of all-comprehensiveness, as above, not being applied to it, so long it is, that whether it be all-comprehensive, whether the whole stock of the matters contained in the dividend be, or be not, lodged in these three condivident portions, and in that way the dividend compartments drained and exhausted of its matter, remains unindicated. If the conditions necessary, as above, to the rendering the division all along exhaustive, and in truth, exhaustive it will be; but in this case, though by the supposition it be exhaustive, yet this is more than it will be shown to be, and, in so far as seeing depends upon showing, seen to be.

    Minerals, vegetables, animals. Here of the all-comprehensive aggregate, designated by the word bodies, we have three condivident portions, which are the result of a division of the three-pronged kind - minerals, vegetables, and animals, subjects of so many kingdoms, formed by some logician when in a poetic mood for the containing of them. Now, so it does happen, that by these several appellatives taken together, all individual bodies whatsoever are designated, and thereby, in the allotment thus made of subjects to and for the three kingdoms, the population of the whole empire, out of which portions were taken to people the dominions of these same three kingdoms, was and is exhausted. Of this exhaustion, the proof may be afforded, and has been afforded, by the application of the test of exhaustiveness, as above described and exemplified. But this is more than either is announced by the name thus given to them, or would be announced in and by any tabular view, in which, without any intimation given of the two dichotomous divisional operations, of which these three compartments are the results, they were exhibited in the character of so many portions of the all-comprehensive aggregate, into which, by one and the same operation, that aggregate had been divided.

    53
  • Title: [20 Feb. 1815 Didacologia 8]
    Description: 20 Feb. 1815

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    In this way to the information which concerning the individual or species in question is conveyed, by referring it to the several appellatives, body and animated body, may be added this further information, conveyed by the referring it to the ulterior additional appellative, sensitive animated body, or to omit the intermediate adjunct as unnecessary (since if the divisional process have been rightly carried on i.e. upon the exhaustive plan as here described, then if the object in question be sensitive it cannot but be animated) to the shorter appellative sensitive body.

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