21 Feb. 1815

Didacologia

11

Ch. Art & Science Division

'. Use

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.

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