19 Aug. 1814

Logic

Ch. Division ?

Dichotomous why

6

19 Jan 1816. Examined these 2 pages with a view to Chrestom v. Nomenclature. Supposed not necessary to be employed.

Ch. ' Of Logical Division [...?]

In the case of a physical aggregate of the physical kind, it has /may have/ been seen, the greatest number of integral parts into which it is capable of being divided is always a determinate number: in a bushel of apples containing 400 apples, 400 is that number; in a bushel of wheat containing 400,000 grains of wheat, 400,000 is that number in a garden-full of plants 40,000 in number each of those of a different species, 40,000 is that number.

These 40,000 plants each of them of a species distinguishable from every other species suppose it required so to divide into subordinate and lesser aggregates the universal or all comprehensive aggregate designated by the /of which by the supposition the word plant is the/ name of plant - to divide it in such sort that by a series of successive divisions by /from/ the descriptions given of the products of these several divisions, {it} should be made to appear in what way /points/ each agreed /coincided/ with and in what points it disagreed with the description given of every other ? + In this case, /The following is/ the only mode of proceeding by which the object can be accomplished is the following. Divide the whole aggregate into two equal parts or say divisions: divide each of these divisions into others which call divisions of the 2d order, calling the two first mentioned divisions being second divisions of the 1st order: each of these divisions dividing always by two divide into divisions of the 3rd order: the total number of divisions eight; and go on dividing always by two until the whole number of the component aggregates thus formed comes to be 40,000,+ the assumed number of different species of plants. This mode of division is termed from the Greek dichotomous; from the Latin, bifurcate, two-forked.

+that instead some power of 2.

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