JB_101_304.xml

Title: [19 Aug. 1814 C Logic 1]

Description: 19 Aug. 1814 C

Logic

1

Ch. Division

'. Synthesis and Analysis

correspond not

7

An inference that presents itself as an obvious one, is - that in the instance of every such aggregate the number of integral parts contained in a logical aggregate being a limited, in a word, a given, a determinate, or, at any rate, a determinable number

{Such accordingly} it would be, were it not for the powers - the unlimited powers, of decomposition and recomposition possessed by the human mind, - of these powers, one effect is to exclude as fruitless every possible attempt at circumscribing within any limited extent the number of such parts into which a logical whole is capable of being divided.

In the case of physical aggregate, it may be done; but not so in the case of logical ones. Take a bushel of apples: the number of integrant parts of that aggregate, each apple constituting one of those integrant parts, will be the number of apples that were put into the bushel, neither more nor less. Some time /years/ ago, the aggregate number of all the species of plants then known was estimated at 40,000. Suppose a garden, and in it a specimen of every one of these 40,000 species; 40,000, neither more nor less, is, in this case, the exact number of integrant parts into which the aggregate here in question is capable of being divided. But, upon this supposition, 40,000 is not equal to the number of integrant parts call species, into which the logical aggregate, designated by the names of plant and vegetable, is capable of being divided.

211

JB_101_293.xml

Title: [19 Aug. 1814 Logic Ch. Division]

Description: 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.

200

JB_101_384.xml

Title: [20 Oct. 1814 Logic 9]

Description: 20 Oct. 1814

Logic

9

Methodization

Ch.

Saunderson p.166

15

Examine Condillac's Logic, by whom denomination[?] is called analysis: and the more pointedly[?] the more extreme the term employed: i.e. the further synthesis is pushed. Dissolving a genus into its species this indeed is analysis.

Unfortunate indeed have been, from the earliest times known to us, these two magnificent species of method, the analytic and the synthetic: a decompounding method which decompounds, and a compounding method which, instead of compounding, decompounds likewise.

Frequent indeed is it to see these two terms especially the word analytic, and its conjugates analysis and analyse, brought to view: never it is believed from the supposed distinction from the supposed contrast has any light been diffused. To the word analysis when standing by itself its proper meaning seems not unfrequently to be annext: but where, as significative of the opposite meaning, the word synthesis is introduced, such is the effect, between the one and the other, both the meaning of the one and of the other are wrapped in clouds.

In Algebra, quantity is considered without regard to figure: in Geometry, not but with regard to figure. The Algebraical is termed the analytic method: the geometrical, the synthetic. But in either of them, what is there either of analysis or of synthesis - of decomposition or of composition - more than in the other.

In both instances, the ideas belonging to them are abstract - general: extensive, in the extreme: in the instance of algebra still more so than in the other, the idea of figure being laid out of the case, and nothing left but that of quantity. But still, in either, what is there of analysis more than of synthesis. The parts of a geometrical proposition are put together, and so are those of an algebraical investigation, and here we have Synthesis. The parts of which they are respectively composed may be considered one after another in the one case and so may they in the other: and here we have analysis.