date

19 Aug. 1814 C Logic 1
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.

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  • 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
  • Title: [19 Aug 1814 Logic 1]
    Description: 19 Aug 1814

    Logic

    1

    C

    Ch. Division

    Sec. 4

    '. Synthesis and analysis compared

    1

    For an example of Synthesis and Analysis see [...?]-[...?], p.4[...?]

    '. Synthesis, like analysis, is distinguishable into physical and psychical. In neither [...?] is the number of degrees established in the analytic order /method/ determined by d of d in synthetic.

    Psychical say logical division supposes the prior /antecedent/ existence of psychical or say logical aggregation. {A bushel of apples - a bushel of wheat - can not be divided, before /until/ it has been collected.} Psychical division has no subject but the ideas commonly called general ideas. These general ideas are all so many aggregate /aggregate ideas/ or say abstract ideas, formed by aggregation and abstraction out of simple ones.

    Of the aggregate thus formed, the extent is determined and measured by that of the import of the term, /the name - the appellative/ employed for the expression of it.

    205
  • Title: [19 Aug. 1814 Logic 2]
    Description: 19 Aug. 1814

    Logic

    2

    Ch. Division

    '. Synthesis and Analysis

    correspond not

    8

    In this supposed case, for every species there is one individual, and no more; for every individual, one species, and no more.

    But as, within the extent of one species, an indefinite number of individuals may be, and habitually are, contained, so from any one individual, much more from a greater number of individuals, an unlimited number of species may be deduced.

    No new species, it is true, can be formed, except so far as in description it is capable of being rendered different from every species which had been described, before it had ever been described. But, in regard to any of the observable species of natural bodies, taken as they come out of the hands of nature, this is a condition, of the failure of which no reasonable probability seems to present itself. Take, for instance, the 40,000 different species of plants, that having, some years ago, been said to be the number of those species already known to be in existence. Of these, there exists not any one which has not some property, or aggregate of properties, which is not to be found in any of the others, and which constitute that difference, or say differential character, whereby it stands distinguished from every other. Of these differences, the ideas were respectively formed in the mind by the process of abstraction. They were formed from the observations made of some individual plant or plants, which, at the time of observation, were respectively considered as belonging to those same species. On this occasion, in the formation of any such species, what was done was, not to take for the character, or essence of the species, every mark whereby the individual in question, the individual, or individuals, then and there observed, was seen to differ from all individuals that had ever been observed before, but only some one or other small number of these marks. For, in all the different species of plants that have thus been formed, take any one whatsoever: answerable to the description, how ample and particular soever of that one species, will be found individuals in a multitude absolutely inexhaustible, no two of them so perfectly similar but that, upon a simultaneous comparison, differences, perceptible and describable differences, between them might be found.

    212