date

22 Aug. 1814 Logic 1
22 Aug. 1814

Logic

1

Ch. Division

'. Synthesis and Analysis

correspond not

10

'. 5. Misapplication of the Terms Synthesis and Analysis to Geometry and Algebra.

Marking /Expressing/ the difference between Geometry and Algebra is another of the purposes to which the opposite terms Synthesis and Analysis, with the methods respectively denominated from them, viz. the Synthetic method, and the Analytic method, have been employed.

But, between these two branches of science, no such difference or distinction will be found as that of which intimation is given, by that pair of correspondent and opposite appellatives.

In Geometry, quantity is never considered but with relation to figure; in Algebra it never is considered with relation to figure: of the difference between these two branches of Mathematics, this account is at once true, short, and clear, and no other account that is in equal, if in any degree at all endowed with these qualities, will, it is believed, be found.

214
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    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.

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  • Title: [22 Aug. 1814 Logic Ch. Division]
    Description: 22 Aug. 1814

    Logic

    Ch. Division

    '. Synthesis and Analysis

    correspond not

    In Geometry /Algebra/ as well as in Geometry in Geometry as well as in Algebra, that which is unknown or supposed to be unknown, is inferred from its relation to that which is known, or supposed to be known: in Algebra, unknown quantities, as expressed by letters, are made known by means of the relation they bear to known ones, as expressed by figures; in Geometry, unknown quantities, as expressed by figure, and supposed to exist as between figure and figure, or parts of the same figure, are made known by means of the relations they bear to known quantities, as expressed by figure.

    In Geometry, true it is, that objects are put together; quantities known and unknown are put together; whereupon, of such as are unknown, a description is given, and a conception conveyed by means of the relation they bear to certain known ones.

    Of Geometry this is true; nor is it less so when applied to Algebra.

    A quantity is mentioned to me, of which I wish to know the amount, it being as yet unknown to me. By the amount, in this case, is always meant the amount in numbers; for, in truth, the subject of Algebra is number - numbers and nothing else. Suppose the number in question six; - in answer to my question, What is the number ? the number six is not mentioned by that name; but I am told it is that number which is as great again as number three, or half as great exactly as number twelve. Simple as they are, either of these answers is already Algebra.

    And it is thus that, by Algebra, the known and unknown quantities being put together, a description of such as are unknown is given, and a conception conveyed by means of the relation they bear to certain known ones.

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    C

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    '. 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.

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