21 Aug 1814

Logic

Ch. Division

'. Synthesis and Analysis

correspond not

4

From /By/ certain terms, which, in the description of this process, have sometimes been employed, (viz. synthesis and analysis) it seems as if it had been taken for granted that the two operations thus denominated were each of them the exact counterpart and converse of the other: that the stages passed over in the one process and in the other would every where and on all occasions be exactly the same, consequently and the number of those stages likewise: and that whatsoever had by synthesis been put together, the putting of that asunder - of that of all that, as far as it /they both/ went/ and no more than that, was that of /in/ which analysis [...?] /the operation performed by analysis/.

Wide indeed from the truth of the case would any such conception however be found. Few have /Small has/ probably been the number of the successive operations of the kind in question, viz. abstractions by which - correspondently small the /that of/ number of the steps at which /stages on /in passing/ or through which/ the idea of the most amply extensive classical aggregate of which the mind is capable of forming to itself the /an/ idea, has in this way been formed. Of this most extensive aggregate, termed by the logicians of antiquity the genus generalissimum, being or existence or entity, is the name. Five or at the utmost six has accordingly been the number of steps successively taken by the mind in its ascent towards this most exalted pinnacle: five, or, at the utmost, six, the number of stages at which it has stopped. Of these abstractions, these distillations, these steps, these stages, the number corresponds to and is indicated by the number of the ramifications exhibited by the famous Porphyrian Tree and of these operations and their results, indication has been given, and at the same time recordation made, by the names respectively employed for the designation of the classical aggregates of different amplitudes which have been their respective products.