date

6 Aug. [1814] + Logic 1
6 Aug. [1814] +

Logic

1

Ch. │ │ Methodization

'. │ │ Subalternation

1

C.10 Sec.5

Relation between Genus & Species.

From methodization on the principle of co-acervation follows the sort of relation that has place between genus and species: the relation by means of which aggregates of different dimensions are, with reference to one another, lodged in the order called subalternate, or in the order of subalternation - or intro-susception.[?]

It is from this order - that is from the practice of ranging ideas in this order by means of correspondent denomination - that the logical operations called Logical Division and Logical Definition took their rise.

The order in which by the Aristotelians the component elements of a system of subalternation are exhibited is the reverse of the historical order in which they made their appearance. By these logicians an immense aggregate is held up to view, the most extensive of which they were capable of conveying or framing a conception: that aggregate is represented as divided or divisible into other aggregates, these again, each of them, into others, and so on till at last comes the last link in this sort of chain - a link consisting of an aggregate which, not having within it any other aggregates, is composed wholly of individuals; which individuals must if those spiritual substances are excepted which on the occasion are commonly introduced will of course, consist of portions of matter, being natural bodies or parts or portions of such bodies.

This order according to which (the principle of methodization being in this respect the principle of priority and posteriority) the object of largest dimension is that which presents itself in the first instance, is called analytic order or the order of analysis: analysis from a Greek word which signifies to melt or break down into a number of parts an object considered in the character of a whole.

291
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    Aggregates - any two aggregates - which are completely included either of them within the other stand with reference to each other in the relation of logical subalternation, and, with reference to each other, may be said to be commensurable. Divide the larger of the two, you may sooner or later divide it into parts, one of which will be the smaller aggregate.

    Aggregates, no one of which is in any part included within the other, may, in like manner, be said to be incommensurable.

    Any number of aggregates which are thus commensurable may be considered as belonging to and may be said to constitute one scale:- and to belong to one and the same scale. And thus we have scales of aggregates, and scales of logical subalternation.

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