I. Motion, motions. In the physical world, in the order of approach to real existence, nest to matter comes motion. But motion itself is spoken of as if it were matter ; and in truth, because, in no other way—such is the nature of language, and such is the nature of things—in no other way cold it have been spoken of.
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Of names of motions (i.e. of names of species, or modifications of motion) vast, not to say infinite is the number and variety.
Genus generalissimum is a term employed by the logicians of old, to indicate the name of any one of those aggregates which is not contained in any other aggregate that hath as yet received a name.
The idea of motion necessarily supposes that of a moving body—a body which is in motion, or in which the motion is ; necessarily supposes—i.e. without the one idea, at any rate, without the one image, the other cannot be entertained.
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When a motion of any kind is considered as having place, it is considered either with reference to some person who is regarded as the author of it, or without such reference. In the latter of these cases, motion, and nothing else, is the word employed : in the other case, action or operation : and in respect of it, the author is termed agent or operator.
II. Quantity. Next to motion and motions, come quantity and quantities.
Quantity is applicable in the first place to matter, in he next place to motion.
Of and in are the prepositions in the company of which it is employed.
A quantity of ink is in the ink-glass which stands before me. Here ink, the real substance, is one substance ; quantity, the fictitious substance, is another which is proceeding, or has proceeded, from ink, the real one.
The ink which is in the ink-glass, exists there in a certain quantity. Here quantity is a fictitious substance—(etc).
In the word quantity, may be seen the name of another genus generalissimum ; another aggregate than which there is no other ore capacious in the same nest of aggregates.
When quantity is considered, it may be considered either with or without regard to the relation between part and whole ; and if considered, in one or other of these ways it cannot but be considered ; the division is, therefore, an exhaustive one.
When quantity is considered, or at least, attempted to be considered, without regard to the relation between part and whole, it is considered with reference to figure. But if, without regard to the relation between part and whole, the idea of figure be indeed capable of being entertained, it is indeterminate and confused.
Quantity, according to the logicians of old, is either continuous or discrete. By continuous quantity, they mean quantity considered with regard to figure, and without regard to the relation between part and whole. By discrete quantity, they mean quantity considered with regard to the relation between part and whole, and without regard to figure.
If the three branches of mathematical discipline be separately considered, continuous quantity is the subject of geometry ; discrete quantity, the subject of arithmetic and algebra.
But is is only by arithmetic that either in relation to any proposition appertaining to geometry, or in relation to any proposition in algebra, any clear conception can be obtained. Divide a circle into any number of parts—for instance, those called degrees ; clear and distinct ideas are obtainable respecting the whole, and those or any other parts into which it is capable of being divided, or conceived to be divided. Refuse all such division ; the best idea you can obtain of a circle will have neither determinate form nor use.
III. Quality Quality is applicable to matter, to motion, and to quantity.
(Etc.)
Vol. VIII, pp. 262-4.
BENTHAM'S THEORY OF FICTIONS by Charles Kay Ogden,
London, New York : Kegan Paul etc., Harcourt etc., pp. xxxvii-xxxixi.