26 Sept. 1814

Logic

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Ch.2. Ontology

Entities classed

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III. Quantity: Quantity has been distinguished into continuous, and 2. discrete.

Discrete quantity (it is commonly said) is number: It should rather be said is composed of numbers: viz. of numbers more than one of separate existence /entities/.

If there were but one entity in the world /existence/ - whether substance or perception, discrete quantity the modification of quantity termed.

It is only by means of discrete quantity i.e. number that continuous quantity can be measured by the mind that any precise idea of any particular quantity can be formed.

To form an idea of any continuous quantity, i.e. of a body as existing in a certain quantity, one of two courses must be taken or conceived to be taken in relation to it. It must be divided, or conceived to be divided, into parts, i.e. into a determinate number of parts, or together with other similar bodies made up into a new, and artificial, and compounded whole.

To divide a body, or conceive a body to be divided into parts, it suffices not to divide it, or conceive it divided, into its constituent bodies, into any such smaller bodies as are contained in it. Either the entire body itself, or its parts respectively, must, by the mind, be conceived to be divided into its several dimensions.

Be the body what it may, not being boundless, it cannot but have some bound or bounds; if one, it is a surface; these bounds, if there be more than one, are surfaces: these surfaces again, not being boundless, have their bounds, - these bounds are lines.

The only bodies that have each of them but one uniform surface are spheres.

Bodies are real entities. Surfaces and lines are but fictitious entities. A surface without depth, a line without thickness, was never seen by any man; no; nor can any conception be seriously formed of its existence.

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