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26 Sept. 1814
Logic
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Ch. Ontology
Entities classed
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Space is the negation or absence of body.
Of any determinate individual portion of space, as clear an idea is capable of being formed as of any body, or of any portion of any body; and besides, being equally determinate as that of body, the idea of space is much more simple.
To space it is difficult either to ascribe or to deny /refuse/ existence without a contradiction in terms; to consider it as nothing or as distinct from nothing.
Body /Of body/ that is of all bodies, whatsoever, - the annihilation may be conceived without difficulty. Why ? Because, in whatsoever place, - that is, within whatsoever portion of space, within whatsoever receptacle, composed of mere space, any body is, at any given time conceived to be, it may thenceforward be conceived to be removed from that place, and so successively from any and every other portion of space.
Of Space - that is, of all portions of space whatever, indeed of so much as any one portion of space, the annihilation cannot easily be conceived. Why ? Because in mere space there
is nothing to remove; nothing that can be conceived capable of being removed. In so far as matter is annihilated, there is less matter than there was before. But, suppose space to be annihilated; is there less space than there was before ?
As /accordingly/ taken in the aggregate no bounds no limits can be assigned to space, so neither can any form or any quantity. It cannot be removed; it cannot be moved; for there is nothing of it or in it to remove; there is no place to which it can be removed.
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Title: [17 Feb. 1815 Didacologia Art]Description: 17 Feb. 1815 Didacologia Art & Science Division 15 15 The attention which it applies to its subjects somatology may either apply indiscriminately to all the properties observable in them, or confine itself to any one or more of them to the exclusion of the rest; in the first case, ageledodiascopic, or, for shortness, ageledoscopic - in the other case, choristodiascopic, or, for shortness, choristoscopic, are the names by which it may respectively be distinguished. Vacuity, rest, time, figure, quantity - all these form so many distinguishable subjects of choristoscopic somatics. Of vacuity it may seem that it belongs not to the properties of body, But, be the body what it may, and be the place which, at the time in question, it occupies what it may, it may as easily be conceived to be absent from as present at, and in that place. To be either in or out of any given place is, therefore, among the properties of body; for, if there were no such being as a body, there would be no such distinction as that between place and place. It is only by abstraction that the idea of rest can be formed any more than that of body: it has for its ground the idea of place. It is the absence of motion, and of motion itself no idea can be formed but what has for its ground the idea of place. Take at any time into consideration any body, considering it with reference to the place which, at that same time, it occupies; but, from that same place conceive it removed, and into that same place suppose no other body or portion of matter introduced. In this way, and no other, is formed the idea of a vacuum or portion of unoccupied space. 21
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Title: [26 Sept. 1814 Logic 4]Description: 26 Sept. 1814 Logic 4 Ch.2. Ontology Entities classed 9 3 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. 31
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