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We know objects by ideas Post Date: Mon, 4 Aug 2008 2:56:15 +0000 The true idea, and the only one deserving the name, is that which our mind possesses when it conceives extension in itself, without any mixture of sensation, and which is, as it were, the seed of the whole science of geometry. 115 It should be observed that the word representation as applied to purely intellectual ideas must be taken in a purely metaphorical sense, unless we eliminate from its meaning all that relates to the sensible order. We know objects by ideas, but they are not represented to us. Autor of the post: Undefined All the world, even irrational Post Date: Mon, 4 Aug 2008 3:11:30 +0000 Re presentation, properly speaking, occurs only in the imagi nation which necessarily relates to sensible things. If I demonstrate the properties of a triangle, it is clear that I must know the triangle, that I must have an idea of it ; but this idea is not the natural representation which is pre sented to me like a figure in a painting. All the world, even irrational animals have this representation, yet we cannot say that brutes have the idea of a triangle. Autor of the post: Undefined 116 The representation Post Date: Mon, 4 Aug 2008 3:29:18 +0000 This representation has no degrees of perfection, but is equally perfect in all. Any one who imagines three lines with an area enclosed, possesses the representation of a triangle with as much perfection as Archimedes ; but the same can not be said of the idea of a triangle, which is evidently susceptible of various degrees of perfection. 116 The representation of a triangle is always limited to a certain size and figure. Autor of the post: Undefined But the idea Post Date: Mon, 4 Aug 2008 3:47:25 +0000 When we imagine a triangle, it is always with such or such extension and with greater or smaller angles. The imagination representing an obtuse angled triangle sees something very different from an acute or right angled triangle. But the idea of the triangle in itself is not subject to any particular size or figure ; it ex tends to all triangular figures of every size. Autor of the post: Undefined 117 It is the same Post Date: Mon, 4 Aug 2008 4:00:41 +0000 The general idea of triangle abstracts necessarily all species of tri angles, whilst the representation of a triangle is necessarily the representation of a triangle of a determinate species. Therefore the representation and the idea are very different, even in relation to sensible objects. 117 It is the same with space. Autor of the post: Undefined There is nothing Post Date: Mon, 4 Aug 2008 4:14:31 +0000 Its representation is not its idea. The representation is always presented to us as something determinate, with a clearness like that of the air illuminated by the sun, or a blackness like the darkness of night. There is nothing of this sort in the idea, or when we reason upon extension and distances. Autor of the post: Undefined For both it is equally Post Date: Mon, 4 Aug 2008 4:30:01 +0000 The idea of space is one ; its representations are many. The idea is common to the blind man and to him who sees. For both it is equally the basis of geometry, but the repve seutation is very different in these two. Autor of the post: Undefined The imagination runs over one Post Date: Mon, 4 Aug 2008 4:44:23 +0000 The latter repre sents space as a confused reproduction of the sensations of sight ; the blind maii can only represent it as a confused repetition of the sensations of touch. The representation of space is only indefinite, and even this progressively. The imagination runs over one space after another, but it cannot at once represent a space with out limits ; it can no more do this than the sight can take in an endless object. Autor of the post: Undefined Space is not represented Post Date: Mon, 4 Aug 2008 4:54:46 +0000 The imagination is a sort of interior sight, it reaches a certain point, but there it finds a limit. It can, it is true, pass beyond this limit, and expand still farther, but only successively, and always with the condi tion of encountering a new limit. Space is not represented as infinite, but as indefinite, that is to say, that after a given limit there is always more space, but we can never advance so far as to imagine an infinite totality. Autor of the post: Undefined All this shows Post Date: Mon, 4 Aug 2008 5:05:02 +0000 It is the contrary with the idea ; we conceive instantaneously what is meant by infinite space, we dispute on its possibility or impossibility, we distinguish it perfectly from indefinite space, we ask if it has in reality limits or not, calling it in the first case finite, in the latter infinite. We see in the word indefinite the impossibility of finding limits, but at the same lime we distinguish between the existence of these limits, and finding them. All this shows that the idea is very different from the representation. 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