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Before com mencing these investigations Post Date: Sun, 3 Aug 2008 12:20:11 +0000 The reader may see by this what sense I attach to the word demonstration, when in the sequel he sees it often em ployed in treating of the deduction of certain consequences which are exceedingly strange, although, in my opinion, deserving a careful attention. I say this not only to ex plain what is passing in my own mind, but also to warn the reader against too great confidence on these points, what ever may be the opinion which he adopts. Before com mencing these investigations on space, I remarked that the arguments on both sides seemed equally conclusive; which shows that the human reason has reached its bounds, and makes us suspect that this investigation is beyond the sphere to which the mind is restricted by a primary condi tion of its nature. Autor of the post: Undefined I shall now proceed Post Date: Sun, 3 Aug 2008 12:32:16 +0000 However this may be, let us continue to conjecture ; and although we cannot pass beyond certain limits, let us exer cise the understanding by examining them in their full ex tent. Thus, if we were placed on a very elevated ground with deep precipices on all sides, we should take pleasure in walking around the circumference, and gazing upon the immense depth under our feet. I shall now proceed to deduce other results, and to solve as far as possible the difficulties which arise, making some applications, the immense importance of which produces uncertainty and causes fear. Autor of the post: Undefined This difficulty, which seems so Post Date: Sun, 3 Aug 2008 12:43:59 +0000 84 IF space is the extension of bodies, it follows that ex tension has no recipient, that is to say, no place in which it can be situated. This seems to be in direct contradiction to our most common ideas ; for when we conceive any thing to be extended, we conceive the necessity of a place equal to it in which it can be contained and situated. This difficulty, which seems so serious at first, immedi ately vanishes if we deny that every extended thing needs a place in which it may be situated. Autor of the post: Undefined This is evi dently impossible Post Date: Sun, 3 Aug 2008 12:58:04 +0000 What is this place ? It is an extension in which the thing may be contained. Does this extension also require another extension in" which it may be placed, or does it not ? If it does, then the same question may be asked of this new place in which the other place is contained, and so on ad infinitum. This is evi dently impossible, and therefore we must admit that it is false that all extension requires another extension in which it may be placed. Autor of the post: Undefined Therefore the necessity Post Date: Sun, 3 Aug 2008 13:14:18 +0000 Just as the extension of space does not require another extension, so the extension of bodies does not require space. There is no disparity between the two cases. Therefore the necessity of a place for every exten sion is merely imaginary, and is opposed to reason. Autor of the post: Undefined This is the explanation Post Date: Sun, 3 Aug 2008 13:27:44 +0000 Ex tension, therefore, may exist in itself, and there is no reason why the extension of bodies may not also exist in this manner. 85 What in this case would be the meaning of chang ing place ? It would simply mean that bodies change their respective position. This is the explanation of motion. Autor of the post: Undefined The change which a new Post Date: Sun, 3 Aug 2008 13:44:21 +0000 Suppose three bodies, A, B, and C, to be situated in space. Their respective distances are the bodies which are interposed between them. The change which a new posi tion causes, is motion. Autor of the post: Undefined This seems at first absurd Post Date: Sun, 3 Aug 2008 14:02:25 +0000 86 Therefore, if there were only one body there could be no motion. For motion is necessarily the passing over a distance, and, there is no distance when there is only one body. This seems at first absurd, because it is opposed to our way of thinking and imagining ; but if we carefully ex amine this way of thinking and imagining, we shall see that the phenomena of our mind are in accordance with this theory. Autor of the post: Undefined We know that we move Post Date: Sun, 3 Aug 2008 14:13:55 +0000 Motion has no meaning for us, we do not feel or perceive it, when we cannot refer it to the position of different bodies among themselves. If we sail down a river, shut up in the cabin of the vessel which bears us on, we really move, though we have no perception of this motion. We know that we move when watching the objects on the shore, we see that they are continually changing. Autor of the post: Undefined When the vessel that carries Post Date: Sun, 3 Aug 2008 14:29:06 +0000 Even then, the motion seems to be in the objects around us, not in our selves, and the phenomena would be absolutely the same with respect to us, if, instead of the objects being at rest, and the vessel in motion, the vessel should be at rest and the objects in motion, supposing the motion of the objects to be properly combined. Therefore, take away the agitation, which is all that in forms us of our own motion, and we are unable to distin guish whether the motion is in us or in the objects ; and we are naturally more inclined to refer the motion to them than to ourselves. When the vessel that carries us leaves the port, we know very well that it is not the port which moves, and yet the illusion is complete, the port seems to retire from us. 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