This is part of a 9 pages long philosophy paper
No.13163926 ViewReplyOriginalReport
Quoted By: >>13163927 >>13164060
I'll post part of the text that deals with geometry. It attempts to answer the problem the author had when in a math class the teacher told him "a point measures nothing and that a straight line is composed of innumerable points", and relates it with philosophy. If you like it I can translate everything by next week.
"Any symbolic system is, therefore, implicitly multidimensional, and geometry cannot escape this, whether modern geometers admit it or not.
Now, a point, if it has no extension, has, however, dimension, contrary to what is believed, because it must be in some direction, otherwise it is nowhere, that is, it doesn't exist.
Well, in how many directions is a point? It is in all directions at the same time, because any line that is imagined, in any plane, will always have a parallel that necessarily passes through this point.
The point is thus the figure that, not possessing extension, is simultaneously in all directions and possesses, therefore, the totality of dimensions.
In this sense, the point represents the logical and ontological principle from which the figures emerge, and not just an 'element' constitutive of them; for an element, in order to contribute to the formation of the figure, should be added to or articulated with other elements of the same kind, with which we would fall into the counter-sense already pointed out, that the sum of inextensive elements would end up producing extension; whereas a formative principle necessarily contains within itself the key to all the phenomena it produces, not needing to be added to anything in order to produce them, and even belonging to an order of reality distinct and superior to that in which these phenomena take place.
Thus possessing all directions and dimensions, the point also contains the formative key to all figures. These, therefore, cannot be formed by adding points, but, on the contrary, by suppressing the directions and dimensions of the point."
"Any symbolic system is, therefore, implicitly multidimensional, and geometry cannot escape this, whether modern geometers admit it or not.
Now, a point, if it has no extension, has, however, dimension, contrary to what is believed, because it must be in some direction, otherwise it is nowhere, that is, it doesn't exist.
Well, in how many directions is a point? It is in all directions at the same time, because any line that is imagined, in any plane, will always have a parallel that necessarily passes through this point.
The point is thus the figure that, not possessing extension, is simultaneously in all directions and possesses, therefore, the totality of dimensions.
In this sense, the point represents the logical and ontological principle from which the figures emerge, and not just an 'element' constitutive of them; for an element, in order to contribute to the formation of the figure, should be added to or articulated with other elements of the same kind, with which we would fall into the counter-sense already pointed out, that the sum of inextensive elements would end up producing extension; whereas a formative principle necessarily contains within itself the key to all the phenomena it produces, not needing to be added to anything in order to produce them, and even belonging to an order of reality distinct and superior to that in which these phenomena take place.
Thus possessing all directions and dimensions, the point also contains the formative key to all figures. These, therefore, cannot be formed by adding points, but, on the contrary, by suppressing the directions and dimensions of the point."
