Viveka wrote: ↑
Mon Dec 04, 2017 7:55 pm
Eodnhoj7 wrote: ↑
Sun Dec 03, 2017 2:39 am
Viveka wrote: ↑
Sat Dec 02, 2017 2:20 am
And? Geometry is founded upon these coordinates. Without Cartesian Coordinates we would not be able to plot geometry.
Cartesian Cooridinates are premised on two interesting lines at a point. Cartesian cooridinates, while not necessarily the premise for geometric shapes, exists because of the point and line as the foundation for all geometric shapes.
The fact that there is a coordinate system has full bearing on what is a line and what is a point.
The line and point form the coordinate system.
There may be a line that never intersects its cooridnates, such as plotting a line that has a irrational number in its slope.
Irrational structures, in this regard, are strictly deficiencies in structure (as perpetual movement through perpetual fractions) that do not exist in themselves but rather through approximation....in this case Cartesian Coordinates as Point and Lines.
The coordinates themselves are prerequisite to making lines and points by quantifying a measuring stick.
The Grid itself is point and lines, and in these respects is not a prerequisite to the point and line.
You can argue against the 1 dimensional point all you want, but prepare to do so ad-infinitum....and I will take it that limit and beyond if necessary, as I get the feeling this discussion is premised on your metaphysics system based upon the zero dimensional point and is more emotional than intellectual (considering the logical structure is falling apart at a quicker rate).
Nothingness cannot conquer being, because it is nothing...that is just strict logic whether you chose to accept it or not.
To say that a one-dimensional point is acceptable in parlance is wrong no matter how you conceptualize it. There is no such thing as a 1-dimensional point in mathematics. That's why you're wrong; debate all about it to infinity and beyond, but you're not going to get anywhere in your own reasoning because it's something that is irrational, literally. Even if you had two lines intersecting to make a point, the lines themselves already consist of points!
And perpetual movement towards a zero dimensional point is "rational"? Actually the one dimensional point is rational as it is pure "dimension" manifesting its own structure ad-finitum. It provides the basis for 1 as a never changing constant, and all further numbers in this regard. A one dimensional point is full "being", while a zero dimensional point is "nothing". Even from the perspective of language "nothing" exists if and only if "thing" exists as "nothing" (or negation) is strictly relativistic. But to get back on point.
What there are in mathematics are a group of axioms which continually expand over time through the use of dialectics. What is not an axiom today could be an axiom tomorrow. The fallacy of authority does not work, as all "progress" or "discovery" is usually labeled contradictory at first until further investigation as to the nature, symmetry and structure of that said observation. Contradiction is merely a deficiency in structure and nothing more. It is remedied through the application of further reasoning, or ratios, that manifests further structure until a form of symmetry exists.
A 1 dimensional point, as ethereal space, must exist for direction to be a constant. In these respects it provides the foundations for "dimensions" also as a self maintained structure.
Order, as embodied through 1, trumps nothingness through its own being.
As to "the line being composed of points" That is what I am saying, the point and line are inevitable. The line may consist of points, but the points exist if and only if their is a line. To argue that the line does not exist because it is composed of points which are zero dimensional, is to argue that the points that make the line do not exist as the line does not exist because it is make of points. It is an infinite regress, dependent on a constant revaluation of the properties of the line which inherently "actualize" it in a simultaneous respect.
The line in these respects, is continually redefined through new axioms.