Post by xxxxxxxxx on Mar 22, 2023 22:22:12 GMT
The simple ‘point’ is the foundation for measurement and observation. This is evidenced by its necessitating the grounds of quantifiability under the number line and the space/time coordinates within mathematics and geometry respectively. It is further evidenced within the act of observation itself as all things are reduced to points from a distance and all things are composed of points when observed closely. Finally we observe the point intuitively in conversation in the respect that all premises are ‘starting points’ and the conclusions are ‘end points’; we reduce conversation to spatial metaphors and as such even ‘non-spatial realities’ require space, under the ‘point’, to understand them further.
Through these respects the ‘point’ has a universal nature that extends through all degrees of knowledge and as such necessitates all things, both a priori and a posteriori, as dependent upon this simple spatial axiom. Under these terms the nature of the a priori, that which occurs before the senses, and the a posteriori, that which occurs through the senses, are a false dichotomy as the point is the connector between the two categories of knowledge; space is both before the senses and after the senses as without the senses only empty space is observed, i.e. a simple point, and with the senses all forms are composed of space, i.e. connected points. From this it may be implied, epistemologically, that our categories of knowledge and knowing, i.e. the ‘a posteriori’ and the ‘a priori’, are fabrications which are relative and subject to a self-negation when analyzed. Space is the universal axiom as the simple ‘point’ is a universal axiom. But do we have to take space, paradoxically and metaphorically as the point of it all, axiomatically? Not within the grounds of philosophical inquiry. No rule prohibits this from us.
To question the point is to question the nature of space itself and with that all forms and knowledge of said forms. This questioning does not occur without contradiction, however, and as such is the grounds for further exploration of this subject. The following arguments point out the absurdities which result when the point is analyzed even further than that state when it is accepted as an unquestionable axiom:
1. The distance between two points is a line segment.
2. This distance between two points is a division of a point into two.
3. The line segment is a division.
4. The line segment as a division is surrounded by space.
5. This surrounding space is composed of infinite points as there are infinite positions around the space of a line segment.
6. The points which compose the line segment contrast the points around the line segment.
7. In introducing a line segment the point is divided; it is divided through the line segment and it is divided against the points around the line segment.
8. The point is self-divisive thus is a contradiction.
1. A point added to another point results in one point, much in the same manner a raindrop added to another raindrop results in one rain drop.
2. A point subtracted from a point results in one point, much in the same manner a raindrop subtracted from a raindrop results in one rain drop.
3. The infinite division of points is the infinite multiplication of points; this infinite division/multiplication of points results in a single point as all the points become indefinite much in the same manner a point is indefinite.
1. The fact that points, which are 0d entities, can be added/subtracted/multiplied necessitates it as quantifiably 1 given 1 is the foundation for all numbers.
2. The 0d point as quantifiable necessitates 0 as quantifiable thus a contradiction occurs.
1. The point cannot be added/subtracted/multiplied/divided as it is a 0d entity and as such is equivalent to 0.
2. The point is added/subtracted/multiplied/divided as evidenced by geometric shapes.
3. Shapes are a contradiction.
1. A line segment is composed of an infinite number of line segments thus an infinite number of points.
2. An infinite number of points is an infinite number of divisions.
3. The line segment is an act of division and yet this division allows for a shape to occur.
4. Shapes occurring through division is the shape as a contradiction as division necessitates opposition as one phenomenon stands apart from another.
1. The division of nothingness is the self-opposition, contradiction, of nothingness as being.
2. Considering nothingness cannot act, as to act makes nothingness a thing, to speak of it as self-contradicting is a contradiction in terms.
3. However the contradiction of nothingness is necessary for being to occur thus requiring a nonsensical argument.
4. The point is nothingness as it is 0 dimensional.
5. The point cannot be divided and yet it is as evidenced by a line segment.
6. The line segment, as the foundation for form, is nonsensical yet the very fact that it is sensed makes it contradictorily sensical.
In conclusion the nature of the point results in absurdity when questioned further. It reduces to space dividing space with this division being a space in itself. As such the point, and space by default, is a contradiction and this contradiction is the grounds for all of our awareness. The point, as evidenced, does not have to be taken axiomatically and this absence of its nature as an axiom results in ambiguity which cannot be ignored. This very same ambiguity connects itself to all aspects of knowledge and as such results in a grounding formlessness to the nature of things where our understanding of reality effectively rests of no-thingness.
Through these respects the ‘point’ has a universal nature that extends through all degrees of knowledge and as such necessitates all things, both a priori and a posteriori, as dependent upon this simple spatial axiom. Under these terms the nature of the a priori, that which occurs before the senses, and the a posteriori, that which occurs through the senses, are a false dichotomy as the point is the connector between the two categories of knowledge; space is both before the senses and after the senses as without the senses only empty space is observed, i.e. a simple point, and with the senses all forms are composed of space, i.e. connected points. From this it may be implied, epistemologically, that our categories of knowledge and knowing, i.e. the ‘a posteriori’ and the ‘a priori’, are fabrications which are relative and subject to a self-negation when analyzed. Space is the universal axiom as the simple ‘point’ is a universal axiom. But do we have to take space, paradoxically and metaphorically as the point of it all, axiomatically? Not within the grounds of philosophical inquiry. No rule prohibits this from us.
To question the point is to question the nature of space itself and with that all forms and knowledge of said forms. This questioning does not occur without contradiction, however, and as such is the grounds for further exploration of this subject. The following arguments point out the absurdities which result when the point is analyzed even further than that state when it is accepted as an unquestionable axiom:
1. The distance between two points is a line segment.
2. This distance between two points is a division of a point into two.
3. The line segment is a division.
4. The line segment as a division is surrounded by space.
5. This surrounding space is composed of infinite points as there are infinite positions around the space of a line segment.
6. The points which compose the line segment contrast the points around the line segment.
7. In introducing a line segment the point is divided; it is divided through the line segment and it is divided against the points around the line segment.
8. The point is self-divisive thus is a contradiction.
1. A point added to another point results in one point, much in the same manner a raindrop added to another raindrop results in one rain drop.
2. A point subtracted from a point results in one point, much in the same manner a raindrop subtracted from a raindrop results in one rain drop.
3. The infinite division of points is the infinite multiplication of points; this infinite division/multiplication of points results in a single point as all the points become indefinite much in the same manner a point is indefinite.
1. The fact that points, which are 0d entities, can be added/subtracted/multiplied necessitates it as quantifiably 1 given 1 is the foundation for all numbers.
2. The 0d point as quantifiable necessitates 0 as quantifiable thus a contradiction occurs.
1. The point cannot be added/subtracted/multiplied/divided as it is a 0d entity and as such is equivalent to 0.
2. The point is added/subtracted/multiplied/divided as evidenced by geometric shapes.
3. Shapes are a contradiction.
1. A line segment is composed of an infinite number of line segments thus an infinite number of points.
2. An infinite number of points is an infinite number of divisions.
3. The line segment is an act of division and yet this division allows for a shape to occur.
4. Shapes occurring through division is the shape as a contradiction as division necessitates opposition as one phenomenon stands apart from another.
1. The division of nothingness is the self-opposition, contradiction, of nothingness as being.
2. Considering nothingness cannot act, as to act makes nothingness a thing, to speak of it as self-contradicting is a contradiction in terms.
3. However the contradiction of nothingness is necessary for being to occur thus requiring a nonsensical argument.
4. The point is nothingness as it is 0 dimensional.
5. The point cannot be divided and yet it is as evidenced by a line segment.
6. The line segment, as the foundation for form, is nonsensical yet the very fact that it is sensed makes it contradictorily sensical.
In conclusion the nature of the point results in absurdity when questioned further. It reduces to space dividing space with this division being a space in itself. As such the point, and space by default, is a contradiction and this contradiction is the grounds for all of our awareness. The point, as evidenced, does not have to be taken axiomatically and this absence of its nature as an axiom results in ambiguity which cannot be ignored. This very same ambiguity connects itself to all aspects of knowledge and as such results in a grounding formlessness to the nature of things where our understanding of reality effectively rests of no-thingness.