Foundation of Mathematics and Geometry:
How many points are there on any line?
How many points are there on an infinitely long line?
How many points are there on an infinitesmally short line?
How many lines can there be in a defined area?
How many lines can there be in an infinitely large area?
How many lines can there be in an infinitesmally small area?
How many points are there in a defined volume?
How many points are there in an infinitely large volume?
How many points are there in an infinitesmally small volume?
How to define the simplest and most basic space unit, if any?
If there is an answer to the above, does it mean space is "constructable" and vice versa, "destructable"? How?
If there is really an answer to the above, then how do we perceive Kant's a priori "space"?
When we talk about a point, we know nothing about it except a defined "negation" being "no length".
When we talk about a line, we invent another 'negation" being "no area".
When we talk about an area (surface), we again come up with another "negation" being "no volume".
When we talk about a volume, what "negation" should we expect, assuming we may follow similar inductive process from the above by extension of the same logical thinking, or shouldn't we? Yes or no, and then why?
How will you deal with a person who only repeats: "Oh, no big deal... no big deal!" ??
There are infinitely many points on any line other than one formed by only one single point.
回覆刪除There are infinitely many points on an infinitely long line.
To my best understanding, the shortest line = a line constituted by one point. Provided this is true, a one-point line is already an infinitely short line. Although the number of point, i.e. 1, is finite, the size of the point can be infinitely small, thus the length of a one-point line can be infinitely short.
There can be infinitely many lines in a defined area.
There can be infinitely many lines in an infinitely large area.
To my best understanding, the smallest area = an area constituted by a one one-point line. Provided this is true, the area occupied by a one-point line is already an infinitely small area. Although the number of point as well as line, i.e. 1, is finite, the size of the area can be infinitely small.
There are infinitely many points in a defined volume.
There are infinitely many points in an infinitely large volume.
There is one point, whose size is infinitely small, in an infinitely small volume.
The simplest and most basic space unit may be defined as one which is simpler and more basic than any other finite space units.
I am not too sure what "constructable" and "destructable" are meant by Doggiedog. In my own terms, I would suggest rather that space is "approachable".
Even if there is really an answer to the above, then how don’t we perceive Kant's a priori "space"? Grateful for more elaboration, please.
May I suggest that we visit another blog with the link:
回覆刪除http://a-well-a-frog.blogspot.hk/
There the original author has some inspiring ideas in more details for our reference. I do not assume the original author who has asked so many questions in such format and then provided his own answers must be correct in approach and in content. But who can decide what is correct in philosophy?
You can also google search for:
"existentiology"
for the same blog as mentioned.