The purpose of this blog is to communicate aspects of life such as philosophy, spiritual, education, psychology, mathematics and science. This blog does not mean political, business oriented, pornography, gender and racial issues. This blog is open and accessible for all peoples. Google Translator may useful to translate Indonesian into English or vise versa. (Marsigit, Yogyakarta Indonesia)
Nov 26, 2012
THE FIRST CRISIS IN THE FOUNDATION OF MATHEMATICS_Documented by Marsigit
THE CRISIS IN THE FOUNDATION OF
MATHEMATICS [Crisis #1] Downfall of the Pythagoreans
1.Commensurability is false (found irrational numbers)
2.Infinite divisibility and discreteness seem
Zeno's paradoxes of motion (4 main
paradoxes) attack philosophical theories of motion which parallel a Pythagorean
view of reality.
The paradox of the arrow—it is
impossible for an arrow to move at any instant of time, the arrow travels over
no space, thus it is stationary if an interval of time is a continuum of
instants, the arrow doesn't move during any of the instants, thus it doesn't
move during the entire interval either.
Thus, the Pythagorean world view was