Archives - Mathematics: Page 10
Author: amparo enriquez (Wed Dec 27, 2006 2:12 am)
Title: Mathematics
The famous mathematical logician Kurt Gödel showed, in 1930, that no matter how powerful a system of rules one might choose to adopt, provided that one accepted that the rules were incapable of being used to demonstrate the truth of some false arithmetical statement, then there would be arithmetical statements which must also be accepted as true, yet which lie beyond the scope of the rules. Thus human understanding, even when limited to the area of arithmetical statements, cannot be encapsulated in any system of rules that are accepted as reliable. The very acceptance of a set of rules is what enables one to transcend them.
Roger Penrose