送交者: steven 于 2006-2-08, 23:56:15:
回答: please elaborate further, if possible. 由 insight 于 2006-2-08, 22:02:16:
In short, Godel's theroem pointed out, in a axiomatic system, which means there is a set of axioms which is considered to be true. In either induction or deduction, you always started with something you known is true, say in mathematical induction, you started with i = 0, some function F(i) to be true, which is a member in the set of axiom. Then you apply logic operations, and then reach your conclusion, so deduction and induction are really the same thing, and the operation is generally called modus ponens. What Godel's incompleteness theorem tells you, as long as you are doing this, there is something you cannot prove to be either true of false.
Don't get trapped into psudomathematics, learn more before you get really get the insight of anything.