if the brain had a mind would it be wise! -
03-03-2006, 01:56 PM
I have had a brief look at the site,"the law of excluded middle"looks like fun!
and the "incoherency argument" that attempts to show that two or more
propostitions,must be correct!
In fact if you reduce anything down far enough,you will find that it is not there?
kind regards michael.
Humilty,coupled with boldness,surprises truth to
reveal herself?
Reductio at absurdum fascinated Euclid, it is said (I've read that this is taken from diaries of some important people of the time) that it produced in him a quasi-orgasmic sensation. I believe it is going the hard way, in fact, it is used by those who instead of construct, they de-construct, either in science, philosophy or mathematics. Fermat's last theorem was proven by being proven that the taniyama conjecture was false if it was assumed to be true, that is, by reductio ad absurdum.
Isn`t if fascinating that we, mathematicians, try to prove something by contradictin ourselfs? And they said math was the science of certainty.
I gues it depends, as well, of the area of math and the school of tought. I had a teacher from France that used reductio ad absurdum all the time. Sometimes he tried to prove the theorems straight forward but always arrived to the same contradiction, proving what he wanted. It is used more for theorems of existence.
I kind of like it because is like trying to full yourself, to prove that you are wrong so finally say you are right.
In other words, there is no proof in the absurd if there is truth involved. It has always puzzled me that there are and have been great thinkers who have yet never realized truth no matter what the degree of their intelligence. Those who scoff at this idea are those who place themselves above the truth and think mathematics to be merely a passtime, that their intent was never to prove any truths but only to impress thermselves. I think that mathematics was not intended for them.
if the brain had a mind would it be wise! -
03-03-2006, 01:56 PM
"There is nothing permanent except change" 
Linear Mode
