A yahoo answer said the only hole in mathematics is godels theom . This authr proves theom is contradictory ,

Question

A yahoo answer said the only hole in mathematics is godels theorm . THis author proves godels theorm is self contradictory and in fact proved that mathematics is inconsistent or self-contradictory and not what mathematician have said he proved ie the impossiblity proof . These demonstrations this author shows that mathematics is at a very fundamental level meaningless and self-contradictory

http://gamahucherpress.yellowgum.com/gamahucher_press_catalogue.htm

Answer 1

I looked at the site, it's a few PDF ebooks about "the philosophy of meaninglessness". Nihilistic philosophy is a niche in post modern thought and also in traditional Buddhist thought. It's nothing new.
The questions raised by the books you cite are purely academic. In practice, math is very useful and meaningful, and an understanding of math is extremely helpful to functioning in today's world.
So if you want to take these books as an excuse not to learn math, to slack off on your homework or have your math requirements waived for your HS or college degree, sorry, but you're out of luck.
Just because we can't fully describe a system in axioms does not make it meaningless. There are all sorts of things in everyday life that we can't fully describe in words and rules, but we still take as meaningful. This is only a limitation of our maps, not a limitation of the territory. A limited map still has meaning and functionality.
See also
http://www.math.hawaii.edu/~dale/godel/godel.html
http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorem
http://www.myrkul.org/recent/godel.htm

PS -- the business about a bumblebee can't fly, but it does, assumes a model based on rigid wings. Bumblebees wings aren't rigid. This is one of those things that people repeat so much that they assume to be true, like the saying that we use only 10% of our brains. That's not true either. We use all of our brains, that's why head injuries are often quite disabling.

Answer 2

Wrong answer (not unusual for yahoo answers). Godel's incompleteness theorem states that any axiomatic system is either inconsistent (you can prove a statement A and prove its opposite "not A") or incomplete (there is a proposition A which cannot be proven). It does this by demonstrating an unprovable statement, basically a mathematical version of "this statement is false".

So godel's provides an example of an unprovable statement. Actually, if I recall correctly (I think I do) "almost all" statements are unprovable.

Godel's does not show that math is meaningless and self contradictory. What it shows is that mathematicians need to be very careful to maintain consistency, which they are, and need to accept the fact that some things cannot be proven. There are still lots of things (infinitely many) that can be, so grad students won't run out of thesis topics anytime soon.

Answer 3

It was a dream for ending XIX and beginning XX century-mathematicians to get the whole world of Mathematics built as a complete formal system starting from very simple and accepted concepts (definitions, and axioms) and from there construct theorems and propositions that yields as result all the mathematical results.

Bertrand and Russell tried to become reality that dream with their "Principia Mathematica" (around the last decade of XIX century) a book that construct arithmetics rooted in their most basic notions and from there building up the all the knowing results in that area.

Unfortunately, Kurt Gödel (german mathematician) destroyed that dream declaring that no solid formal system could be constructed without an incompletness rooted in the system itself. Why? Because there would be always statements that can not be qualified as true or false, they are "undecidable" in logic terms (for example the famous paradox to declare oneself : "I am a liar").

For worse, the more solid you built a formal system the weaker it gets.

I recommend you to read the classic book:

"Gödel, Escher and Bach: an Eternal Golden Braid" de Douglas Hofstadter.

Good luck!

Answer 4

It seems silly to try to prove that mathematics is meaningless since it works when applied to engineering, chemistry, biology, economics ... and everything else.

It is a bit like the engineer saying that according to physics a bumblebee cannot fly ... it ignores the reality.

Answer 5

uhm,,ok, but IK am notg going to buy an e-book to look at the theory. The internet use to be and was made to make information easily accesible, but now Coroprate have taken over and we are not encouraged to learn. So I remain not knowing.