Godel's Incompleteness Theory

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Godel's Incompleteness Theory

Postby Pondero » May 28th, 2015, 1:26 am

Back in 1931, an Austrian mathematician, proved that you can't prove Euclids's five axioms, which we know to be true, but accept without proof. This set the mathematical world on edge.They love to prove everything. I remember at a History of Math course I took,that Russell and someone else (Alfred North Whitehead) wrote a book called Principia Mathematica* and discovered to their horror that they couldn't prove the basic assumptions of symbolic logic to their surprise.They wrote this book before 1931, so I guess Godel didn't have anything to do with it.

Well, Godel (spelt with two dots over the 'o') certainly blew the Theory of Everything out of the water.He did prove that no matter what Russell and Whitehead did by rewriting the book, they still couldn't prove it.

*Not to be confused with the Philosophiae Naturalia Principia Mathematica book written by Isaac Newton, which I, to my great surprise, the library at St.Michaels College, University of Toronto, allowed me to borrow and take home to read (it was in Latin) so as I couldn't read it but I tried to follow the mathematics** or some of it - with great difficulty.

**Calculus or "fluxions".

Edited to correct errors.

I just came across Godels Incompleteness Theory tonight.after all these years.
Last edited by Pondero on May 28th, 2015, 10:38 am, edited 1 time in total.
Let nothing disturb you.
Let nothing make you afraid.
All things are passing.
God alone never changes.
Patience gains all things.
If you have God you will want for nothing.
God alone suffices.

— St. Teresa, The bookmark of Teresa of Ávila, [28]
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Re: Godel's Incompleteness Theory

Postby GregB » May 28th, 2015, 7:04 am

This book on the subject might be of interest:
http://www.amazon.co.uk/gp/product/0814 ... d_i=266239

I haven't read it myself (maths was never my forte) but I did try to read another book by Hofstadter some years ago, which is about the unlikely trio of Gödel, Escher* and Bach. Thought (and headache) provoking.
http://www.amazon.co.uk/Godel-Escher-Ba ... 6ZE2XZ03S3

[* A Belgian artist who drew pictorially coherent but physically impossible pictures:
http://files.harrowakker.webnode.nl/200 ... Omlaag.jpg
http://www.colegiosansaturio.com/deptom ... enes/1.gif ]
"I hate reality but it's still the best place to get a good steak."
- Woody Allen
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Re: Godel's Incompleteness Theory

Postby Pondero » May 28th, 2015, 10:53 am

The pictures are fascinating, Greg. While we are on the subject, I wonder what Godel's theorem has to say about the attempt by scientists at CERN to find "The God Particle". The mysterious particle, beyond which nothing is left to discover, once found of course.They think they have found it, but that leaves the graviton yet to be discovered.

In Leon Ledermans's book, The God Particle, he never mentions Godel at all! Of course Lederman is not a religious person, although a Jew, but he speaks respectfully about religious Jews in his book. I doubt if he has made up his mind about the existence of God.
Let nothing disturb you.
Let nothing make you afraid.
All things are passing.
God alone never changes.
Patience gains all things.
If you have God you will want for nothing.
God alone suffices.

— St. Teresa, The bookmark of Teresa of Ávila, [28]
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Pondero
 
Posts: 12807
Joined: October 25th, 2007, 11:03 am
Location: Etobicoke,Ontario, Canada


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