This page is keyboard accessible:
• Use Tab, Shift + Tab keys to traverse the main menu. To enter a sub-menu use the Right Arrow key. To leave a sub-menu use the Left Arrow or the Escape key.
• The Enter or the Space key opens the active menu item.
• To skip the menu and move to the main content, press Tab after the page loads to reveal a skip button.
• To get back to the top of the page anytime, press the Home key.
• For more information, click here: Accessibility   Close this tip.

Note: Full functionality of this web page requires JavaScript to be enabled in your browser.
 

Blog Archive

8 Apr 2016    Are we alone in the Universe?

I was recently reading a book entitled The Eerie Silence - Are we alone in the Universe? by Paul Davies, when I came to the chapter musing on what humans might include in a message to aliens. In this chapter Davies says:

 

The deepest products of the human mind are arguably the mathematical theorems that have been constructed by some of the world’s most brilliant thinkers. Gödel’s incompleteness theorem, for example, is so profound that it is possible that no theorem in the universe can trump it.

 

No. Rather than being profound, Gödel’s incompleteness proof is a demonstration of how to wrap up trite banality in so much superficial glitter that it appears profound to the simple-minded, whereas an intelligent analysis reveals it to be erroneous, as is demonstrated in various pages on this website. Similar methods are used by creationists and intelligent design fanatics to impress those who are have limited intellectual capacity or who are simply too intellectually lazy to evaluate the claims.

 

I wonder would an advanced civilization be more amused or appalled by the claim that the incompleteness ‘theorem’ might be the most important mathematical theorem that there can ever be. Would an advanced civilization even want to communicate with primitive beings that are so steeped in the promotionPicture: A galaxy of such illogical statements? Even if they did commence a communication, it would seem quite possible that human mathematicians, logicians and philosophers would actually try to argue their case against the superior intelligence, being so entrenched in their herd mentality in the correctness of incompleteness proofs.

 

Apart from anything else, there is no real world application of an incompleteness proof, so why should such a proof be adjudged as superior to all the mathematical advances that have led to the development of modern technology? It is very difficult to fathom why, even given that a person has a belief that the incompleteness proof is correct, that a person should find it profound in any way. After all, all it supposedly proves is that if a formal system could refer to its own statements, then it would not be able to prove certain self-referential statements. But it says absolutely nothing about whether the formal system could prove or not prove other statements that are not self-referential. After all, if a mathematical system could logically state the equivalent of “This statement is not provable”, what would be so profound about not being able to prove it?

 

It is noteworthy that the notion of incompleteness has been used to promote all sorts of wacky claims, such as that it demonstrates the existence of god, see Gödel’s Incompleteness: The #1 Mathematical Breakthrough of the 20th Century, and Gödel’s Incompleteness Theorem. It has also been claimed that it proves the non-existence of god, see Incompleteness and God, and that it proves the existence of spirituality, see Either God exists or one must accept mystery. Of course, the original ‘proof’ of incompleteness was written by Kurt Gödel, who, according to his wife “was religious and read the Bible in bed every Sunday morning”, and who attempted an ontological proof of god’s existence. He also thought that his incompleteness ‘proof’ helped to prove Platonism, that is, that mathematical concepts are actually real but non-physical things. Davies cites Gödel as one of the “world’s most brilliant thinkers”, but Gödel was actually a believer in intelligent design, and said:

 

I don’t think the brain came in the Darwinian manner. In fact, it is disprovable. Simple mechanism can’t yield the brain. I think the basic elements of the universe are simple. Life force is a primitive element of the universe and it obeys certain laws of action. These laws are not simple, and they are not mechanical.

 

I believe that mechanism in biology is a prejudice of our time which will be disproved. In this case, one disproof, in my opinion, will consist in a mathematical theorem to the effect that the formation within geological times of a human body by the laws of physics (or any other laws of a similar nature), starting from a random distribution of the elementary particles and the field, is as unlikely as the separation by chance of the atmosphere into its components.

(Sections 6.2.11 and 6.2.12 in the book A Logical Journey by Hao Wang MIT Press, 1996.)

 

Here Gödel is just one of the first in a long line of creationists and intelligent design fanatics who think that it is possible to produce a meaningful probability value that suggests a designer, despite our having no means of calculating such a probability (for example, if there are many universes, then we have no way of knowing how many universes are like ours).

 

People say that incompleteness proofs prove that there are limitations to what formal systems can do. But that isn’t profound, since we knew that anyway. We know that there are physical limitations to any system of expressing mathematical notions; it is not possible to prove all possible mathematical proofs by less than a given number of symbols. That means that there is a practical limit to the length of mathematical proofs - so that regardless of any incompleteness proof, there will be mathematical statements that we cannot prove to be correct or incorrect. But that is hardly a profound realization.

 

 

Diverse opinions and criticisms are welcome, but messages that are frivolous, irrelevant or devoid of logical basis will be blocked. Difficulties in understanding the site content are usually best addressed by contacting me by e-mail. Note: you will be asked to provide an e-mail address - any address will do, it does not require verification. Your e-mail will only be used to notify you of replies to your comments - it will never be used for any other purpose and will not be displayed. If you cannot see any comments below, see Why isn’t the comment box loading?.

 

 

Please wait for comments to load …  

 

The Lighter Side

 

NEWS

Lebesgue Measure

There is now a new page on Lebesgue measure theory and how it is contradictory.

 

 

Illogical Assumptions

There is now a new page Halbach and Zhang’s Yablo without Gödel which demonstrates the illogical assumptions used by Halbach and Zhang.

 

 

Peter Smith’s ‘Proof’

It has come to my notice that, when asked about the demonstration of the flaw in his proof (see A Fundamental Flaw in an Incompleteness Proof by Peter Smith PDF), Smith refuses to engage in any logical discussion, and instead attempts to deflect attention away from any such discussion. If any other reader has tried to engage with Smith regarding my demonstration of the flaw, I would be interested to know what the outcome was.

 

 

Easy Footnotes

I found that making, adding or deleting footnotes in the traditional manner proved to be a major pain. So I developed a different system for footnotes which makes inserting or changing footnotes a doddle. You can check it out at Easy Footnotes for Web Pages (Accessibility friendly).

 

 

O’Connor’s “computer checked” proof

I have now added a new section to my paper on Russell O’Connor’s claim of a computer verified incompleteness proof. This shows that the flaw in the proof arises from a reliance on definitions that include unacceptable assumptions - assumptions that are not actually checked by the computer code. See also the new page Representability.

 

 

New page on Chaitin’s Constant

There is now a new page on Chaitin’s Constant (Chaitin’s Omega), which demonstrates that Chaitin has failed to prove that it is actually algorithmically irreducible.

 

Previous Blog Posts  

 

Links  

 

For convenience, there are now two pages on this site with links to various material relating to Gödel and the Incompleteness Theorem

 

– a page with general links:

Gödel Links

 

– and a page relating specifically to the Gödel mind-machine debate:

Gödel, Minds, and Machines

 

Printer Friendly

 

All pages on this website are printer friendly, and will print the main content in a convenient format. Note that the margins are set by your browser print settings.


Note: for some browsers JavaScript must be enabled for this to operate correctly.

 

Comments

 

Comments on this site are welcome, please see the comment section.

 

Please note that this web site, like any other is a collection of various statements. Not all of this web site is intended to be factual. Some of it is personal opinion or interpretation.

 

If you prefer to ask me directly about the material on this site, please send me an e-mail with your query, and I will attempt to reply promptly.

 

Feedback about site design would also be appreciated so that I can improve the site.

 


Copyright © James R Meyer 2012 - 2017  
www.jamesrmeyer.com