Saturday, February 16, 2013

New Online Journal Publishes Tripe about Gödel

A new online journal, Sententias, has published its first issue. It claims to be devoted to "philosophy, theology, and science", but its real goal can be deduced by clicking on the tab labeled "ministry tools". Why, all academic journals come with "ministry tools", don't they?

The first issue is not promising at all. One article is entitled "The argument from reason and incompleteness theorems" by Ryan Thomas. The author writes about Gödel's theorems, but it's clear he doesn't understand them. Too bad Thomas did not read Torkel Franzén's book, Gödel's Theorem: An Incomplete Guide to Its Use and Abuse; he might have saved himself some embarrassment.

Thomas thinks that Gödel proved that "within a consistent and complete set of axioms there will be at least one statement that is improvable within the system" and "a consistent and complete set of axioms cannot demonstrate its own consistency". Leaving aside the strange use of "improvable" instead of "unprovable", and leaving aside that one does not usually talk about being "within" a set of axioms, Thomas misses the point. The important thing is not that a logical theory has statements that are unprovable -- after all, we'd be unhappy if false statements had proofs in our theory. The interesting facet is the existence of true statements that have no proofs in the theory. Furthermore, Thomas doesn't seem to know that Gödel's theorem does not apply to all axiom systems, but only ones that are sufficiently powerful. There do indeed exist logical theories that can prove their own consistency.

Thomas thinks that Gödel's theorem has some profound consequences for understanding the human brain -- but this is a common misconception. Gödel's theorem is about logical deductions from axioms; but this is only one small and relatively unimportant facet of human reasoning. Most of our reasoning - even down to the level of assigning meanings to words and connecting those words to the physical world - seems probabilistic in nature. We use probabilistic reasoning all the time without being excessively worried about proving its "completeness" or "consistency"; why should logical deduction be any different?

Judging from Thomas's contribution, this journal has an inauspicious debut.


Anonymous said...

If a system is consistent, then there are some statements which can't be proved. (This can be a definition of consistency.)

If a system is complete, then all true statements can be proved. (This can be a definition of completeness.)

So, if a system is consistent and complete ...


Anonymous said...

It's almost enough to make one wish that Goedel had used somewhat more obfuscatory language-- rather than Con(PA), talk about Hilbert(PA), and rather than "PA does not prove Con(PA)", something like "PA is not a fixed point under the Hilbert-extension map". Then all these alchemists would stop trying to hijack it to prove that the human brain is supernatural, quantum, or whatever is the flavor du jour for that kind of thing.

Reginald Selkirk said...

Maybe they could improve their credibility by publishing some Bigfoot genomics papers.

Anonymous said...

When I saw an announcement of Sententias, I took it to be a religious journal which covered some other topics in the hope of gaining an aura of respectability.

Following your post, I downloaded the first issue. And, yes, it turns out that it is a religious journal trying to look respectable.

Gödel's theorem does seem to be widely misunderstood.

Anonymous said...

I will quote the wisdom and sagacity of Monsieur Chretien,
"A proof is a proof. What kind of a proof? It's a proof. A proof is a proof. And when you have a good proof, it's because it's proven."

Jean Chretien


Takis Konstantopoulos said...

Is this a kind of `creationistic' journal?

I like the cover. Very artsy.

But then, when I looked inside, and saw that
"Papers should be in a Word document, Turabian
I realized that this is not serious... Word? Why word? Bad taste...

Anonymous said...

This journal also has the least coherent copyright statement I've ever seen:

"The author[s] in this journal maintain all copyright over their material and reserve the right to cross reference their material with other sources or publications should the choose to do so. maintains copyright over the journal and the contents, in partnership with the author[s] sovereign copyright of their own material, and should be cited appropriately."

Anonymous said...

Mr. Shallit,

Thanks for your interest in my article. It's always good to hear some feeback--both positive and negative--on one's work.

To begin with, the language that I use in my paper is reflective of the language used by the authors of my sources, all of which come from academic journals of good repute. T be honest, I find it somewhat unbecoming of a professional philosopher to employ what is widely recognized as a rather cheap, underhanded tactic--that is, criticizing the grammar rather than the content of an argument. And of course, in this case your criticism was unfounded.

As for my understanding of Godel's theorem, it is admittedly confined to what I gleaned from my sources. Please keep in mind that the paper was not meant to explicate Godel's theorems, but rather to show that Lewis' argument follows from its broadest philosophical implications.

I also fail to see how probabilistic reasoning factors into this. We write computer programs on the basis of axiom sets, yet these programs can surely produce probabilistic outcomes. If the future will probably resemble the past, then we are warranted in saying that someone who doesn't believe that the sun will rise tomorrow is being unreasonable; he or she is in violation of the aforementioned rule. It seems irrelevant to me whether or not the claim that the sun will rise tomorrow is only verifiable in terms of inductive methodology. So again, if the human mind is best thought of as a formal system (like a computer), then how do you maintain that Godel's theorem says nothing regarding it whatsoever?

Jeffrey Shallit said...

Actually, I didn't criticize your work on the basis of grammar; I simply pointed out that I found it a strange use of terminology. Then again, every discipline has its own private vocabulary, so it doesn't surprise me that philosophers might use terms in a way that mathematicians and computer scientists don't.

I really feel like I am unable to satisfactorily remedy your confusions without further work on your part. So I can only suggest again that you read Franzen's book. The popular and philosophical literature is loaded with misunderstandings and bogus interpretations of Goedel's theorem, starting with the work of John Lucas and continuing with the work of Penrose (and your own), and Franzen has done a better job than I can in a blog post.

Takis Konstantopoulos said...

Jeff, you say
"...bogus interpretations of Goedel's theorem ... the work of Penrose"

Do you mean Roger Penrose? If so, can you please briefly explain--if possible--what you mean and give a reference?


Jeffrey Shallit said...

Yes - in both of his books, Emperor's New Mind and Shadows of the Mind Penrose uses a Lucas-style argument to say that Goedel's theorems imply that brains are not computers. Of course, this is bunk. Feferman's article discusses some of the problems, and other articles are easily findable using a google search.

Anonymous said...

Mr. Shallit,

Ok, so I thought it odd that you criticized me for using a word that I never used in my paper (improvable) so I looked at the actual journal and sure enough, every instance of "unprovable" was replaced with "improvable". I have the original e-mail that I used to submit my paper, and the paper therein uses "unprovable" (just in case you don't believe me, I can send you the e-mail if you wish). So I'm guessing that Word may have auto-corrected all the instances of "unprovable" to read "improvable" when Max downloaded the paper since the former is not recognized as a real word...or something like that. Thanks for pointing this out, and my apologies for not catching it!

Takis Konstantopoulos said...

Thank you very much. Very interesting that Penrose made this point. But then again, it's not surprising: several people who have achieved a certain status due to work in one area tend to convince themselves that they are experts in everything. Oliver Penrose (Roger's older brother) was my colleague in Edinburgh. He was a very down-to-earth and rather humble person. His area was (hope still is, because, allegedly, he's ill) statistical physics.

Jeffrey Shallit said...

So I'm guessing that Word may have auto-corrected all the instances of "unprovable" to read "improvable" when Max downloaded the paper

Maybe you should stick to journals of better quality.