I’m definetly buying the book. Berlinski is one of my favorite authors — Incidently his contribution to Uncommon Descent as the last chapter of the book- his paper titled “The Deniable Darwin” was my favorite piece in the book. I especially liked his question and answer responces at the end of the paper to all of the usual God hating suspects – such as Dawkins, Dennet and Scott.

and as for anyone who doesnt know about this treasure chest of wisdome I find it appropriate to post for anyone wondering what the book will read like-

http://www.discovery.org/scrip.....Posts=true

enjoy everyone.

So the real question is “what does this say about logical reasoning and its back bone intution?

Maybe our ability to create sets (which almost all mathematics and all of logic is built upon) – is a form of incompleteness? That is what I take his proof to mean for the larger philosophical question and its exponents.

We cant group everything together and make useful proposiitons out of such a concept. As soon as we begin ot group we begin to break reality up- so that we can draw lines and so it has meaning. The concept of all things being “1 is equal to 1″ is a virtually useless thought by itsef. So unless we are speaking of infinity- and all things- there will remain logical and arithmatical incompleteness. and that seems very logical to me.

“The way I see, there is only one such system and that is reality. If it exists, it is complete and consistent. Otherwise it could not exist.”

You make no sense in your statement above. Reality is not a formal system that is beyond reproach or ironies or paradoxes. If it was you would have to deduce its rules and structure of course and prove that opinion. But those rules and structures have to be consistent if they are to be understood as truly representing your consistent reality. How can we know if a system is consistent and complete– Critique it with logic. If a paradox exists (which it does in logic) then you have to come to one of two conclusions- either

A. Reality in its completeness contains paradoxes and therefore logic as commonly understood is forever incomplete or inconsistent-

or

B. The paradox is the result of a flaw in the logical system or that the logical system is primitive and could be replaced by a better one that is logically sound and impervious to those paradoxes and capable of representing reality as it is according to your intuition.

“Existent is synonymous with logical.”

No it is not. Things can exist that are not logical. Logic has to do with understanding reality. Existence has to do with reality itself. I see a clear problem here of equating the ontological with the epistemological.

Do you mean that objective reality is complete? Because if so I see know reason to dispute this intuition and I largely share it- But Gödel’s critique of logic is a critique of the limits of the mind to formally express itself. And the formal expressions of the mind is not representative of all objective reality itself. Reality as a whole is very likely complete- but certainly things in reality are not- for example an unfinished English essay or a bike that is not yet put together- thus all things are not complete- so why would logic (defined as the mental system we use to formalize reason) not be included in this class of things?

Logic IS one of those things from the formalistic perspective- and in Gödel’s second theorem he translates that into arithmetic and shows it to be incomplete.

If one cannot prove the inconsistency of a formal system from within itself then where would or even could one go about doing so?

To say that nothing can be incomplete is false- and intuitively obviously false- and to rule it out for logical systems is simply a metaphysical bias apriori.

The best argument against Gödel’s proof is that since it undermines logic and it is at the same time logical- one comes to the inescapable skepticism of it— How can it be trusted if it is incomplete by its own virtue?

But you see you cannot logically critique the system on that basis unless you commit to the theorems truth to begin with. That is to say that since it undermines logic you have to admit that it did undermine logic. In other words to beg the question proves the point. His incompleteness may be incomplete- but it is just as complete as anything else that formal system can produce- thus one must by that token throw out all of the propositions and proofs (including his) based upon their incompleteness- Yet there is no good logical reason to justify keeping them all except Gödel’s just because Gödel destroyed all of logic’s persuit for perfection- even if his theory does infact commit suicide AFTER the homicide has already been committed.

The way I see, there is only one such system and that is reality. If it exists, it is complete and consistent. Otherwise it could not exist. Existant is synonymous with logical, in my opinion. So, it suffices to deduce the logical basis of reality and use that as our logical system. I realize that this is a partially baked idea that needs a more formal description but that’s all I’ve got at this time.

Just as quantum theory is intuition’s graveyard, incompleteness is logic’s.

You can rest assured that QT has just as much to be desired as spacetime physics. Having said that, let me add that, of all scientific theories, I like QT the most, flaws and all. At least, it is based on particles, properties and interactions. And it is not just a math theory a la Newton or Einstein with their fictitious and illogical spaces and spacetimes.

“You cannot use logic to prove the incompleteness of a logical system because the proof is itself part of the system.

Then how logically can you prove completeness of a logical system?

If you cant use logic at all to critique the formation of the system- and that means that logic is inherently illogical. If it is inherently illogical then there is no logical reasoning by your standards to dismiss incompleteness- because there are no formal rules, ruling it out.

By your same mode of reasoning you would not be able to conclude the completeness of any system since its completeness comes from within the system itself. You are just eliminating the possibility of incompleteness apriori. That’s Your intuition and your prerogative but I fee like you are the one acting like the elitist intellectual elitists dismissing a real logical proof based dimply upon personal sense and feelings. It seems to me under your system of thinking – that if logic cant be used to critique itself – it can never be logically complete at all- your meta-reasoning, not mine.

It makes a lot more sense to me to just let the logical system stand on its own two feet and see where it takes us- and if no contradiction in paradox occurs – then its completeness is intact. But as we know Godel has proved otherwise.

There is no line of reasoning to me that would constitute the law- that you cant use logic to prove its own incompleteness.

The only argument you use to undermine his flawless logic is that by proving logic incomplete one then has to consider his proof incomplete and therefore —> “dismiss it.” But one should not logically dismiss it because the sensible way and ironically “logical” way to deal with it is to allow one to “have doubt” about “the completeness” of his theorem. This resultant thinking constitutes the point that he was trying to make. That “man is not the measure of all things” but that in fact arithmetic was a reality of its own separate from the confines of human formal control and domination. Platonism.

Maybe one day logic will be fixed by some anti-Gödel- in a logically critical way that logically excludes the possibility of incompleteness.

I have said all that I want to say on this issue unless you surprise me with some well argued and new- but I want to end on the note of why I think his theorem is very important and good…

Gödel’s incompleteness is to me liberating- and to me supports theism because it puts man in his place as the paradigm of al animals with a intuitive soul but not the “complete” master of all things. This never destroyed logic. It would be quite sad to wake up one day and find out that man has the ability to know all- it would say that life is as it is to man – which to me is quite a let down from the hopes of a larger more ideal reality that is not simply beyond ours but interacts within it. The theorem to me merely put logic it in its place, allowing us to exist with logic but also with a sense of something more- the human soul and the divine will of God- which we can not formally know in cold and physically concrete terms but are meant to fully understand.

But not yet.

One a side note- I wonder what ever happened to “Kariosfocus” and his “always linked”. I would have loved to seen his view on all of this. But I havent seen him on here in a long time.

No. Sorry.

The way I see it, if Gödel was right, then any self-contained system, including the universe in which we exist, is either incomplete or inconsistent. Somehow, I find that very hard to accept. It seems to me that Gödel’s theorem is a very clever way for the denialists to claim that there is no such thing as absolute truth in reality. The ancient serpent is a very subtle beast indeed. And an accomplished liar, no doubt.

At any rate, I glanced over the link (thanks) about Popper and Einstein (I’ll read it in full later). I would like to comment on something that I find odd in it. Popper is given as an Einstein admirer who publically complimented Einstein on the falsifiability (testability) of relativity. However, in an earlier book “Objective Knowledge” (1966), Popper wrote the following in a paragraph titled “Realism and Subjectivism in Physics”:

There was also another intrusion of the subject, or of the observer, when Einstein brought in the observer in a number of imaginary thought experiments intended to elucidate relativity; but this is a field from which the observer was exorcised, slowly but steadily, by Einstein himself.

I think that Popper’s supposed admiration for Einstein was not as solid as many would suppose. Sir Karl had a clever way of taking oblique pot shots at his “friend” and getting away with it.

As you can see, I am very skeptical of big science and I take everything that comes out of it with a grain of salt. I find so many things wrong with organized science that I marvel that the entire house of cards in the air that it has built itself over the years has not come crumbling down years ago.

I’ll conclude with one of my favorite quotes from one of my favorite critics of big science:

And a more detailed analysis of successful moves in the game of science (‘successful’ from the point of view of the scientists themselves) shows indeed that there is a wide range of freedom that demands a multiplicity of ideas and permits the application of democratic procedures (ballot-discussion-vote) but that is actually closed by power politics and propaganda. This is where the fairy-tale of a special method assumes its decisive function. It conceals the freedom of decision which creative scientists and the general public have even inside the most rigid and the most advanced parts of science by a recitation of ‘objective’ criteria and it thus protects the big-shots (Nobel Prize winners; heads of laboratories, of organizations such as the AMA, of special schools; ‘educators’; etc.) from the masses (laymen; experts in non-scientific fields; experts in other fields of science): only those citizens count who were subjected to the pressures of scientific institutions (they have undergone a long process of education), who succumbed to these pressures (they have passed their examinations), and who are now firmly convinced of the truth of the fairy-tale. This is how scientists have deceived themselves and everyone else about their business, but without any real disadvantage: they have more money, more authority, more sex appeal than they deserve, and the most stupid procedures and the most laughable results in their domain are surrounded with an aura of excellence. It is time to cut them down in size, and to give them a more modest position in society.

From ‘Against Method’ by Paul Feyerabend

Sorry for the long post.

“All I am saying is that one cannot use a logical system to prove that the system cannot be trusted because anything you claim within that system becomes suspect, including the “proof” that the system cannot be trusted. Self-reference is the main problem with Gödel’s theorem. This should be obvious, no? I mean, one does not need to be a rocket scientist to get it, does one?

Ok, im not having any problem understanding your criticism of Gödel- even though I am not a rocket scientist.

To say that if one finds a contradiction in a system that it cannot be representative of the character of that system is moot and superfluous because it would be no different than saying that if the system is always on the mark and verifiable it cannot be taken seriously because it is always good and has no flaws so how can we trust a system that cant be wrong or proven wrong? Would that make any sense? No.

In other words the character of the system is… the character of the system. And Gödel proved that logic and arithmetic is incomplete- through his theorem

As I said before one can take the Wittgenstein view and say that all he did was form a useless paradox that was little more than a trick of the mind- (as you seem to elude to in your point about its contributions to science and philosophy) that is the theorem “said nothing” that makes any sense.

But I think that the concept of “the set of all sets that do not contain themselves” is a big conceptual problem for logic and hence I maintain that logic is incomplete and more importantly “flawed” as a tool to represent and understand reality as it actually is- formally.

But you i think are seeing past the point of Gödel’s proof-

You seem very smart Mapou and i think that your view has a certain` degree of truth to it- i also share your frustration with the intolerance of the orthodoxy in entertaining new ideas- and i want you to know that that is why I have entertained your’s though i certainly disagree with your interpretation, rejection and view of Gödel- yet, I do not dismiss it. In the end your sensibilities could be right- but not for the present.

On the Popper critique check this out…

http://elm.eeng.dcu.ie/~tkpw/t.....0000000000

Here the author, who is a lawyer… talks about the verifications of Einstein’s theories and explains why he think the experiments were either misinterpreted or neglected the scrutiny they deserved.

I find his critique of Relativity to be very plausible based on the logic he evokes- yet like conspiracy theories I would need to hear the debunker of the debunker before I could accept that a perfectly rational theory (as even popper admits) that is accepted by almost everyone, is somehow very mistaken and wrong—

The critique is very god but my intuition tells me that if these charges were true Einstein would have been killed along time ago- I for one don’t think of Einstein as one of the elitist intellectual useful idiots and therefore i think they would have destroyed him if he was wrong.

Darwin on the other hand who is fully accepted by this crowed — since I first read of his theory in 9th grade biology- thought that it made no sense. How could all of this just happen by chance- what guided it- what started it … Etc ..etc

So Einstein, gets the pass from me for now- but thank you a lot for bringing to light this interesting critique of his theory- that I had never before read or heard of.