Jean Yves Girard On Goedel Escher Bach

[From GoedelEscherBach]:

Warning flag for the overly enthusiastic reader: there's at least this brilliant mathematician who has essential contributions to Logic and ComputerScience, namely JeanYvesGirard, who characterizes this book as a "masterpiece of vulgarity". He ridicules the book's treatment of Goedel's results under these words:

Next come the clowns, nostalgic for the final solution (to re-use this expression typical of German scientism) to the problem of coherence. Their procedure is even more twisted: hail Goedel as the greatest logician of all time, mount the absurdities of Goedel numbering on a pin, and make it a sort of super-puzzle. This burying-under-flowers is characteristic of that monument of vulgarity, "Goedel, Escher, Bach". The implicit message is clear: Goedel's theorem is an artificial, unnatural result, which cannot alter the triumphant march of positive science.

But it's a simple matter, this theorem. It says that Parliament cannot grant itself an amnesty by the vote of one of its sub-committees, nor by itself: it must at least bring in some members from the outside. Isn't that just common sense? Or, alternatively, that you can't fix your glasses while keeping them on your nose.

Perhaps obfuscation is the logical opposite of vulgarity. I rather doubt that JeanYvesGirard uses any obfuscation, on the contrary his writings on the subject are clearer than anything else I've read. of course, you'd have to read the whole article (and probably a few others ) to get the context.

"Les Fondements Des Mathematiques",

See also: for a collection of excellent articles (some in English, most in French). For some people, they might be a lot more enjoyable than reading GoedelEscherBach, and some articles are really funny and exquisite simultaneously.

I don't think he read the same book I did. -- EricHodges In the context of the source article Monsieur Girard seems to be accusing Hofstadter of being part of some hallucinatory Germanic "Positivist" reactionary tendency. Regardless of Girard's contributions to Logic and ComputerScience, his contribution to the history of ideas here has to be seen as a (hopefully out of character?) lapse into cultural chauvinism and surprising bad faith. No doubt in this idiosyncratic version of history August Comte was a German and Hegel was secretly a Frenchman. Lamentable. For the record GEB is in no way an attempt to rescue a positivist scientism from the challenge posed to it by the Incompleteness Theorem, quite the opposite. [Also, IMO, referring to the holocaust in an unrelated intellectual argument is the last refuge of the scoundrel]. -- PaulBowman

I think that to accuse JeanYvesGirarde? of chauvinism is absolutely ridiculous, and without any basis whatsoever in reality. There's no actual reference to the holocaust, there's a play of words , the "final solution" where quite possibly he's referring to an expression used by Hilbert or his school. He definitely write "this expression typical for the German scientism". The fact that he mentions German scientism can in no way be interpreted as chauvinism, unless in "surprising bad faith". The fact is that the formalist program he critiques belonged to the German school around Hilbert, on the other hand one needs to forget the positive references Girard makes about the contribution of Goedel and Gentzen. Not to mention that it takes a strong leap of (bad) faith to suspect that in criticizing Hilbert's program, Girard's dismisses the otherwise huge contribution that Hilbert made to modern mathematics. -- CostinCozianu

Interestingly, a professor of mine years ago decried GEB on the basis that it was anti-positivist (and anti-rationalist) in it's focus on Zen, contra-positives and StrangeLoops?. Of course, he was Italian, not French, but I suspect that national character had less to do with it that his support for RogerPenrose's TheEmperorsNewMind and its rejection of ArtificialIntelligence. -- JayOsako

I think that Girard is entitled to ridicule a whole book that fantasizes about these "strange loops" to "explain" in an awkward and almost mystical language what can be done in one page, like Girard just does in the article. From the point of view of a important mathematician and a professor of mathematics (Girard is both ) there's no redeeming scientific or educational value in GoedelEscherBach. Girard also conjectures that the implicit message of GEB is that "Goedel's theorem is an result 'against the nature' that can't derail the triumphant march of the positive science". All I can say is that I had the same impression when I read some handwaving towards the end where Hofstadter expresses his conviction that in those "strange loops" scientists will be able to unravel whatever mysteries.

It was some time ago, and I can't guarantee the accuracy of my judgement on the book, but I can guarantee those were my distinct impressions. Another distinct impression was that the book was very hard to read (almost a torture) and that was not because of the difficult mathematical content (actually there was nothing new to me in there), but because the author throws a lot of irrelevant verbiage around some simple mathematical content. I strongly believe that for somebody who hasn't taken a prior course in mathematical logic and theory of computation GEB confuses more than enlightens. If somebody asks me for advice, my advice is definitely not to read GEB before getting a proper mathematical exposition of the Goedel theorem ( I'm convinced that somebody like Girard can do it in one lecture and fascinate his audience), after which he's less likely to have enough appetite to put up with the long and contorted exposition in GEB. Definitely GEB has a pop culture status way over its value (does it have any scientific or pedagogical value at all??), and it is therefore surprising to see such reactive/deffensive responses directed to Girard's comments about the book. -- CostinCozianu

GEB is a philosophical book, not a science or mathematics text, though it has some information on those thrown in. It's a book about self-reference, so it shouldn't be surprising that it uses strange loops in places they aren't needed - not to display the subject at hand, but to give familiarity with self-reference. Girard's description doesn't seem to match the book I've read.

As to confusing, GEB uses slightly different terms than a logic text would - e.g. it always talks about truth in a philosophical sense, rather than the rigorous logical definition. I don't think the difficulties that result are severe. At any rate, not everyone should have to take a symbolic logic course before being allowed some idea of what the important results are.

GEB isn't a college mathematics text; several of my friends and me read it as a children's book, and got considerable value out of it. I can see how it might be disliked by those who've already seen all the material, who disagree strongly with the philosophy, or who mind superfluous prose. On the other hand, I can also see where its reputation came from. I find it odd that people are willing to tolerate differences of opinions on most books, but this one has to be liked or has to be hated.

And to help us clarify the issues can you resume for us what do you think is the "philosophical thesis" of this book? I agree that not everyone should have to take a mathematical logic course in order to get acquainted with the important results, but while a writer like Girard (or to take a neutral party, somebody like Gregory Chaitin) can outline Goedel's theorem in half a page to a few pages at the "popularization of science" level, Hofstadfter manages to do that in quite a lot of pages and leave many of his readers confused on the subject.

For example, somebody exclaimed on wiki "It convinced me that free will is an illusion". What's the link between Goedel and free will can only be puzzling for a mathematician, and if the book can inspire such sentiments, we may be able to prove some objectively bad qualities, regardless of one or the other's subjective like or dislike. -- CostinCozianu

[Have you read GEB? There's a lengthy section toward the end about the illusion of free will.]

The belief that a particular problem may be someday explained by science, even if we don't have an explanation yet, is hardly positivism.

Just because you didn't understand the parallels and couldn't be bothered to read about them, doesn't mean they weren't there.

It's not my job to explain the contents to you, since I'm not interested in forcing you to like the book - indeed, if memory serves you hate pretty much everything to do with philosophy, so I'd expect you to dislike it.

But your particular preferences for mathematical proof over philosophical dialectic aren't universal (obviously they are for math, but not necessarily in fields like philosophy), and thinking that because this book doesn't contain the sort of argument you'd prefer it must be objectively bad is simple arrogance.

Girard's opinions might normally be worth something, but he misunderstood the point of the book as understood by those who've read it thoroughly, so in this case they aren't very useful.

Well, as I said, Girard's description ignores the main point of the book - or at the very least, doesn't explain why more ore than a third of the topics it covers are in there. But as I've said from the start, you're both welcome to think what you want.

Whatever. Strange loop just means recursive representation, and is neither undefined nor intended to be mystical. I don't want to discuss this with you, since your mind was apparently made up even before you read through the book. I'd simply prefer you acknowledge other people's opinions - the many mathematicians, programmers, philosophers and whatnot - as valid; but if you don't want to do that, I suspect no-one will care that much.

'Now really. Incidentally I sifted through the index of the book and I was able to find a "definition" (pseudo-definition, that is) which has nothing to do with yours. And may I find out what you think "recursive representation" is? Is it about formal systems or is it about natural world? Or both? We know we have recursive function. These are quite well defined concepts. We even have some MetaCircularInterpreter, probably a "strange loop" although there's nothing strange about it. However none of these exhibit "free will", "consciousness", whatever Hofstadter is trying to explain. So what exactly is a "recursive representation", and where do they get their "consciousness" from?

I'll acknowledge other people's self delusion with GEB, argument by the numbers, impossibility to define anything to any remotely acceptable rigor, and their defensive reaction by lashing out childishly when I posted this page. Excuse me, but claiming that JeanYvesGirard just "doesn't get it" is a little bit too much. And the proof of that being an argument by the numbers. Whether Hofstadter properly defines his concepts, properly makes a connection between Goedel and his ideas, whether his arguments are more than just handavinng or less, those are no longer a matter of de gustibus. You either are able to explain rationally or you don't.

The basic point of the book is discussing how consciousness could be an emergent phenomenon. Before he does this, Hofstadter spends a lot of time familiarizing the reader with recursion by developing a number of examples. These include Goedel's theorem, and he doesn't outline it in half a page because he's not trying to establish the result, but exhibiting the relationship between its proof and self-representation. He also spends a lot of time playing with biochemistry, art, music, and Zen, in what's meant to be a general and entertaining fashion. There's no direct syllogistic link between these things and consciousness, but there is a thematic link: they exhibit the same underlying principles he later discusses.

I wonder what people who think this book is primarily about Goedel's theorem make of the other two names in the title.

Maybe GEB is just not French enough. From


The French prefer the esthetical motivation for geometry, rather than the more metaphysical motivation of the logicians. Look at the work of Rudy Rucker: everything which bears on geometry has been translated in French, none of his book on logic have been.

Still, after the parution [??] of Hofstadter's "Goedel, Escher Bach" I have discovered how much the French, including some logicians, like to minimize the importance of Goedel. Take Jean-Yves Girard, one of the biggest important logician of the day (especially for his invention of LINEAR LOGIC). Not only he likes to ridicule Hofstadter's book, but he has invented a new *disease*: the Goedelite, which symptom consists in appreciating too much Goedel's theorem. Of course it is true that many pseudo-philosophers has developed invalid consequences of Goedel's, but to dismiss the importance of Goedel from that is invalid too!

Now let us remember that the French have been unlucky with their logicians because the biggest one - Jacques Herbrand - dies at the age of 20 (falling from a mountain). Other logicians died in the defense against Nazis, like Jean Cavailles.

This "parution [??]" above I would think is likely to be French "apparition", which is a "false friend" in English (it's an English word, too, albeit with a different meaning) and therefore often copied through without translation, but which is better translated as English "appearance" in this context; it would fit perfectly.


Just to dispell the myth of Girard's chauvinism or the allegation that "GEB is not French enough". Here's the opinion of an anonymous Amazon reader from Kawasaki, Kanagawa Japan :

I quite agree with the reviewer from East Hartford. Maybe I am not extremely eligible to comment on the portions dealing with Escher and Bach, respectively (I have no appetite for Escher. I like chamber music of Bach and sometimes play his keyboard music but my performance level is, of course, that of amateur.) But I must say the part dealing with Goedel's Theorem of Incompleteness is *complete garbage*. I am convinced anyone with a degree of mathematics will agree with me: for those who have no background in mathematics, I assure you that Goedel's theorem concerns a problem in "formal logic" and has nothing to do with human-cogno-something. If this book were meant to be a cult literature, that would be okay: I don't care anyway. But if this is meant to be an entertainment for people with no scientific background, I rate this alchemy or pseudo-science at best.

The translation above would seem to be a little more literal than it might be. How about this? My French is very rusty indeed, so it may be all wrong. Also, I couldn't find any idiomatic way to express "ensevelissement sous les fleurs" in English, which may be partly because I'm not certain what it means. Is it meant to convey the idea of neutralizing something by smothering it in praise? -- GarethMcCaughan

ThankYou for the translation, I put it above. Obviously you're a much better English speaker :) What do you think about JeanYvesGirard's take on the history of logic in 20th century? I'd be interested in your comments. -- CostinCozianu

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