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:
Perhaps obfuscation is the logical opposite of vulgarity.
- 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.
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", ftp://iml.univ-mrs.fr/pub/girard/wtls.ps.gz
See also: http://iml.univ-mrs.fr/~girard/Articles.html
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
- But Eric, you have to recall the French sense of humor; JerryLewis?, n'est ce pas? And that's just the French popular humor. For true mirth, the French read philosophy...
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.]
- As a matter of fact, I didn't read it cover to cover, life's just too short to be wasted like that. But now that you mentioned it, I went for the index. Sure enough, I found the "convincing" explanation of free will and consciousness , it starts with the conclusive "I believe ... " and it continue with "strange loops" where the upper level influences the lower level and is influenced by it and the kind of BlahBlahBlah pervasive throughout the book.
- It's not meant to be a proof, it's meant to be an argument. As far as I'm concerned it's a very good one, but then, I read the book before I made my judgements. Note that's required to evaluate the argument, but not the book as a whole. In any case, this gets back to personal preferences, and there's no point in disputing those.
- Let's quote it: "My belief is that the explanations of 'emergent' phenomena in our brains - for instance, ideas, hopes, images, analogies, and finally consciousness and free will - are based on a kind [sic!] of Strange Loop, an interaction between levels in which the top level reaches back down towards the bottom level and influences it, while at the same time, being itself determined by the bottom level. In other words a self-reinforcing "resonance" between different levels - quite like the Henkin sentence which, by merely asserting its own provability , actually becomes provable. The self comes into being at the time it has the power to reflect itself." [p. 708] And it goes worse and worse from there. In judging such BlahBlahBlah writing, it is no longer a matter of personal preference that should be applied, but admit that Girard was right. It's pseudo-scientific, pretentious gibberish of worst kind. All those strange loops are totally a matter of fiction, their connection with Goedel's theorem still a matter of fiction, where the author presents nothing of mathematical or scientific substance but a lot of pretentious phrases and handwaving philosophy, unwarranted references to everything under the sun (from Goedel and Turing to Smalltalk) all seemingly designed to fool his gullible readers into thinking that he has some kind of argument. Maybe he has come up with something of substance in the meantime (though I doubt) but he had nothing when he wrote GEB.
- I understand the connections and sort of effects he was talking about; it's certainly not scientific, but we don't have any good scientific model of how consciousness works, and it doesn't hurt to have some ideas of what directions to explore. Girard doesn't talk about this at all - above he claims the book is about the triumph of positivism over the unnatural result of Goedel, and that is neither the theme of the book nor a position it takes, so regardless of the book's quality his description is inaccurate. As to the rest, the disagreement of various wikizens about exactly how "blah blah" this book is should easily show you this is entirely personal opinion, so quit claiming your opinions are somehow better than everyone else's.
- Do you mean "I understand" or something more like "I feel it in my guts"? Can you substantiate what it is that you understand? Well, this question is kind of rhetorical because Hofstadter failed to do it in some 800 pages, but if you could answer it, you'd demolish all criticisms of the book. Therefore I won't quit so easily, but thanks very much for the suggestion. Not all opinions are created equal, and not all opinions can stand closer scrutiny equally well. We have the opinion of one JeanYvesGirard that happens to know quite a little bit about the subject of the book, we have lots of informed opinion of other readers, and on the other hand we have readers who did like the book, but can't explain it unless as a work of SF - clearly not the intent of the book.
- As to the accuracy of Girard's characterization, Hofstadter does exhibit naive positivism when , at the end of the book, in spite having nothing to show as an argument, and in spite drawing no real connections between whatever he wants to discuss (consciousness, etc) and a rather banal theorem of formal logic, he manifests his strong belief that future science will unravel the mysteries of the brain/consciousness/etc exactly on the path that he was handwaving about in 700 prior pages. It is the same kind of naive attitude that Hilbert had about his program. The big difference between Hilbert and Hofstadter is that Hilbert's mistake is quite understandable, he had made at the time quite a lot of progress in the axiomatization of Mathematics after all. While Hofstadter had nothing to show for his program at the time he wrote the book.
The belief that a particular problem may be someday explained by science, even if we don't have an explanation yet, is hardly positivism.
- You mean the unsubstantiated belief that the explanation will someday be found by science will be down a particular path.
- Yes, I do. It's not entirely unsubstantiated, however - although he doesn't provide an explanation, he explains why he thinks it will lie along that particular path. He could be wrong, of course, but that's why he says things like "my belief"; he's not pretending its conclusive.
Just because you didn't understand the parallels and couldn't be bothered to read about them, doesn't mean they weren't there.
- Handwaving parallels were there, plenty of them. But it's not only me, it's apparently quite a lot of people with background on the subjects treated in the book that deny any validity to them. Therefore attacking me ain't gonna explain a lot.
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.
- If the book made it clear it was entirely about philosophical speculations, than it would be a very different ball game.
- Well, a lot of the material he touches on isn't philosophy, but I think the book makes it very clear that the central thesis is a philosophical one. As I said, he doesn't pretend what he says certain, and argues in a very philosophical style. And heck, he has a chapter on Zen. So I don't think you have grounds to complain in this particular department.
- Whether it makes clear that it's "philosophy" I'm not so sure. Excursion into scientific things that have nothing to do with his philosophical musings (no, there's no connection between Goedel and whatever "strange loops" Hofstadter thinks are in his brain), are designed to fool the gullible and impressionable reader into thinking that his thesis has some kind of scientific legitimacy.
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.
- Following your line of thought it looks like we have only two alternatives of thoughtful inquiry: either mathematical proof or "philosophical dialectic". I wonder what these scientists must be using in physics, biology, medicine, chemistry, etc? Maybe it's just my limited understanding but I'm not aware of any "philosophical dialectic" that is accepted as valid argument in any natural science.
- That's true, science uses an intermediate approach - actually several different ones, since physics and psychology are not entirely similar. But Hofstadter isn't doing science, and never pretends to be. He's giving reasons why he thinks a particular avenue is worth exploring, and scientific methodology doesn't lend itself to this sort of pre-science.
- Oh, no. He prefers to muddle the waters and confuse his readers with unsubstantiated SF.
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.
- That, or the more plausible alternative that he understands better that the readers of this book are sucked into very dubious pseudo-science.
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.
- There's no need for a critique to explain coherently that which is incoherent. When Hofstadter departs from Goedel and derives some undefined "strange loops" that presumably would explain human mind, and presumably would be some kind of universal principles that have also some connections with Bach or Escher, that is as valid as departing from 1+1=2 and deriving that the Big Bang was caused by "bago bago" "energy vibrations", that also appear in Metallica's latest album, and in the late period of Picasso.
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
'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.
- My bet is that Goedel's name is in the title for the same reason as the other two: the splash factor.
- Oh yes, the public is clamoring for books with Goedel's name in the title. I hear the next Tom Clancy novel will be called "Rainbow Six, Goedel Nothing". Tom Cruise and Harrison Ford are being considered for the movie. Putting those three names in the title of one book was nothing but shameless hucksterism.
- You confuse the targeted market of GEB with the market for Tom Cruise and Harrison Ford. EGB is for those people who want to feel good and intellectual because they were able to suffer through 700 pretentious pages and feel smart because they did it. For that kind of crowd, sure enough, Goedel and Bach are very good brand names.
- And Girard is a good name for people who want intelligent and respectful discourse about serious issues.
Maybe GEB is just not French
enough. From http://email@example.com/msg03647.html:
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
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