In search of GodelThink: Kurt Godel is one of the greats, or so you’ll routinely be told. The leading authority on his work says it went something like this:
Kurt Friedrich Gödel (1906-1978) was an Austrian, and later American, logician, mathematician, and philosopher. Considered with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, A. N. Whitehead, and David Hilbert were pioneering the use of logic and set theory to understand the foundations of mathematics.He’s right up there with Frege—and with Aristotle, who “defined motion as the actuality of a potentiality as such.” (For additional details, click here.)
Godel is considered one of the greats. In her 2005 book, Incompleteness: The Proof and Paradox of Kurt Godel, Professor Goldstein ranks Einstein, Heisenberg and Godel as the great revolutionary thinkers of the last century.
We’re not saying Professor Goldstein is wrong! We’re merely wondering what it is that Godel determined, devised or discovered. Why is Godel one of the greats? This is where our love affair with bad explanation comes in.
Why is Godel one of the greats? And can it be explained to us rubes? As we noted in yesterday's post, Professor Goldstein’s book was aimed as non-specialists—and it was hailed by three other professors for being “remarkably accessible.”
Is Professor Goldstein able to explain what Godel said or did? In a series of posts, we plan to let you be the judge.
What the heck did Godel say, determine or discover? Early in her book, Professor Goldstein’s explanation starts as shown below.
She pictures Godel (“the logician”) in one of his conversations with Einstein, the friend of his later life. The two men often strolled through the streets of Princeton:
GOLDSTEIN (pages 20-21): The topics of their daily conversations range over physics and mathematics, philosophy and politics, and in all of these areas the logician is likely to say something to startle Einstein in its originality or profundity, naivete or downright outlandishness. All his thinking is governed by an “interesting axiom,” as Ernst Gabor Straus, Einstein’s assistant from 1944 to 1947, once characterized it...An “interesting axiom” governed Godel’s thought, we’re told as our journey begins.
The reader leans forward, expectant. But here’s what the reader gets next:
GOLDSTEIN: The topics of their daily conversations range over physics and mathematics, philosophy and politics, and in all of these areas the logician is likely to say something to startle Einstein in its originality or profundity, naivete or downright outlandishness. All his thinking is governed by an “interesting axiom,” as Ernst Gabor Straus, Einstein’s assistant from 1944 to 1947, once characterized it. For every fact, there exists an explanation as to why that fact is a fact; why it has to be a fact...Below, we’ll provide the full text of this lengthy paragraph. But in our view, our long day’s journey into bad explanation rather plainly starts here.
In that passage, Professor Goldstein endorses the view that Godel’s thought stemmed from “an interesting axiom.” She then presents two formulations of that axiom.
One of her formulations seems completely mundane. The other is quite hard to parse.
This is how bad explanation starts! Let’s consider the two formulations which constitute Godel’s “interesting axiom,” at least as explained by Professor Goldstein.
(1) “For every fact, there exists an explanation as to why that fact is a fact.”
On its face, that seems to be the most mundane assertion on earth. On its face, that claim would seem startling, controversial or insightful to almost no one.
Almost everyone is familiar with the idea that factual claims must be supported. You can’t simply make a factual claim. You have to back it up.
For every fact, there exists an explanation as to why that fact is a fact? On its face, it’s hard to see how this could possibly constitute “an interesting axiom,” let alone serve as the foundation for revolutionary thought.
On its face, that seems like a mundane statement. Let’s move on to Professor Goldstein’s second formulation:
(2) “For every fact, there exists an explanation as to why that fact has to be a fact.”
For every fact, there exists an explanation as to why it has to be a fact? Do you have any idea what that means?
Frankly, we do not. Consider:
“Boise is the capital of Idaho.” Most people would regard that as a statement of fact.
You could explain why it’s a fact. But could you explain why it has to be a fact? Would you even have any idea what such a request would mean?
Frankly, we would not. For ourselves, we have no idea what that second formulation means.
At this point, we’re flirting with bad explanation! Professor Goldstein has given us two formulations of the “interesting axiom” which lies at the heart of Godel’s revolutionary thinking.
One formulation seems highly mundane; the other seems incoherent. But Professor Goldstein doesn’t seem to notice this problem. She simply moves ahead in this, her complete, rather flowery paragraph:
GOLDSTEIN: The topics of their daily conversations range over physics and mathematics, philosophy and politics, and in all of these areas the logician is likely to say something to startle Einstein in its originality or profundity, naivete or downright outlandishness. All his thinking is governed by an “interesting axiom,” as Ernst Gabor Straus, Einstein’s assistant from 1944 to 1947, once characterized it. For every fact, there exists an explanation as to why that fact is a fact; why it has to be a fact. This conviction amounts to the assertion that there is no brute contingency in the world, no givens that need not have been given. In other words, the world will never, not even once, speak to us in the way that an exasperated parent will speak to her fractious adolescent: “Why? I’ll tell you why. Because I said so!” The world always has an explanation for itself, or as Einstein's walking partner puts it, Die Welt is vernunftig, the world is intelligible. The conclusions that emanate from this rigorously consistent application of the “interesting axiom” to every subject that crosses the logician’s mind—from the relationship between the body and soul to global politics to the very local politics of the Institute for Advanced Study itself—often and radically diverge from the opinions of common sense. Such divergence, however, counts as nothing for him. It is as if one of the unwritten laws of his thought processes is: If reasoning and common sense should diverge, then so much the worse for common sense! What, in the long run, is common sense, other than common?Die Welt is vernunftig, Gödel said. He hadn’t read this book!
If you’re an obedient student or reader—if you’re in the (very bad) habit of deferring to intellectual authority—you may simply say all those words to yourself and just continue reading. You’ll fail to note that you have no idea what this professor is talking about, if she knows herself.
If you are one of her fellow professors, you will agree to compose a back-of-book blurb about how “beautifully written” or “artfully written” this “remarkably accessible” book is (Professors Lightman and Greene). If you’re Professor Pinker, you’ll blurb that “this book is a gem,” that it has been “written with grace and passion” by a “gifted novelist and philosopher.”
If you’re less inclined to defer to authority, less flattering thoughts may enter your head. You may consider the possibility that this long paragraph is an example of pure argle-bargle, composed by a gifted novelist who may not be real clear as to what she’s talking about.
You may note that this large bouquet of flowery language emerges from that one highlighted passage, in which the novelist attributes two ideas to Godel—one of which seems completely mundane, one of which seems incoherent.
Let’s be fair! In our view, Professor Goldstein swings and misses as she tries to explain the “interesting axiom” at the heart of GodelThink.
But in fairness, her book has barely started. Speaking of incompleteness, Professor Goldstein’s “Introduction” starts on page 13; pages 1-12 are unaccounted for. The professor’s explanation is just getting started as this passage appears.
As advocates of fairness, we didn’t stop reading at this point. Generously, we moved ahead, hoping for clarity.
We were quickly rewarded. On page 23, Professor Goldstein quotes an account of Godel’s seminal incompleteness theorem in which, she says, that theorem is “rendered in more or less plain English.”
In our next post, we’ll show you that rendering. For ourselves, we would say that the rendering in question doesn’t involve “plain English” at all. The fact that Professor Goldstein thinks it does may teach a key lesson about a key topic—where bad explanation comes from.
In one area after another, our American national discourse is built around bad explanations. In a slightly more rational world, ranking professors would push back, skillfully and hard, against that state of affairs.
In our world, professors hand us work like this; other professors praise such work for its remarkable clarity. When our ranking professors function this way, we are all lambs in the end.
It matters not how plain the language is, it's still language.ReplyDelete
As Alfred Korzybski put it, "The map is not the terrain."
Aristotle and Socrates can be forgiven; they had no access to General Semantics.
Its bad enough that modern day professors and philosophers use muddy language, what's worse is that they praise each other for it.
I think, in their defense, explaining reality is probably impossible. Describing it not so much. This is why I object to many "complete theories" of something, because they only describe process and explain causative factors but not why why why. Of course the desire for epistemic closure is strong.ReplyDelete
You should note that one-third of those favorable comments on the back of her book cover, the one from Stephen Pinker, is from her husband Stephen Pinker.ReplyDelete
I like you suspect that author Goldstein really doesn't understand Godel's Proof based on her failure in the book to explain it, really to not even try to explain the most interesting parts.. I liked the portions of her book were she talked about Godel's melieu in Vienna and background. As it turns out I am a mathematician and already knew about the proof so that fault in the book didn't bother me.
Like you I took a number of philosophy courses and have done a lot of reading in it so I, with more nerve than sense, will take a swing at what Goldstein was trying to get at. Godel was an extreme Platonist in which the ultimate reality was in things like logic and mathematics. The mundane world is ruled by necessity. You know know how Pangloss proclaimed this was the best of all possible world? Goldstein is implying that Godel believed this was the only possible world, if we correctly reasoned we could derive the world from first principles.
That our universe/system is "the only possible world" is what I got from the statement that a fact HAS to be a fact, as well.Delete
C.S. Lewis argued that from a theological standpoint, I'd be interested in seeing how that is worked out from a non-theist view.
Who said it was non-theist? I don't know if Godel was a theist or not. If you want a handle on these issues i would recommend Bertrand Russel's History of Western Philosophy. He covers the non-theological philosophers failrly well, in my opinion. As I recall, St. Augustine inclined toward this view on non-theological grounds, but don't hold me to that.Delete
I'm not sure that I want a handle on these issues or not.Delete
The 'must be because it can be no way else' thing is fairly interesting.
does god exist? not a very interesting question to me.Delete
does anyone believe god exists? I do not think so, but it would be interesting to be shown proof. Theistic philosophers do not convince me in either their arguments or by their mere existence.
Prof Goldstein may be a wonderful philosopher, for all I know. But, Gödel's result is mathematics, not philosophy. I think a mathematically trained person could explain it more clearly.ReplyDelete
In particular, I will again recommend "Gödel's Proof" by Nagel and Newman. This book came out shortly after Gödel's result. It's still in print.
And, everyone should read "Gödel, Escher, Bach: An Eternal Golden Braid" by Douglas R. Hofstadter. This book is so rich and creative it's mind-blowing. I think it's the only mathematics book to win a Pulitzer Prize for Literature! (I call it mathematics, but it's incredibly wide-ranging in addressing music of Bach, art of Escher and others, and quite a bit on artificial intelligence.)
Instead of railing about a bad book, Bob could serve his readers better by discussing Hofstadter's great, great book
Gödel, Escher, Blech: Endless Garbagey Bullshit I remember slogging through this when it came out figuring at every page that the brilliant part just had to be coming up. From Amazon, 777 pages and 2 pounds shipping weight, the answer to the question "How can you fit ten pounds of crap in a two pound container?"Delete
Maybe it's just me. Can you tell me what you learned? In less than 777 pages, I mean. Thanks in advance.
I thoroughly enjoyed it too, DInC. It's not for everyone.Delete
deadrat, I'd have to find my copy and go through it to mention all the things I learned. You can get an idea from the Amazon reviews and Wikipedia.Delete
One concept that stayed with me was Jumping out of the system Another was Aunt Hillary, the conscious ant colony. It showed how a group of separate entities could also be a single entity. This is an analogy to how brain cell can make up a brain. I loved the art discussions, since I know little about art. I confess that I never did fully understand the Artificial intelligence discussion, which is a key part of the book.
But, I reluctantly must agree with AnonymousMay 4, 2014 at 5:24 PM. The book isn't for everyone. I respect your giving it a try, deadrat.
A visit to Wikipedia finds "In the book, [the author] presents an analogy about how the individual neurons of the brain coordinate to create a unified sense of a coherent mind by comparing it to the social organization displayed in a colony of ants."
This is the kind of crap I remember from stoned members of my college class: "So, man, you're saying that the solar system is like an atom in a bigger universe that contains our universe?" Invariably followed by "You're blowing my mind, man!" and "Don't bogart that number; pass it."
What I remember was the self-conscious punning that took the place of any serious discussion of the biology of social insects, neurology, computational complexity, and the esthetics of representational art. Wikipedia says that Hofstadter has denied that GEB was about mathematics, art, and music, so at least I got that right.
I think the book should be retitled The Unbearable Lightness of Being Douglass Hofstadter.
Deadrat, trying to mock D in C just makes you look even more outclassed.Delete
When you have time between butting into conversations to which you're not exactly a party, please try to consider how much I appreciate your opinion. This in light of how much time you've evidently spent following the exchanges between DAinCA and me.
My criticism of DAinCA falls on his apparent inability to check his cherished opinions against fact. And while my responses have often been harsh to the point of rudeness, I do him the courtesy of actually checking things, from the text of the ACA, to federal court rules about executive discretion to Florida homicide law. He does me the courtesy of not calling me a jerk or worse, a forbearance I admire. If you think his living in a world of his own opinion "outclasses" me, then let me suggest that this tells more about you than me.
In the particular case of GEB, DAinCA's opinion is not amenable to fact-checking. He says he learned much from the book;I didn't. As I said, maybe it's just me. My mockery is reserved for the author, which you're free to consider tells more about me than Hofstadter.
Clear? Good. Now piss off.
Stephen Pinker and Neil DeGrasse Tyson, pop figures who throw out a few facts accessible to any 5th grader and become heroes of the left who likes to identify with "the smart people" and so begins the charade of nonsense explanations and feigned understanding.ReplyDelete
Yeah, so much unlike the heroes of the right who "likes" to identify with ignoramuses.Delete
Pinker is not a leftist. Read his books.Delete
I caught that "likes" error too, deadbeat. Further proof that we're geniuses, you and I.Delete
I like Pinkers dreamy hair.Delete
Mathematical logic and general relativity are never going to get across to a lay audience - they require very specialized background. What needs explaining are more mundane things like how Social Security works. About 95% of what gets in the popular media about that is based on false premises, often deliberately so. Too many think they understand SS - and other economic matters - but really don't.ReplyDelete
I think what our howling friend is getting at here is that there are all these books which claim to explain complex and esoteric matters and don't live up to there claims. Perhaps the authors should instead engage in the world and explain matters of more public importance.Delete
I have no problem with bob's choosing a book to criticize rather than recommend. What I have a problem with is this:ReplyDelete
"In our world, professors hand us work like this; other professors praise such work for its remarkable clarity. When our ranking professors function this way, we are all lambs in the end."
Our world is pretty big and includes, I think, more than the one professor who wrote this book and the three who provided blurbs for the back cover. Even among the "ranking professors," the spectrum is a great deal broader than he suggests.
And with this:
"If you’re less inclined to defer to authority, less flattering thoughts may enter your head. You may consider the possibility that this long paragraph is an example of pure argle-bargle, composed by a gifted novelist who may not be real clear as to what she’s talking about."
The insinuation that the only unthinking deference to the supposed authority of the blurb-writers could account for any reader's positive evaluation of this book -- well, it is nothing but a nasty insinuation. Bad explanation is an interesting topic. Perhaps bob could try approaching it by a route that doesn't involve sheer nastiness.
Come to think of it, when is bob anything but incredibly nasty? (Well, yes, he can get terribly sentimental about black children, but even then, he presents himself as they only person who cares about them.) I don't remember him being this way all the time a few years ago.
Godel and I share the same birthday. That is my contribution to this discussion.ReplyDelete
Just a coincidence?Delete
"In our world, professors hand us work like this; other professors praise such work for its remarkable clarity. When our ranking professors function this way, we are all lambs in the end."ReplyDelete
Three professors wrote blurbs, one of whom was the author's husband. Were they "ranking" professors? Pinker isn't a phillosopher, so why does his opinion matter at all? Isn't the problem that people are willing to buy or read a book without determining first what the actual leading (ranking) philosophers think about it? Caveat emptor.
When people buy and read such a book without being themselves philosophers (who are no doubt busy reading and writing scholarly works not popular introductions to complex subjects), does it matter whether the books are informative or accurate? Wouldn't a book that was massively flawed provide more entertainment value, since even a layman could readily pick it apart?
It is a major waste of time for professors to go around pointing out all the flawed human efforts around them, so that non-professors won't trip over them. I think Somerby has a distorted idea of what professors are supposed to do in our society. They are supposed to be contributing new knowledge and teaching what they know to students. They are not supposed to be critics of the everyday world or explainers of popular culture (unless that is their field of study) or translators of difficult thought into easy-to-grasp sound-bites. Some of them are better at their jobs than others (as in any field), but they are all not supposed to get distracted by fame or media access and they are not supposed to spend their time writing "philosophy light" as Pinker and Golstein do. That is chasing the personal dollar not working as a professor. It often signals that one's real career (meaningful contribution to a field) is over.
Porno, Porno izle, Türk PornoReplyDelete
Porno, Porno izle, Sikiş izle
Porno, Porno izle, Sikiş izle, Sikiş
Porno, Porno izle, Sikiş izle, Sikiş
Porno, Porno izle, Sikiş izle, Türk porno
Porno izle, Porno, Sikiş izle
Porno, Sex, Porno izle
Porno, Porno izle
Porno Sikiş, Porno, Porno izle
Porno, Porno izle, Sikiş izle
Porno, Porno Sex Sikiş, Porno izle
Porno, Sikiş izle, Türk Porno, Kızlık Bozma
Porno, Sikişme izle, Türk Porno, Kızlık Bozma
Türk Porno izle, Türk Pornosu, Türk Sex, Türk Sikiş
Porno Film izle, Türk Porno, Sikiş
Porno izle, Porno video seyret
Türk Porno Resim, Türk Porno, Türk Porno izle, Türk sikiş,ReplyDelete
Porno, Porno izle, Sikiş izle, Türk porno,Mobil Porno,
Porno, Porno izle, Sikiş izle, Türk porno,Mobil Porno,
Porno, Porno izle, Sikiş izle, Sikiş, Türk porno, Mobil Porno,
Porno, Sikişme izle, Türk Porno, Kızlık Bozma, Porno izle,sikiş,
Porno izle, Porno video seyret, Türk porno ve sikiş seyret, Porno,
Türk Porno izle, Türk Pornosu, Türk Sex, Türk Sikiş,Türkçe Sex,
Türk Porno, Türk Pornosu, Türk Sikiş, Türk porno izle, Porno izle, Porno,
Porno, Sikiş, Porno izle, Mobil Porno, Türk Porno, Sikiş izle, Seks izle