Gödel: A Life of Logic

This book, "Godel, the life of logic", is a book that has a lot of junk bio, but it also has ideas that one is compel to reread. For example the Godel Number and Turing Machine. It does draw the reader with interest. I thought I knew everything about logic (Boolean logic mostly) but I was not properly informed.The whole book drives with the idea of truth (semantics) and proof (syntax). Syntax is the logical machinery that produce all the mathematical (logical) statements. It also can be said that syntax is the formalization. There is no mathematical intuition that allows one to see all the mathematical statements. Therefore all the syntactical statements are statements proved (or disproved). So we can map out what are proved and disproved. There will be statements that will be not ( proved and not proven).There were sections about AI and there are bio that are equally uninteresting (except Godel apparently starved himself which seems so appropriate of a logician.) The second to the last chapter "The Complexity and the Complexity". A chapter on computerized number theory is very interesting. I never found number theory interesting in school but this one was a kicker. For example, Godel's Theorem (Diophantine Equation Version)---there exist a Diophantine equation that has no equation but no theory can prove this. Diophantine equations are equations that have two or more variables, and it should have integer solutions. For example, x^2+y^2=z^2 can have solution of x=3, y=4, z=5 (for z being the length of the slope of a Pythagorean triangle).As I said, I am going back and reread sections of this book: Godel Number and Turings Machine, etc...If you are new to modern logic this will be an eye opener.

After rereading Godel, Escher, and Bach three times, I may have reached 15% comprehension but the topic still interested me. This book on Godel is designed well for non mathematicians or PhD logicians. It is well written. The authors explain the concepts clearly, provide intersting context and background and avoid condescension. Godel's work reminds us of the limits of our certainty and would be useful for both atheists and fundamentalists to read.

This book gives clear insights in the life of one of the greatest mathematicians of the 20th century. Where Gödel’s intellectuality is easily noticeable, his anxious nature is hidden under a layer of introversion. Both the biographical details as well as the comprehensible explanation of Gödel’s groundbreaking accomplishments in mathematical logic and philosophy make this book a delight to read.

Even in books that I greatly enjoy and inevitably recommend, there are always at least a few problems. If/when I write a review of such a book, I find it difficult not to focus mainly on the apparent gaffs or simple imperfections (my wife says I'm just grouchy, I don't think so, but perhaps she's right). Through the first seven chapters, `Gödel: A life of Logic' was well enough presented that the text had given me nothing to grumble about. The exposition of humankind's greatest logician, both his curious and quirky personal life and his stunning accomplishments in mathematical logic and metamathematics, was highly enjoyable and, so far as I could discern, highly accurate. So good as to essentially overpower the shortcomings of the last three chapters.Ah, but now for the afore-mentioned grumbling (I'll skip a small issue with the introduction of complexity in chapter nine). The abrupt little final chapter (10), a philosophical summation, struck me as being something of a disintegration. "Gödel's mathematical philosophy was resolutely Platonistic," record Casti and DePauli, and in this they are obviously correct. But now it gets rather muddled and I expect Godel, a lover of accuracy, would have done a little grumbling himself had he read the following:[Godel held] "a Platonic view of mathematical objects, no doubt about it. For the Platonist, objects are thus intuitively presented. By way of contrast, an Intuitionist or Constructivist considers them inventions of the human mind . . . For Godel . . . we find a typically Platonist intertwining of an objective concept of reality with a kind of extrasensory perception of abstract, Platonic ideas." (so far, so good, but--) "Interestingly, Godel also had a Intuitionist streak in his mostly Platonic view of mathematics. Formalists and Platonists are diametrically opposed in their view on the question of [mathematical reality]." The authors have already sketched out this philosophical opposition, but how are they categorizing Godel now? "Although Gödel's mathematical philosophy was Intuitionist, his logical methods were Formalistic . . . This is classical Platonism in its purest form."Okay, some of this is salvageable, but what a muddle. Had the authors just thrown in the towel? And this is followed by a brief whimsy about Gödel's similarity to "Copernicus, Darwin, and Freud," on the grounds that they all undercut our fantasies of human omnipotence. Godel, of course, would absolutely have found 2/3 of those associations (exempting Copernicus) problematic on various fronts, and I have to wonder--who but the most delusional of the intellectually handicapped have ever seriously expected anything that could accurately be described as human omnipotence? No one in the Eastern or Western intellectual histories comes to mind, and not even a potency-obsessive psychopath like Hitler was quite that crazy.So that's my grumble, I may have failed but I tried to keep it concise. If we can set aside the last fading paragraphs, and a sentence here or there, the book was quite good. The expositions on Gödel's relationship to the Vienna Circle, as well as on Godel Numbering and how it has enabled analysis, are well presented. The exposition on computation and Artificial Intelligence is mostly accurate and succinct, but it too fades in its conclusions (perhaps this is well enough explained as basic intellectual dispassion on the part of the authors).

I am not a mathematician or a logician but i am interested in the incompleteness theorem. the authors were very skilled in bringing the material down to my level. fortunately, they have an easy, comfortable style that is kind to the non expert reader.

Godel was a mathematical iconoclast. He upended the work of Hilbert and Bertrand Russell and showed that not everything that is true in mathematics can actually be proved. Fascinating and clearly written.

It is not the book I hate. It is the book that arrived and turned out to be a misprint. So I could not read it. So I return it and ask for a replacement. It arrives and is also a misprint, the same type of misprint. Not amused obviously.

L'ouvrage se veut une première introduction à la vie et à l'oeuvre de godel (le plus grand logicien depuis aristote). Il s'agit en effet d'une introduction, tout est un peu court et lorsque des détails sont donnés, il est nécessaire de s'accrocher (notamment lorsque les auteurs expliquent la théorie physique de Godel en lien avec la théorie de la relativité). L'ouvrage constitue cependant une bonne introduction même si on ne trouve rien de neuf. La démonstration du théorème est très proche de la présentation proposée par Hofstadter dans "Godel Escher et Bach".Signalons enfin que la typographie n'est pas géniale et que les phrases ont tendance à se terminer dans la reliure...Une intéressante première approche mais qui mériterait quelques développements supplémentaires.