INCOMPLETENESS THE PROOF AND PARADOX OF KURT GODEL PDF

By Rebecca Goldstein. After all, she's not just a novelist, but a philosophy professor. His Platonism also set him apart from his intellectual contemporaries. A biography with two focuses -- a man and an idea -- Incompleteness" unfolds its surprisingly accessible story with dignity, tenderness and awe. For centuries, science seemed to be tidying the mess of the real world into an eternal order beautiful and pure -- a heavenly file cabinet labeled mathematics. You can hardly blame them.

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Get A Copy. Paperback , pages. Published February 17th by W. Norton Company first published More Details Original Title. Great Discoveries. Other Editions Friend Reviews. To see what your friends thought of this book, please sign up.

To ask other readers questions about Incompleteness , please sign up. Lists with This Book. Community Reviews. Showing Average rating 3. Rating details. More filters. Sort order. Dec 07, BlackOxford rated it really liked it Shelves: science , mathematics , biography-biographical.

To me the implication is that no matter how much we learn, we will still be wrong. We are not unsure only about mathematics. Physics for example will always exhibit paradoxes like those of quantum theory. People unaccountably will always do things which are bad for them. And my socks will continue to disappear in the dryer. In an age rocked by the counter-intuitive implications of things like Relativity Theory and Quantum Mechanics, which present paradoxes that seem resolvable by further thought, the Incompleteness Theorem is even more of a scandal.

It exists in logic not in observation. It will remain in force no matter what else we learn about the world.

It applies to the deepest thinker, the wealthiest entrepreneur, the most powerful politician, as well as to any random cog in the modern economic machine and to those who have been rejected by it.

It is the modern form of the ancient Christian doctrine of Original Sin, formulated so forcefully by the great saint, Augustine of Hippo. Just as Original Sin, Incompleteness affects us all.

We inherit it, not through our genes, but through our memes. Incompleteness comes packaged in language itself. To engage the world through language is to enter the domain of Incompleteness, and therefore of profound doubt. And just as Augustine said in his religious idiom, Godel has restated the situation in his: There is no escape. The user of language is trapped and is incapable of extricating himself from an existence of rational error - about himself as well as the world around him.

Like many before him and since, Augustine fills the intellectual vacuum with the magic of a divine saviour, the guarantor of the ultimate rationality of human and other life on Earth. For Augustine Christ is the deus ex machina who is capable of correcting, literally remaking, flawed human nature into something reliable.

Augustine, of course, merely demonstrates the extent to which the basic human flaw can make us crazy. His solution is actually the greatest delusion produced by his fundamental insight. He neurotically invents in order to avoid his own logic, and then projects his neurosis onto the world as a defect which must be eliminated. He is the first Christian terrorist.

What Godel allows us to see, however, is that mathematics is a genre of poetry with its own arbitrary, but still rather satisfying, conventions.

Prospects, bleak or not, - whether spiritual or material - have nothing to do with the matter, therefore. Mathematics, like the rest of poetry, is important in the continuous present. For my money he was more spiritual than Augustine, as well as more committed to the idea of truth. He knew there was something permanently beyond human reach. As a committed Platonist, he considered this to be the abstract realm of numbers, which exist quite independently of human thought about them.

The principle difference however is that numbers make no absolute demands and pass no judgments. And very few have felt compelled to use violence to defend number theory. Rather, it is rationality run amuck, the inventive search for explanations turned relentless. View all 19 comments. About his time at the Vienna Circle a. The proof itself is rather simplified and no great mathematical knowledge is required. Logical understanding is very helpful, however!

Everything outside this reality, all meta-mathematics, was meaningless and of no importance to them. The final chapter shows the incessant descent of this brilliant thinker quite impressively, as I find. Apart from the formal parts of the third chapter, this is a very easy to grasp and recommendable reading for all those who want to make themselves more familiar epistemology, history of science, meta-mathematics and logic.

View 2 comments. Jan 21, Szplug rated it really liked it. The more I think about language, the more it amazes me that people ever understand each other at all. Goldstein quite clearly harbors a fondness and admiration for the eccentric logician, whom she once saw in person at a Princeton house party, and she does an excellent job of situating him within his time period, his academic milieu, his long tenure at the Princeton-adjunct Institute for Advanced Studies and, especially, in describing both his two Incompleteness Theorems—having first outlined his graduate student dissertation on Completeness—and explaining the immense impact they had upon the mathematical, scientific, and philosophic world once they had interpenetrated these disciplines of the mind.

That the latter proclaims first that in a formal mathematical system of assumed consistency there will exist a statement that is both true and unprovable; and second that said formal system's consistency cannot be proved from within itself, is, as Goldstein argues, from the same mental territory that Wittgenstein drew from in his early thought.

Two brilliant Viennese, one a Platonist amidst a sea of Positivists, the other—well, a sui generis explorer on the roiling seas of language.

To finite man the infinite is an awesome, disturbing, and chaotic beast, forever mocking human aspirations and advances with its eternities and paradoxes and circularities. We have always been able to intuit it, yet without restraining it and fixing it into place, and the quiet genius showed that this cannot be effected.

What implications does this bring to the existence of God, of a Platonic world of abstract ideals, of all that the mind can conjure but never empirically locate? View all 10 comments. Kurt Godel's fame was established by his proof of something called "the Incompleteness Theorem.

Namely, that in closed systems, there will be true statements that cannot be proved. Until Godel's proof, many leading mathematicians assumed the opposite was true. This is a challenging subject to write about, but Goldstein makes it easily accessible to a casual reader of science and philosophy like me. Godel's personal story is interesting. He was not a Jew, but had many colleagues who were. Yet, he failed to take a stance against the Nazis, instead choosing to continue his work even as Hitler's policies forced the Universities of Germany and Austria to purge Jewish faculty members.

It is unclear how much he knew about the worst atrocities perpetrated by the Nazis. Godel struggled with mental illness and, ultimately, it contributed to his death.

In the meantime, I recommend the book highly and I am deeply impressed with Goldstein. I look forward to reading more of her stuff. View 1 comment. I can figure out everything for myself.

The world is thoroughly logical and so is my mind—a perfect fit. It would explain much about the man he would become. But as is known to anyone who has given a popular mathematics lecture or written about a famous theorem for an audience of nonmathematicians, doing justice to the mathematics in question is almost impossible in those circumstances.

Mar 20, K York rated it it was amazing Shelves: philosophy. What a wonderful book. Goldstein not only lays out Godel's famous theorems in relatively understandable terms for the layman an accomplishment in itself, but provides an original, funny, and lucid account of the intellectual atmosphere in which these theorems arose.

She discussed Godel's relation to the Logical Positivists and Formalists, which sheds great light upon the meaning of his discoveries.

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Incompleteness: The Proof and Paradox of Kurt Gödel

Click Here to Order. From the jacket: A masterly introduction to the life and thought of the man who transformed our conception of math forever. His monumental theorem of incompleteness demonstrated that in every formal system of arithmetic there are true statements that nevertheless cannot be proved. The result was an upheaval that spread far beyond mathematics, challenging conceptions of the nature of the mind.

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