This book serves as an excellent introduction to Gödel's theorem, clearly distinguishing what it is and what it isn't.

It presents numerous examples of how the theorem has been utilized by people and delves into the discussion of why only certain of those uses are valid. The book is of moderate technicality. It provides sufficient information to enable an understanding of the mathematics underlying the theorem, yet only sketches out various proofs.

However, the organization of the book is somewhat cumbersome. For instance, computability and Gödel numbering are extensively employed in chapter 2 but are not fully explained until chapter 3. The author justifies this choice by stating that only a superficial understanding is initially required, and deeper explanations can follow. Nevertheless, I found this to be confusing whenever it occurred.

After perusing this book, I have a significantly better grasp of the concepts of completeness and consistency of formal systems. I also comprehend how computability factors into the incompleteness theorem. This is undoubtedly an informative book.

The second half of the book examines various applications that people have made of Gödel's incompleteness theorems and how those applications often have little to do with the actual theorem. It also explores some ways in which Gödel's theorem is related to Kolmogorov Complexity and Turing machines. The author is mainly responding to statements made by others, and his responses are sometimes interesting and at other times rather tedious.

Overall, despite its organizational flaws, this book offers valuable insights into Gödel's theorem and its related concepts.

This is really poorly written.

It lacks coherence, and the ideas seem to be jumbled together without any clear structure. The sentences are often short and choppy, making it difficult for the reader to follow the flow of thought.

There are also several grammar and spelling mistakes, which further detract from the overall quality of the writing.

It is essential to take the time to proofread and edit one's work carefully to ensure that it is clear, concise, and free of errors.

By doing so, the writer can effectively communicate their ideas and engage the reader.

In conclusion, this piece of writing needs significant improvement to be considered of any value.

Gödel's Incompleteness Theorem is a truly remarkable and profound concept in the field of mathematics and logic. It揭示了数学系统中存在的一些内在局限性。

This theorem states that in any consistent formal system that is powerful enough to express basic arithmetic, there will always be statements that are true but cannot be proven within that system. It challenges our traditional understanding of the completeness and certainty of mathematical knowledge.

The book that presents this theorem is not only a valuable resource for understanding the theorem itself but also notable for providing interesting examples of the misuses of the Theorem. These examples serve as cautionary tales, highlighting the importance of using the theorem correctly and not overextending its implications.

Overall, Gödel's Incompleteness Theorem is a fascinating and thought-provoking topic that continues to have a significant impact on various fields, including mathematics, philosophy, and computer science.

A somewhat deeper reflection on the incompleteness theorems and their frequent misinterpretations. It's okay, but I think the level is unbalanced according to the chapter. Sometimes they explain very basic things to you; in others, more complicated things are taken for granted. In my case, there's no problem, but I would warn anyone who knows nothing about the subject to be a bit careful.

Ta chulo.

The incompleteness theorems are profound and important results in mathematics. However, they are often misinterpreted or misunderstood. It's crucial to have a proper understanding of these theorems to avoid incorrect conclusions. The unbalanced level in the chapter can be a bit of a challenge. While the basic explanations are helpful for those new to the subject, the assumption of more complicated things without proper elaboration can leave some readers confused. It's advisable for beginners to approach the topic with caution and seek additional resources if needed to fully grasp the concepts.

Ta chulo.

This book is not intended for general readers or those without a background in mathematics. As someone with a math degree, I found it quite challenging. For a person with little math experience, it would be a very difficult read.

However, it is a concise and well-written overview. It covers Gödel's two incompleteness theorems and several important related topics such as the completeness theorem, compactness theorem, non-standard analysis, and large cardinals. The level of detail is just right for a reader with math experience, providing enough to understand the principles of the proofs without getting too bogged down in the technical machinery.

The best part was the debunking. I have long believed that Gödel's theorem is overhyped, and it was great to read Franzen's takedowns of several half-baked arguments, especially those of Penrose and Chaitin. In my opinion, Gödel's theorems are very similar to Anselm's ontological proof of the existence of God. In both cases, a piece of slick a priori logic seems to have huge implications in the real world. I don't trust such arguments. They seem to me to be scholastic. It's as if people were to invest the Liar's Paradox with some deep significance and spend decades arguing about its applications to the real world. The truth is that the Liar's Paradox (and Gödel's theorems, which are closely related to it) have no applications in the real world. My theory is that we will learn about consciousness and the brain the hard way, by actually studying it empirically, not by divining its secrets with fascinating but ultimately trivial bits of logic.

An elegant book on clarifying the Gödel's incompleteness theorems, and their margins.

It not only presents a clear and comprehensive account of these profound theorems but also does an excellent job of clarifying some of the common misconceptions that often surround them.

However, contrary to what might be somewhat implied in the introduction, the content is actually quite compact.

One cannot simply breeze through this book and expect to understand it fully. In fact, it requires the reader to pick up a pen and a piece of paper and actively engage with the material by opening up the details of the explained subjects on their own.

This hands-on approach is necessary in order to truly grasp the complexity and significance of Gödel's incompleteness theorems.

Overall, this book is a valuable resource for anyone interested in delving deeper into the fascinating world of mathematical logic and the limitations of formal systems.

This book provides a detailed exploration of what Gödel's theorem truly entails.

It is not the most straightforward read, especially if, like myself, you lack a formal mathematical education.

However, if you invest the time to read, reread, contemplate, and then reread once more, you can ultimately grasp its concepts (as I was able to).

Gödel's theorem is often mentioned briefly in numerous books.

This particular book equips you with the means to verify whether what is being claimed actually pertains to Gödel's theorem.

Surprisingly, in many instances, it does not.

By delving into this book, you will gain a deeper understanding of Gödel's theorem and be able to distinguish between accurate and inaccurate interpretations.

It offers a valuable resource for those interested in exploring the fascinating world of mathematics and logic.

Whether you are a novice or have some prior knowledge, this book can help you navigate the complex terrain of Gödel's theorem and enhance your comprehension.

So, if you are willing to put in the effort and engage with the material, this book can provide you with a rewarding learning experience.

From one of the most suitable angles, this book can be regarded as a very well-written, detailed, and temperate defusing-vademecum. Its aim is, among other things, to offer a useful diorama for the overschooled pundits, later postmodernists, and Deleuzian fanboys who apparently are still proficient in confusing themselves with special relativity-, QM-, and obviously Gödel-babbling. For example, they claim that his theorems would impose any sort of curb or an incompleteness advice to the limits of mathematics and science, and so on and so forth.

It turns out to be excellent, completely on target, and rewarding to read. Franzén indeed does a very valuable job, especially in expounding how the theorems do not overshadow some supposedly, and once unassailable, concept of Logical Truth. He shows how this was not its reach at all or its scientific heritage, and how it concretely applies solely at the axiomatic level. It is like the impossibility of an algorithm to decide whether _all_ true arithmetical propositions are... true. Moreover, it is not even that 'normal' for a science to be based on axiomatic formulations. To quote Hintikka: the theorem casts absolutely no shadow on the notion of truth.

Given that the book is neither so entry level (despite being full of quite good verbal criticism) as it requires a little intuitive understanding of set theory and some algebra, nor a highbrow literary sensation like anything out of Hofstadter's hands could be. Alas, the ones who may need it the most won't ever be able to understand it.

I simply can't bring myself to give this book just two stars. In fact, I would prefer to rate it at 2.5. Franzén does a reasonably good job of explaining some of the ways in which Gödel's theorems are misused. However, his mathematical prose leaves a lot to be desired. It is rather confusing and makes it difficult for the reader to fully grasp the concepts. I have come across many other expositions on the same or similar topics that are much clearer and easier to understand. The lack of clarity in Franzén's writing detracts from what could have been a more engaging and informative read.

Incompleteness is likely the most appropriate adjective for my reading status, and it will remain so for an indefinitely long time.

I find myself constantly dipping in and out of books, never fully committing to one until the end. There are always new titles that catch my eye, pulling me away from the ones I've already started.

I just can't seem to think like Franzen, who is able to focus intently on a single work and bring it to a satisfying conclusion.

Maybe it's because I have too many interests, or perhaps I'm easily distracted. Whatever the reason, I know that my reading habits need to change if I want to truly appreciate the depth and beauty of literature.

I'm determined to make a conscious effort to finish the books I start and to approach each one with a more focused and dedicated mindset. Only then can I hope to achieve a sense of completeness in my reading and gain a deeper understanding of the world around me.

This was likely the finest “popular” mathematics book that I have ever perused.

Before delving into this book, I had supposed that Goedel’s theorems would forever remain too abstruse for me to fathom. Indeed, my previous endeavors in understanding them had been fruitless.

Franzen’s book, however, is astonishingly lucid and cogent, captivating and enjoyable. The dissections of incorrect applications of the theorems in both popular and technical literature are particularly entertaining and instructive simultaneously.

I truly hope that there are more books of this caliber. It not only makes complex mathematical concepts accessible but also presents them in an engaging manner. It serves as an excellent example of how mathematics can be made interesting and understandable for a wider audience.

One can only imagine the impact that more such books could have on激发人们对数学的兴趣 and promoting a better understanding of this fascinating subject.

The book is truly fascinating. It has the power to capture the reader's attention and draw them into its world.

However, the Hungarian edition has some significant drawbacks. The presence of typos is quite distracting and can make it difficult for the reader to fully understand the content.

Moreover, the symbology used in the book is very bad. It is not clearly defined or explained, which makes it hard to follow the mathematics.

This is a real pity, as the book itself has a lot to offer. The ideas and concepts presented are interesting and thought-provoking.

It is hoped that the publishers will take note of these issues and correct them in future editions. This would make the book more accessible and enjoyable for a wider audience.

Until then, readers will have to struggle with the current edition and try to make the most of what it has to offer.