Logical Dilemmas: The Life and Work of Kurt Gödel

by John W. Dawson Jr.

This authoritative biography of Kurt Goedel relates the life of this most important logician of our time to the development of the field. Goedel's seminal achievements that changed the perception and foundations of mathematics are explained in the context of his life from the turn of the century Austria to the Institute for Advanced Study in Princeton.

Genres: Biography, Science, Mathematics, Logic, Philosophy, History, Nonfiction

376 pages, Paperback

First published January 1, 1997

Reviews

[Rory Fox · Rating 3 out of 5]

A biography written in the style of a text book.

The fourteen chapters essentially break up Godel’s life into chronological sections, each of which narrate the events of Godel’s life and his interactions with other figures. It makes for an informative read, especially the way that Godel’s mental health issues impacted upon so many aspects of his thinking and decision making.

At 376 pages this is not a small book, but there were many places in the text where I found myself wishing it had said more about what it was narrating. For example, in the very first chapter the book tells us about Godel’s 14 Principles, which summed up his philosophy of life. The chapter focuses on the first principle: ‘the world is rational,’ as that explained much of Godel’s worldview.

But then the book moved on and effectively ignored the rest of the principles. Yet there are some important issues buried in those principles. The sixth principle, for example, stresses that there is ‘incomparably more’ that can be known a priori than is currently known. The final principle is that religions for the most part are bad, but religion itself isn’t. There are some really interesting ideas buried in those principles, and it would have been interesting to get more of a sense of what Godel meant by the principles and why he believed they were true.

While the book generally covered the significant features of Godel’s life and thinking, it didn’t particularly explain the wider significance of what it was conveying. For example, in chapter 7 we heard of Bertrand Russell’s horror to discover that Godel was an ‘unadulterated Platonist.’ But the word ‘platonist’ can mean many different things. What did it mean for Godel to be one, and why would it matter to someone like Russell? Understanding issues like that are important to being able to appreciate Godel’s thinking, but all we got was glimpses at possible answers. Those issues still have a relevance today, as Mathematical Platonism remains an issue lurking in the closet of Metamathematics. It would be interesting for readers to get a better insight into why Godel felt that Platonism was the right approach.

And perhaps the most surprising thing of all is that Godel’s ‘famous’ work on incompleteness is narrated descriptively, but again without any sense of why it had such a momentous impact upon the world of mathematics. There are hints in chapter 11 where we hear that Godel’s work brought Hilbert’s program to a crashing close. But why would it have had that impact… and again, what is the significance of that? Why did Hilbert’s work matter, so that Godel’s impact upon it also mattered?

Overall, I enjoyed reading about Godel, but I also found the book quite frustrating in that it didn’t press the more philosophical questions about Godel, which I was particularly interested in. Instead, the book was mainly a narrative description of Godel’s life and mathematics, with occasional forays to explain specific aspects of Mathematics. This means that it is a book which will probably be enjoyed most by those who are interested in Godel for mathematical reasons, rather than those who are interested in the philosophical aspects of Godel’s thinking.

[Hooper Bring]

KB mentioned this as a work that talked about Gödel’s fixation on Leibniz and the suppression of his work.

[Fawzy Hegab · Rating 3 out of 5]

I've finished reading a week ago.

The book is full of details of the life of Godel, which is good.
It shows how Kurt Godel worked on his research in close, how his life was full of struggle and it shows his desire to rationalize the world. It also shows how the mathematical and philosophical communities reacted to his incompleteness theorems. It exposes briefly a sketch of mathematical logic and set theory, just a primer so that the layman can appreciate what is going on. It exposes his philosophical attitudes and it was surprising for me to know that Godel (like his close friend, Einstein) was not appreciating Quantum mechanics! more importantly, it shows how he worked hard in order to achieve his amazing results which show that getting those great theorems needs hard work and not only a genius.

I've also good some intuitions of some mathematical notions in the work of Godel. Also, from the book, I get to know some of the articles written by Godel, which will be a great thing to read.

I should re-read the book again, and I will do that when possible and there will be a second more extended review.

[Kyle Strand · Rating 3 out of 5]

The subject matter was phenomenal, but unfortunately Dawson, though a good researcher (and presumably a good mathematician), is just not a very good writer.