Surprisingly good. The author focuses more on the culture around Gödel rather than on the man himself which makes the book all the more interesting. WSurprisingly good. The author focuses more on the culture around Gödel rather than on the man himself which makes the book all the more interesting. Will write a longer review later. ...more
Rebeccca Goldstein is an American philosopher and writer. This book managed to dive into who Gödel was and what his views on mathematics really meant.Rebeccca Goldstein is an American philosopher and writer. This book managed to dive into who Gödel was and what his views on mathematics really meant. I was intrigued by this myth of a man; a man who seemed only to get more quiet as he grew older. He never seemed to argue against the popular trends of the day yet was quite certain of his own opinion. In fact the last great philosopher he admired was Leibniz. I was interested in how Gödel was formed as a person and given his infamous secrecy this was quite hard for mrs. Goldstein to show. She did a good job despite this difficulties and hints at an early life crisis at the age of 5 when Gödel realized he was smarter than his parents. What does one do in such a situation? How does a child handle that type of uncertainty? One of Goldsteins theories is that Gödels whole life was a reaction to this insight and an attempt to find stable mathematical ground given the uncertainty of the world.
Much has been written about Kurt Gödel and his incompleteness theorem. It is a mathematical theorem which has managed to enthrall even those persons (myself included) who are not mathematicians and has therefore begun to live a life of its own. Wikipedia defines the axiom (or rather axioms as there are two) in the following way:
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers. For any such consistent formal system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.
I am to this day not quite sure what this means but I interpret it as saying there is something magical to human intuition which cannot be boiled down to the pure rules of a system. You cannot prove a system is true within the system and like the Austrian economists say, you cannot find an objective value to things which can only be evaluated subjectively by an individual. It was also interesting to learn that Gödel was a mathematical platonist, i.e. one who believes in that mathematics exists in reality and are not a system created by humans. Why else would you be able to use math in physics (which explore how the real universe works)?
A delightful read and I recommend it to anyone interested in the history!...more
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