In 'Impossibility', John D. Barrow - one of our most elegant and accomplished science writers - argues convincingly that there are limits to human discovery, that there are things that are ultimately unknowable, undoable, or unreachable. Barrow first examines the limits of the human mind: our brain evolved to meet the demands of our immediate environment, and much that lies outside this small circle may also lie outside our understanding. He investigates practical impossibilities, such as those imposed by complexity, uncomputability, or the finiteness of time, space, and resources. Is the universe finite or infinite? Can information be transmitted faster than the speed of light? The book also examines deeper theoretical restrictions on our ability to know, including Gödel's theorem, which proved that there were things that could not be proved.
本书共分8部分,内容包括:一致性问题、一致性的绝对证明、形式逻辑的系统编码、一个成功的一致性绝对证明的例子、映射的概念及其在数学中的应用等。
However, few scholars were unable to understand Gödel’s ideas. Ernest Nagel and James Newman provide a readable and accessible explanation of the main ideas and broad implications of Gödel's discovery.
To theōrēma tou Godel
Gödel kanıtlaması
Gia to theōrēma mē-plērotētas tou Godel
Der Gödelsche Beweis
In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics...
An introduction to the work of the mathematical logician Kurt Godel, which guides the reader through his Theorem of Undecidability and his theories on the completeness of logic, the incompleteness of numbers and the consistency of the axiom ...